27.596 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.148 * * * [progress]: [2/2] Setting up program. 0.152 * [progress]: [Phase 2 of 3] Improving. 0.153 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.153 * * [simplify]: Extracting # 0 : cost 0 0.153 * * [simplify]: Extracting # 1 : cost 0 0.153 * * [simplify]: Extracting # 2 : cost 0 0.153 * * [simplify]: Extracting # 3 : cost 0 0.153 * * [simplify]: Extracting # 4 : cost 0 0.153 * * [simplify]: Extracting # 5 : cost 0 0.153 * * [simplify]: Extracting # 6 : cost 0 0.153 * * [simplify]: Extracting # 7 : cost 0 0.153 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.160 * * [simplify]: Extracting # 0 : cost 0 0.160 * * [simplify]: Extracting # 1 : cost 0 0.160 * * [simplify]: Extracting # 2 : cost 0 0.160 * * [simplify]: Extracting # 3 : cost 0 0.160 * * [simplify]: Extracting # 4 : cost 0 0.160 * * [simplify]: Extracting # 5 : cost 0 0.160 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.173 * * [simplify]: Extracting # 0 : cost 0 0.173 * * [simplify]: Extracting # 1 : cost 0 0.173 * * [simplify]: Extracting # 2 : cost 0 0.173 * * [simplify]: Extracting # 3 : cost 0 0.173 * * [simplify]: Extracting # 4 : cost 0 0.173 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.186 * * [simplify]: Extracting # 0 : cost 0 0.186 * * [simplify]: Extracting # 1 : cost 0 0.186 * * [simplify]: Extracting # 2 : cost 0 0.186 * * [simplify]: Extracting # 3 : cost 0 0.186 * * [simplify]: Extracting # 4 : cost 0 0.186 * * [simplify]: iteration 3 : 119 enodes (cost 16 ) 0.256 * * [simplify]: Extracting # 0 : cost 0 0.257 * * [simplify]: Extracting # 1 : cost 0 0.258 * * [simplify]: Extracting # 2 : cost 0 0.259 * * [simplify]: Extracting # 3 : cost 0 0.259 * * [simplify]: Extracting # 4 : cost 0 0.260 * * [simplify]: iteration 4 : 313 enodes (cost 16 ) 0.458 * * [simplify]: Extracting # 0 : cost 0 0.459 * * [simplify]: Extracting # 1 : cost 0 0.460 * * [simplify]: Extracting # 2 : cost 0 0.461 * * [simplify]: Extracting # 3 : cost 0 0.462 * * [simplify]: Extracting # 4 : cost 0 0.463 * * [simplify]: iteration 5 : 853 enodes (cost 16 ) 1.934 * * [simplify]: Extracting # 0 : cost 0 1.941 * * [simplify]: Extracting # 1 : cost 0 1.947 * * [simplify]: Extracting # 2 : cost 0 1.952 * * [simplify]: Extracting # 3 : cost 0 1.957 * * [simplify]: Extracting # 4 : cost 0 1.962 * * [simplify]: iteration 6 : 3196 enodes (cost 16 ) 3.911 * * [simplify]: Extracting # 0 : cost 0 3.923 * * [simplify]: Extracting # 1 : cost 0 3.933 * * [simplify]: Extracting # 2 : cost 0 3.942 * * [simplify]: Extracting # 3 : cost 0 3.952 * * [simplify]: Extracting # 4 : cost 0 3.962 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 3.962 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3.963 * * [progress]: iteration 1 / 4 3.963 * * * [progress]: picking best candidate 3.968 * * * * [pick]: Picked # 3.968 * * * [progress]: localizing error 4.000 * * * [progress]: generating rewritten candidates 4.000 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 4.040 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 4.046 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 4.082 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 4.172 * * * [progress]: generating series expansions 4.172 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 4.173 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 4.173 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 4.173 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.173 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.173 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.173 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.173 * [taylor]: Taking taylor expansion of 0.5 in k 4.173 * [backup-simplify]: Simplify 0.5 into 0.5 4.173 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.173 * [taylor]: Taking taylor expansion of 1.0 in k 4.173 * [backup-simplify]: Simplify 1.0 into 1.0 4.173 * [taylor]: Taking taylor expansion of k in k 4.173 * [backup-simplify]: Simplify 0 into 0 4.173 * [backup-simplify]: Simplify 1 into 1 4.173 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.173 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.173 * [taylor]: Taking taylor expansion of 2.0 in k 4.173 * [backup-simplify]: Simplify 2.0 into 2.0 4.173 * [taylor]: Taking taylor expansion of (* n PI) in k 4.173 * [taylor]: Taking taylor expansion of n in k 4.173 * [backup-simplify]: Simplify n into n 4.173 * [taylor]: Taking taylor expansion of PI in k 4.173 * [backup-simplify]: Simplify PI into PI 4.173 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.173 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.173 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.173 * [backup-simplify]: Simplify (- 0) into 0 4.174 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.174 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.174 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.174 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.174 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.174 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.174 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.174 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.174 * [taylor]: Taking taylor expansion of 0.5 in n 4.174 * [backup-simplify]: Simplify 0.5 into 0.5 4.174 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.175 * [taylor]: Taking taylor expansion of 1.0 in n 4.175 * [backup-simplify]: Simplify 1.0 into 1.0 4.175 * [taylor]: Taking taylor expansion of k in n 4.175 * [backup-simplify]: Simplify k into k 4.175 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.175 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.175 * [taylor]: Taking taylor expansion of 2.0 in n 4.175 * [backup-simplify]: Simplify 2.0 into 2.0 4.175 * [taylor]: Taking taylor expansion of (* n PI) in n 4.175 * [taylor]: Taking taylor expansion of n in n 4.175 * [backup-simplify]: Simplify 0 into 0 4.175 * [backup-simplify]: Simplify 1 into 1 4.175 * [taylor]: Taking taylor expansion of PI in n 4.175 * [backup-simplify]: Simplify PI into PI 4.175 * [backup-simplify]: Simplify (* 0 PI) into 0 4.175 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.176 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.177 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.178 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.178 * [backup-simplify]: Simplify (- k) into (- k) 4.178 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.178 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.179 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.180 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.180 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.181 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.181 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.181 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.181 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.181 * [taylor]: Taking taylor expansion of 0.5 in n 4.181 * [backup-simplify]: Simplify 0.5 into 0.5 4.181 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.181 * [taylor]: Taking taylor expansion of 1.0 in n 4.181 * [backup-simplify]: Simplify 1.0 into 1.0 4.181 * [taylor]: Taking taylor expansion of k in n 4.181 * [backup-simplify]: Simplify k into k 4.181 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.181 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.181 * [taylor]: Taking taylor expansion of 2.0 in n 4.181 * [backup-simplify]: Simplify 2.0 into 2.0 4.181 * [taylor]: Taking taylor expansion of (* n PI) in n 4.181 * [taylor]: Taking taylor expansion of n in n 4.181 * [backup-simplify]: Simplify 0 into 0 4.181 * [backup-simplify]: Simplify 1 into 1 4.181 * [taylor]: Taking taylor expansion of PI in n 4.181 * [backup-simplify]: Simplify PI into PI 4.181 * [backup-simplify]: Simplify (* 0 PI) into 0 4.181 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.182 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.183 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.184 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.184 * [backup-simplify]: Simplify (- k) into (- k) 4.184 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.184 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.185 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.186 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.187 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.187 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.187 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.187 * [taylor]: Taking taylor expansion of 0.5 in k 4.187 * [backup-simplify]: Simplify 0.5 into 0.5 4.187 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.187 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.187 * [taylor]: Taking taylor expansion of 1.0 in k 4.187 * [backup-simplify]: Simplify 1.0 into 1.0 4.187 * [taylor]: Taking taylor expansion of k in k 4.187 * [backup-simplify]: Simplify 0 into 0 4.187 * [backup-simplify]: Simplify 1 into 1 4.187 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.187 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.187 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.187 * [taylor]: Taking taylor expansion of 2.0 in k 4.187 * [backup-simplify]: Simplify 2.0 into 2.0 4.187 * [taylor]: Taking taylor expansion of PI in k 4.187 * [backup-simplify]: Simplify PI into PI 4.187 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.188 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.188 * [taylor]: Taking taylor expansion of (log n) in k 4.188 * [taylor]: Taking taylor expansion of n in k 4.188 * [backup-simplify]: Simplify n into n 4.188 * [backup-simplify]: Simplify (log n) into (log n) 4.188 * [backup-simplify]: Simplify (- 0) into 0 4.189 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.189 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.190 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.191 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 4.191 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.192 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.193 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.193 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.194 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.195 * [backup-simplify]: Simplify (- 0) into 0 4.195 * [backup-simplify]: Simplify (+ 0 0) into 0 4.195 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 4.196 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.197 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.198 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.198 * [taylor]: Taking taylor expansion of 0 in k 4.198 * [backup-simplify]: Simplify 0 into 0 4.198 * [backup-simplify]: Simplify 0 into 0 4.199 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.200 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.200 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.200 * [backup-simplify]: Simplify (+ 0 0) into 0 4.201 * [backup-simplify]: Simplify (- 1) into -1 4.201 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.202 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.203 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 4.205 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 4.207 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 4.208 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.208 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.210 * [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 4.210 * [backup-simplify]: Simplify (- 0) into 0 4.211 * [backup-simplify]: Simplify (+ 0 0) into 0 4.211 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.212 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.213 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.215 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.215 * [taylor]: Taking taylor expansion of 0 in k 4.215 * [backup-simplify]: Simplify 0 into 0 4.215 * [backup-simplify]: Simplify 0 into 0 4.215 * [backup-simplify]: Simplify 0 into 0 4.215 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.217 * [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 4.218 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.219 * [backup-simplify]: Simplify (+ 0 0) into 0 4.219 * [backup-simplify]: Simplify (- 0) into 0 4.219 * [backup-simplify]: Simplify (+ 0 0) into 0 4.220 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.222 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.224 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 4.229 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 4.244 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 4.245 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 4.245 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 4.245 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.245 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.245 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.245 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.246 * [taylor]: Taking taylor expansion of 0.5 in k 4.246 * [backup-simplify]: Simplify 0.5 into 0.5 4.246 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.246 * [taylor]: Taking taylor expansion of 1.0 in k 4.246 * [backup-simplify]: Simplify 1.0 into 1.0 4.246 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.246 * [taylor]: Taking taylor expansion of k in k 4.246 * [backup-simplify]: Simplify 0 into 0 4.246 * [backup-simplify]: Simplify 1 into 1 4.246 * [backup-simplify]: Simplify (/ 1 1) into 1 4.246 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.246 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.246 * [taylor]: Taking taylor expansion of 2.0 in k 4.246 * [backup-simplify]: Simplify 2.0 into 2.0 4.246 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.246 * [taylor]: Taking taylor expansion of PI in k 4.246 * [backup-simplify]: Simplify PI into PI 4.246 * [taylor]: Taking taylor expansion of n in k 4.246 * [backup-simplify]: Simplify n into n 4.246 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.247 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.247 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.247 * [backup-simplify]: Simplify (- 1) into -1 4.247 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.248 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.248 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.248 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.248 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.248 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.248 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.248 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.248 * [taylor]: Taking taylor expansion of 0.5 in n 4.248 * [backup-simplify]: Simplify 0.5 into 0.5 4.249 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.249 * [taylor]: Taking taylor expansion of 1.0 in n 4.249 * [backup-simplify]: Simplify 1.0 into 1.0 4.249 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.249 * [taylor]: Taking taylor expansion of k in n 4.249 * [backup-simplify]: Simplify k into k 4.249 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.249 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.249 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.249 * [taylor]: Taking taylor expansion of 2.0 in n 4.249 * [backup-simplify]: Simplify 2.0 into 2.0 4.249 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.249 * [taylor]: Taking taylor expansion of PI in n 4.249 * [backup-simplify]: Simplify PI into PI 4.249 * [taylor]: Taking taylor expansion of n in n 4.249 * [backup-simplify]: Simplify 0 into 0 4.249 * [backup-simplify]: Simplify 1 into 1 4.250 * [backup-simplify]: Simplify (/ PI 1) into PI 4.250 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.251 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.251 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.251 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.251 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.253 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.254 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.255 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.255 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.255 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.255 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.255 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.255 * [taylor]: Taking taylor expansion of 0.5 in n 4.255 * [backup-simplify]: Simplify 0.5 into 0.5 4.255 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.256 * [taylor]: Taking taylor expansion of 1.0 in n 4.256 * [backup-simplify]: Simplify 1.0 into 1.0 4.256 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.256 * [taylor]: Taking taylor expansion of k in n 4.256 * [backup-simplify]: Simplify k into k 4.256 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.256 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.256 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.256 * [taylor]: Taking taylor expansion of 2.0 in n 4.256 * [backup-simplify]: Simplify 2.0 into 2.0 4.256 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.256 * [taylor]: Taking taylor expansion of PI in n 4.256 * [backup-simplify]: Simplify PI into PI 4.256 * [taylor]: Taking taylor expansion of n in n 4.256 * [backup-simplify]: Simplify 0 into 0 4.256 * [backup-simplify]: Simplify 1 into 1 4.256 * [backup-simplify]: Simplify (/ PI 1) into PI 4.257 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.258 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.258 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.258 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.258 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.260 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.261 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.262 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.262 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.262 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.263 * [taylor]: Taking taylor expansion of 0.5 in k 4.263 * [backup-simplify]: Simplify 0.5 into 0.5 4.263 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.263 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.263 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.263 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.263 * [taylor]: Taking taylor expansion of 2.0 in k 4.263 * [backup-simplify]: Simplify 2.0 into 2.0 4.263 * [taylor]: Taking taylor expansion of PI in k 4.263 * [backup-simplify]: Simplify PI into PI 4.263 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.264 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.264 * [taylor]: Taking taylor expansion of (log n) in k 4.264 * [taylor]: Taking taylor expansion of n in k 4.264 * [backup-simplify]: Simplify n into n 4.264 * [backup-simplify]: Simplify (log n) into (log n) 4.264 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.264 * [taylor]: Taking taylor expansion of 1.0 in k 4.265 * [backup-simplify]: Simplify 1.0 into 1.0 4.265 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.265 * [taylor]: Taking taylor expansion of k in k 4.265 * [backup-simplify]: Simplify 0 into 0 4.265 * [backup-simplify]: Simplify 1 into 1 4.265 * [backup-simplify]: Simplify (/ 1 1) into 1 4.265 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.266 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.267 * [backup-simplify]: Simplify (- 1) into -1 4.267 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.268 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.269 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 4.270 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.271 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.272 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.273 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.275 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.275 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.276 * [backup-simplify]: Simplify (- 0) into 0 4.276 * [backup-simplify]: Simplify (+ 0 0) into 0 4.277 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.278 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.279 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.281 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.281 * [taylor]: Taking taylor expansion of 0 in k 4.281 * [backup-simplify]: Simplify 0 into 0 4.281 * [backup-simplify]: Simplify 0 into 0 4.281 * [backup-simplify]: Simplify 0 into 0 4.282 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.283 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.286 * [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 4.286 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.286 * [backup-simplify]: Simplify (- 0) into 0 4.287 * [backup-simplify]: Simplify (+ 0 0) into 0 4.287 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.288 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.289 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.291 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.291 * [taylor]: Taking taylor expansion of 0 in k 4.291 * [backup-simplify]: Simplify 0 into 0 4.291 * [backup-simplify]: Simplify 0 into 0 4.291 * [backup-simplify]: Simplify 0 into 0 4.291 * [backup-simplify]: Simplify 0 into 0 4.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.292 * [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 (+ (* 0.5 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 (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.301 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.301 * [taylor]: Taking taylor expansion of 0 in k 4.301 * [backup-simplify]: Simplify 0 into 0 4.301 * [backup-simplify]: Simplify 0 into 0 4.302 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.302 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 4.303 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 4.303 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.303 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.303 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.303 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.303 * [taylor]: Taking taylor expansion of 0.5 in k 4.303 * [backup-simplify]: Simplify 0.5 into 0.5 4.303 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.303 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.303 * [taylor]: Taking taylor expansion of k in k 4.303 * [backup-simplify]: Simplify 0 into 0 4.303 * [backup-simplify]: Simplify 1 into 1 4.303 * [backup-simplify]: Simplify (/ 1 1) into 1 4.303 * [taylor]: Taking taylor expansion of 1.0 in k 4.303 * [backup-simplify]: Simplify 1.0 into 1.0 4.303 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.303 * [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))) 4.304 * [backup-simplify]: Simplify (+ 1 0) into 1 4.304 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.304 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.304 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.304 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.304 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.304 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.304 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.304 * [taylor]: Taking taylor expansion of 0.5 in n 4.304 * [backup-simplify]: Simplify 0.5 into 0.5 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 4.305 * [taylor]: Taking taylor expansion of -2.0 in n 4.305 * [backup-simplify]: Simplify -2.0 into -2.0 4.305 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.305 * [taylor]: Taking taylor expansion of PI in n 4.305 * [backup-simplify]: Simplify PI into PI 4.305 * [taylor]: Taking taylor expansion of n in n 4.305 * [backup-simplify]: Simplify 0 into 0 4.305 * [backup-simplify]: Simplify 1 into 1 4.305 * [backup-simplify]: Simplify (/ PI 1) into PI 4.305 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.306 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.306 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.306 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.308 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.308 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.308 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.308 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.308 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.308 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.309 * [taylor]: Taking taylor expansion of 0.5 in n 4.309 * [backup-simplify]: Simplify 0.5 into 0.5 4.309 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.309 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.309 * [taylor]: Taking taylor expansion of k in n 4.309 * [backup-simplify]: Simplify k into k 4.309 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.309 * [taylor]: Taking taylor expansion of 1.0 in n 4.309 * [backup-simplify]: Simplify 1.0 into 1.0 4.309 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.309 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.309 * [taylor]: Taking taylor expansion of -2.0 in n 4.309 * [backup-simplify]: Simplify -2.0 into -2.0 4.309 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.309 * [taylor]: Taking taylor expansion of PI in n 4.309 * [backup-simplify]: Simplify PI into PI 4.309 * [taylor]: Taking taylor expansion of n in n 4.309 * [backup-simplify]: Simplify 0 into 0 4.309 * [backup-simplify]: Simplify 1 into 1 4.309 * [backup-simplify]: Simplify (/ PI 1) into PI 4.309 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.310 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.310 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.310 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.311 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.312 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.313 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.313 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.313 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.313 * [taylor]: Taking taylor expansion of 0.5 in k 4.313 * [backup-simplify]: Simplify 0.5 into 0.5 4.313 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.313 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.313 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.313 * [taylor]: Taking taylor expansion of k in k 4.313 * [backup-simplify]: Simplify 0 into 0 4.313 * [backup-simplify]: Simplify 1 into 1 4.313 * [backup-simplify]: Simplify (/ 1 1) into 1 4.313 * [taylor]: Taking taylor expansion of 1.0 in k 4.314 * [backup-simplify]: Simplify 1.0 into 1.0 4.314 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.314 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.314 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.314 * [taylor]: Taking taylor expansion of -2.0 in k 4.314 * [backup-simplify]: Simplify -2.0 into -2.0 4.314 * [taylor]: Taking taylor expansion of PI in k 4.314 * [backup-simplify]: Simplify PI into PI 4.314 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.315 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.315 * [taylor]: Taking taylor expansion of (log n) in k 4.315 * [taylor]: Taking taylor expansion of n in k 4.315 * [backup-simplify]: Simplify n into n 4.315 * [backup-simplify]: Simplify (log n) into (log n) 4.316 * [backup-simplify]: Simplify (+ 1 0) into 1 4.316 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.317 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.318 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.319 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 4.321 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.322 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.323 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.324 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.326 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.326 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.326 * [backup-simplify]: Simplify (+ 0 0) into 0 4.327 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.328 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.330 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.332 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.332 * [taylor]: Taking taylor expansion of 0 in k 4.332 * [backup-simplify]: Simplify 0 into 0 4.332 * [backup-simplify]: Simplify 0 into 0 4.332 * [backup-simplify]: Simplify 0 into 0 4.333 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.334 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.338 * [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 4.338 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.339 * [backup-simplify]: Simplify (+ 0 0) into 0 4.340 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.341 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.343 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.345 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.345 * [taylor]: Taking taylor expansion of 0 in k 4.346 * [backup-simplify]: Simplify 0 into 0 4.346 * [backup-simplify]: Simplify 0 into 0 4.346 * [backup-simplify]: Simplify 0 into 0 4.346 * [backup-simplify]: Simplify 0 into 0 4.347 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.349 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.355 * [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 4.355 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.356 * [backup-simplify]: Simplify (+ 0 0) into 0 4.357 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.359 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.361 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.364 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.364 * [taylor]: Taking taylor expansion of 0 in k 4.364 * [backup-simplify]: Simplify 0 into 0 4.364 * [backup-simplify]: Simplify 0 into 0 4.366 * [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)))))) 4.366 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 4.366 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.366 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.366 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.366 * [taylor]: Taking taylor expansion of 1.0 in k 4.366 * [backup-simplify]: Simplify 1.0 into 1.0 4.366 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.366 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.366 * [taylor]: Taking taylor expansion of k in k 4.366 * [backup-simplify]: Simplify 0 into 0 4.366 * [backup-simplify]: Simplify 1 into 1 4.367 * [backup-simplify]: Simplify (/ 1 1) into 1 4.367 * [backup-simplify]: Simplify (sqrt 0) into 0 4.368 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.368 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.369 * [taylor]: Taking taylor expansion of 1.0 in k 4.369 * [backup-simplify]: Simplify 1.0 into 1.0 4.369 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.369 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.369 * [taylor]: Taking taylor expansion of k in k 4.369 * [backup-simplify]: Simplify 0 into 0 4.369 * [backup-simplify]: Simplify 1 into 1 4.373 * [backup-simplify]: Simplify (/ 1 1) into 1 4.374 * [backup-simplify]: Simplify (sqrt 0) into 0 4.375 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.376 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.376 * [backup-simplify]: Simplify 0 into 0 4.377 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.378 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.378 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.380 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.381 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.381 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.382 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.384 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.385 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.386 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.387 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.387 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.387 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.387 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.387 * [taylor]: Taking taylor expansion of 1.0 in k 4.387 * [backup-simplify]: Simplify 1.0 into 1.0 4.387 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.387 * [taylor]: Taking taylor expansion of k in k 4.387 * [backup-simplify]: Simplify 0 into 0 4.387 * [backup-simplify]: Simplify 1 into 1 4.387 * [backup-simplify]: Simplify (sqrt 0) into 0 4.388 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.388 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.388 * [taylor]: Taking taylor expansion of 1.0 in k 4.388 * [backup-simplify]: Simplify 1.0 into 1.0 4.388 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.388 * [taylor]: Taking taylor expansion of k in k 4.388 * [backup-simplify]: Simplify 0 into 0 4.388 * [backup-simplify]: Simplify 1 into 1 4.388 * [backup-simplify]: Simplify (sqrt 0) into 0 4.389 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.390 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.390 * [backup-simplify]: Simplify 0 into 0 4.390 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.391 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.393 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.394 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.394 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.396 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.398 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.398 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.399 * [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)))))))) 4.399 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.399 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.399 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.399 * [taylor]: Taking taylor expansion of 1.0 in k 4.399 * [backup-simplify]: Simplify 1.0 into 1.0 4.399 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.400 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.400 * [taylor]: Taking taylor expansion of -1 in k 4.400 * [backup-simplify]: Simplify -1 into -1 4.400 * [taylor]: Taking taylor expansion of k in k 4.400 * [backup-simplify]: Simplify 0 into 0 4.400 * [backup-simplify]: Simplify 1 into 1 4.400 * [backup-simplify]: Simplify (/ -1 1) into -1 4.400 * [backup-simplify]: Simplify (sqrt 0) into 0 4.401 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.401 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.401 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.401 * [taylor]: Taking taylor expansion of 1.0 in k 4.401 * [backup-simplify]: Simplify 1.0 into 1.0 4.401 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.401 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.401 * [taylor]: Taking taylor expansion of -1 in k 4.401 * [backup-simplify]: Simplify -1 into -1 4.401 * [taylor]: Taking taylor expansion of k in k 4.401 * [backup-simplify]: Simplify 0 into 0 4.401 * [backup-simplify]: Simplify 1 into 1 4.402 * [backup-simplify]: Simplify (/ -1 1) into -1 4.402 * [backup-simplify]: Simplify (sqrt 0) into 0 4.403 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.403 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.403 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.404 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.405 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.407 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.408 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.408 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.410 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.413 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.413 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.414 * [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))))) 4.414 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 4.414 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.414 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.414 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.415 * [taylor]: Taking taylor expansion of 2.0 in n 4.415 * [backup-simplify]: Simplify 2.0 into 2.0 4.415 * [taylor]: Taking taylor expansion of (* n PI) in n 4.415 * [taylor]: Taking taylor expansion of n in n 4.415 * [backup-simplify]: Simplify 0 into 0 4.415 * [backup-simplify]: Simplify 1 into 1 4.415 * [taylor]: Taking taylor expansion of PI in n 4.415 * [backup-simplify]: Simplify PI into PI 4.415 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.415 * [taylor]: Taking taylor expansion of 2.0 in n 4.415 * [backup-simplify]: Simplify 2.0 into 2.0 4.415 * [taylor]: Taking taylor expansion of (* n PI) in n 4.415 * [taylor]: Taking taylor expansion of n in n 4.415 * [backup-simplify]: Simplify 0 into 0 4.415 * [backup-simplify]: Simplify 1 into 1 4.415 * [taylor]: Taking taylor expansion of PI in n 4.415 * [backup-simplify]: Simplify PI into PI 4.415 * [backup-simplify]: Simplify (* 0 PI) into 0 4.415 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.415 * [backup-simplify]: Simplify 0 into 0 4.416 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.417 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.418 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.418 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.419 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.419 * [backup-simplify]: Simplify 0 into 0 4.420 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.420 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.420 * [backup-simplify]: Simplify 0 into 0 4.421 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.422 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.422 * [backup-simplify]: Simplify 0 into 0 4.423 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.424 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 4.424 * [backup-simplify]: Simplify 0 into 0 4.425 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.427 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 4.427 * [backup-simplify]: Simplify 0 into 0 4.429 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 4.431 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 4.431 * [backup-simplify]: Simplify 0 into 0 4.431 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.432 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 4.432 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.432 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.432 * [taylor]: Taking taylor expansion of 2.0 in n 4.432 * [backup-simplify]: Simplify 2.0 into 2.0 4.432 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.432 * [taylor]: Taking taylor expansion of PI in n 4.432 * [backup-simplify]: Simplify PI into PI 4.432 * [taylor]: Taking taylor expansion of n in n 4.432 * [backup-simplify]: Simplify 0 into 0 4.432 * [backup-simplify]: Simplify 1 into 1 4.433 * [backup-simplify]: Simplify (/ PI 1) into PI 4.433 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.433 * [taylor]: Taking taylor expansion of 2.0 in n 4.433 * [backup-simplify]: Simplify 2.0 into 2.0 4.433 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.433 * [taylor]: Taking taylor expansion of PI in n 4.433 * [backup-simplify]: Simplify PI into PI 4.433 * [taylor]: Taking taylor expansion of n in n 4.433 * [backup-simplify]: Simplify 0 into 0 4.433 * [backup-simplify]: Simplify 1 into 1 4.434 * [backup-simplify]: Simplify (/ PI 1) into PI 4.434 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.435 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.436 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.436 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.436 * [backup-simplify]: Simplify 0 into 0 4.438 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.439 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.439 * [backup-simplify]: Simplify 0 into 0 4.440 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.441 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.441 * [backup-simplify]: Simplify 0 into 0 4.442 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.442 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.442 * [backup-simplify]: Simplify 0 into 0 4.443 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.444 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.444 * [backup-simplify]: Simplify 0 into 0 4.445 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.446 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.446 * [backup-simplify]: Simplify 0 into 0 4.446 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 4.446 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 4.446 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.446 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.446 * [taylor]: Taking taylor expansion of -2.0 in n 4.446 * [backup-simplify]: Simplify -2.0 into -2.0 4.447 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.447 * [taylor]: Taking taylor expansion of PI in n 4.447 * [backup-simplify]: Simplify PI into PI 4.447 * [taylor]: Taking taylor expansion of n in n 4.447 * [backup-simplify]: Simplify 0 into 0 4.447 * [backup-simplify]: Simplify 1 into 1 4.447 * [backup-simplify]: Simplify (/ PI 1) into PI 4.447 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.447 * [taylor]: Taking taylor expansion of -2.0 in n 4.447 * [backup-simplify]: Simplify -2.0 into -2.0 4.447 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.447 * [taylor]: Taking taylor expansion of PI in n 4.447 * [backup-simplify]: Simplify PI into PI 4.447 * [taylor]: Taking taylor expansion of n in n 4.447 * [backup-simplify]: Simplify 0 into 0 4.447 * [backup-simplify]: Simplify 1 into 1 4.447 * [backup-simplify]: Simplify (/ PI 1) into PI 4.448 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.448 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.449 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.449 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.449 * [backup-simplify]: Simplify 0 into 0 4.450 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.450 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.450 * [backup-simplify]: Simplify 0 into 0 4.451 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.452 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.452 * [backup-simplify]: Simplify 0 into 0 4.453 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.453 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.453 * [backup-simplify]: Simplify 0 into 0 4.454 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.455 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.455 * [backup-simplify]: Simplify 0 into 0 4.456 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.457 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.457 * [backup-simplify]: Simplify 0 into 0 4.457 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 4.458 * * * * [progress]: [ 4 / 4 ] generating series at (2) 4.458 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 4.458 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 4.458 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 4.458 * [taylor]: Taking taylor expansion of 1.0 in n 4.458 * [backup-simplify]: Simplify 1.0 into 1.0 4.458 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 4.458 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 4.458 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.458 * [taylor]: Taking taylor expansion of k in n 4.458 * [backup-simplify]: Simplify k into k 4.458 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.458 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 4.458 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.458 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 4.459 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.459 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.459 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.459 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.459 * [taylor]: Taking taylor expansion of 0.5 in n 4.459 * [backup-simplify]: Simplify 0.5 into 0.5 4.459 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.459 * [taylor]: Taking taylor expansion of 1.0 in n 4.459 * [backup-simplify]: Simplify 1.0 into 1.0 4.459 * [taylor]: Taking taylor expansion of k in n 4.459 * [backup-simplify]: Simplify k into k 4.459 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.459 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.459 * [taylor]: Taking taylor expansion of 2.0 in n 4.459 * [backup-simplify]: Simplify 2.0 into 2.0 4.459 * [taylor]: Taking taylor expansion of (* n PI) in n 4.459 * [taylor]: Taking taylor expansion of n in n 4.459 * [backup-simplify]: Simplify 0 into 0 4.459 * [backup-simplify]: Simplify 1 into 1 4.459 * [taylor]: Taking taylor expansion of PI in n 4.459 * [backup-simplify]: Simplify PI into PI 4.459 * [backup-simplify]: Simplify (* 0 PI) into 0 4.459 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.460 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.462 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.463 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.463 * [backup-simplify]: Simplify (- k) into (- k) 4.463 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.463 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.464 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.466 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.467 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.467 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.467 * [taylor]: Taking taylor expansion of 1.0 in k 4.467 * [backup-simplify]: Simplify 1.0 into 1.0 4.467 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.467 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.467 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.467 * [taylor]: Taking taylor expansion of k in k 4.467 * [backup-simplify]: Simplify 0 into 0 4.467 * [backup-simplify]: Simplify 1 into 1 4.468 * [backup-simplify]: Simplify (/ 1 1) into 1 4.468 * [backup-simplify]: Simplify (sqrt 0) into 0 4.470 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.470 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.470 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.470 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.470 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.470 * [taylor]: Taking taylor expansion of 0.5 in k 4.470 * [backup-simplify]: Simplify 0.5 into 0.5 4.470 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.470 * [taylor]: Taking taylor expansion of 1.0 in k 4.470 * [backup-simplify]: Simplify 1.0 into 1.0 4.470 * [taylor]: Taking taylor expansion of k in k 4.470 * [backup-simplify]: Simplify 0 into 0 4.470 * [backup-simplify]: Simplify 1 into 1 4.470 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.470 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.470 * [taylor]: Taking taylor expansion of 2.0 in k 4.470 * [backup-simplify]: Simplify 2.0 into 2.0 4.470 * [taylor]: Taking taylor expansion of (* n PI) in k 4.470 * [taylor]: Taking taylor expansion of n in k 4.470 * [backup-simplify]: Simplify n into n 4.470 * [taylor]: Taking taylor expansion of PI in k 4.470 * [backup-simplify]: Simplify PI into PI 4.470 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.470 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.470 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.471 * [backup-simplify]: Simplify (- 0) into 0 4.471 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.472 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.472 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.472 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.472 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.472 * [taylor]: Taking taylor expansion of 1.0 in k 4.472 * [backup-simplify]: Simplify 1.0 into 1.0 4.472 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.472 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.472 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.472 * [taylor]: Taking taylor expansion of k in k 4.472 * [backup-simplify]: Simplify 0 into 0 4.472 * [backup-simplify]: Simplify 1 into 1 4.473 * [backup-simplify]: Simplify (/ 1 1) into 1 4.473 * [backup-simplify]: Simplify (sqrt 0) into 0 4.475 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.475 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.475 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.475 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.475 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.475 * [taylor]: Taking taylor expansion of 0.5 in k 4.475 * [backup-simplify]: Simplify 0.5 into 0.5 4.475 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.475 * [taylor]: Taking taylor expansion of 1.0 in k 4.475 * [backup-simplify]: Simplify 1.0 into 1.0 4.475 * [taylor]: Taking taylor expansion of k in k 4.475 * [backup-simplify]: Simplify 0 into 0 4.475 * [backup-simplify]: Simplify 1 into 1 4.475 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.475 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.475 * [taylor]: Taking taylor expansion of 2.0 in k 4.475 * [backup-simplify]: Simplify 2.0 into 2.0 4.475 * [taylor]: Taking taylor expansion of (* n PI) in k 4.475 * [taylor]: Taking taylor expansion of n in k 4.475 * [backup-simplify]: Simplify n into n 4.475 * [taylor]: Taking taylor expansion of PI in k 4.475 * [backup-simplify]: Simplify PI into PI 4.475 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.475 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.476 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.476 * [backup-simplify]: Simplify (- 0) into 0 4.477 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.477 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.477 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.477 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.478 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 4.482 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.482 * [taylor]: Taking taylor expansion of 0 in n 4.482 * [backup-simplify]: Simplify 0 into 0 4.482 * [backup-simplify]: Simplify 0 into 0 4.483 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 4.484 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 4.485 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 4.485 * [backup-simplify]: Simplify (- 1) into -1 4.485 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.487 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 4.488 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 4.488 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.490 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 4.492 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.492 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 4.492 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 4.492 * [taylor]: Taking taylor expansion of +nan.0 in n 4.492 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.492 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.492 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.492 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.492 * [taylor]: Taking taylor expansion of 0.5 in n 4.492 * [backup-simplify]: Simplify 0.5 into 0.5 4.492 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.492 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.492 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.492 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.492 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.492 * [taylor]: Taking taylor expansion of 1.0 in n 4.492 * [backup-simplify]: Simplify 1.0 into 1.0 4.492 * [taylor]: Taking taylor expansion of (log PI) in n 4.492 * [taylor]: Taking taylor expansion of PI in n 4.492 * [backup-simplify]: Simplify PI into PI 4.493 * [backup-simplify]: Simplify (log PI) into (log PI) 4.494 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.495 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.495 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.496 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.496 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.496 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.496 * [taylor]: Taking taylor expansion of 1.0 in n 4.496 * [backup-simplify]: Simplify 1.0 into 1.0 4.496 * [taylor]: Taking taylor expansion of (log n) in n 4.496 * [taylor]: Taking taylor expansion of n in n 4.496 * [backup-simplify]: Simplify 0 into 0 4.496 * [backup-simplify]: Simplify 1 into 1 4.496 * [backup-simplify]: Simplify (log 1) into 0 4.497 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.497 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.497 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.497 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.497 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.497 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.497 * [taylor]: Taking taylor expansion of 1.0 in n 4.497 * [backup-simplify]: Simplify 1.0 into 1.0 4.497 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.497 * [taylor]: Taking taylor expansion of 2.0 in n 4.497 * [backup-simplify]: Simplify 2.0 into 2.0 4.497 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.498 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.500 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.500 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 4.502 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 4.503 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 4.504 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 4.506 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.508 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 4.509 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 4.511 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.511 * [backup-simplify]: Simplify 0 into 0 4.512 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 4.512 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 4.514 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 4.515 * [backup-simplify]: Simplify (- 0) into 0 4.515 * [backup-simplify]: Simplify (+ 0 0) into 0 4.516 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 4.517 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 4.518 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.519 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.522 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.526 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 4.531 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 4.531 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 4.531 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 4.531 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 4.531 * [taylor]: Taking taylor expansion of +nan.0 in n 4.531 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.531 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.531 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.531 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.531 * [taylor]: Taking taylor expansion of 0.5 in n 4.531 * [backup-simplify]: Simplify 0.5 into 0.5 4.531 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.531 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.531 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.531 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.531 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.531 * [taylor]: Taking taylor expansion of 1.0 in n 4.531 * [backup-simplify]: Simplify 1.0 into 1.0 4.531 * [taylor]: Taking taylor expansion of (log PI) in n 4.532 * [taylor]: Taking taylor expansion of PI in n 4.532 * [backup-simplify]: Simplify PI into PI 4.532 * [backup-simplify]: Simplify (log PI) into (log PI) 4.533 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.534 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.534 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.535 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.535 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.535 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.535 * [taylor]: Taking taylor expansion of 1.0 in n 4.535 * [backup-simplify]: Simplify 1.0 into 1.0 4.535 * [taylor]: Taking taylor expansion of (log n) in n 4.535 * [taylor]: Taking taylor expansion of n in n 4.535 * [backup-simplify]: Simplify 0 into 0 4.535 * [backup-simplify]: Simplify 1 into 1 4.535 * [backup-simplify]: Simplify (log 1) into 0 4.536 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.536 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.536 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.536 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.536 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.536 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.536 * [taylor]: Taking taylor expansion of 1.0 in n 4.536 * [backup-simplify]: Simplify 1.0 into 1.0 4.536 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.536 * [taylor]: Taking taylor expansion of 2.0 in n 4.536 * [backup-simplify]: Simplify 2.0 into 2.0 4.536 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.537 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.539 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.539 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 4.541 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 4.542 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 4.543 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 4.545 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.545 * [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 4.545 * [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 4.545 * [taylor]: Taking taylor expansion of +nan.0 in n 4.545 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.545 * [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 4.545 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.545 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.545 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.545 * [taylor]: Taking taylor expansion of 0.5 in n 4.545 * [backup-simplify]: Simplify 0.5 into 0.5 4.545 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.545 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.545 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.545 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.545 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.545 * [taylor]: Taking taylor expansion of 1.0 in n 4.545 * [backup-simplify]: Simplify 1.0 into 1.0 4.545 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.545 * [taylor]: Taking taylor expansion of 2.0 in n 4.545 * [backup-simplify]: Simplify 2.0 into 2.0 4.546 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.546 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.547 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.547 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.547 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.547 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.547 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.547 * [taylor]: Taking taylor expansion of 1.0 in n 4.548 * [backup-simplify]: Simplify 1.0 into 1.0 4.548 * [taylor]: Taking taylor expansion of (log PI) in n 4.548 * [taylor]: Taking taylor expansion of PI in n 4.548 * [backup-simplify]: Simplify PI into PI 4.548 * [backup-simplify]: Simplify (log PI) into (log PI) 4.548 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.549 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.549 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.549 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.549 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.550 * [taylor]: Taking taylor expansion of 1.0 in n 4.550 * [backup-simplify]: Simplify 1.0 into 1.0 4.550 * [taylor]: Taking taylor expansion of (log n) in n 4.550 * [taylor]: Taking taylor expansion of n in n 4.550 * [backup-simplify]: Simplify 0 into 0 4.550 * [backup-simplify]: Simplify 1 into 1 4.550 * [backup-simplify]: Simplify (log 1) into 0 4.550 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.550 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.550 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.551 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.551 * [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) 4.552 * [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)) 4.553 * [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))) 4.554 * [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) 4.554 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.554 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.554 * [taylor]: Taking taylor expansion of 2.0 in n 4.554 * [backup-simplify]: Simplify 2.0 into 2.0 4.554 * [taylor]: Taking taylor expansion of (* n PI) in n 4.554 * [taylor]: Taking taylor expansion of n in n 4.554 * [backup-simplify]: Simplify 0 into 0 4.554 * [backup-simplify]: Simplify 1 into 1 4.554 * [taylor]: Taking taylor expansion of PI in n 4.554 * [backup-simplify]: Simplify PI into PI 4.554 * [backup-simplify]: Simplify (* 0 PI) into 0 4.555 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.556 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.557 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.557 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.559 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 4.561 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.563 * [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)) 4.566 * [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))) 4.569 * [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)))))) 4.574 * [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)))))))) 4.580 * [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)))))))) 4.586 * [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)))))))) 4.588 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 4.588 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 4.590 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 4.592 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 4.592 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.593 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 4.594 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 4.595 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 4.597 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 4.597 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 4.598 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 4.599 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 4.600 * [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 4.601 * [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 4.603 * [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 4.604 * [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 4.604 * [backup-simplify]: Simplify (- 0) into 0 4.604 * [backup-simplify]: Simplify 0 into 0 4.604 * [backup-simplify]: Simplify 0 into 0 4.605 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.606 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 4.607 * [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 4.608 * [backup-simplify]: Simplify (- 0) into 0 4.608 * [backup-simplify]: Simplify (+ 0 0) into 0 4.609 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 4.610 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 4.611 * [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))) 4.611 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.614 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.621 * [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)))))))) 4.627 * [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)))))))) 4.627 * [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 4.627 * [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 4.627 * [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 4.627 * [taylor]: Taking taylor expansion of +nan.0 in n 4.627 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.627 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 4.627 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 4.627 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 4.627 * [taylor]: Taking taylor expansion of 0.5 in n 4.628 * [backup-simplify]: Simplify 0.5 into 0.5 4.628 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 4.628 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 4.628 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.628 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.628 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.628 * [taylor]: Taking taylor expansion of 1.0 in n 4.628 * [backup-simplify]: Simplify 1.0 into 1.0 4.628 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.628 * [taylor]: Taking taylor expansion of 2.0 in n 4.628 * [backup-simplify]: Simplify 2.0 into 2.0 4.628 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.629 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.630 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.630 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 4.630 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.630 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.630 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.630 * [taylor]: Taking taylor expansion of 1.0 in n 4.630 * [backup-simplify]: Simplify 1.0 into 1.0 4.630 * [taylor]: Taking taylor expansion of (log n) in n 4.630 * [taylor]: Taking taylor expansion of n in n 4.630 * [backup-simplify]: Simplify 0 into 0 4.630 * [backup-simplify]: Simplify 1 into 1 4.630 * [backup-simplify]: Simplify (log 1) into 0 4.631 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.631 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.631 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.631 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.631 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.631 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.631 * [taylor]: Taking taylor expansion of 1.0 in n 4.631 * [backup-simplify]: Simplify 1.0 into 1.0 4.631 * [taylor]: Taking taylor expansion of (log PI) in n 4.631 * [taylor]: Taking taylor expansion of PI in n 4.631 * [backup-simplify]: Simplify PI into PI 4.631 * [backup-simplify]: Simplify (log PI) into (log PI) 4.632 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.633 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.633 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.635 * [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) 4.636 * [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)) 4.637 * [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))) 4.639 * [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) 4.639 * [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 4.639 * [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 4.639 * [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 4.639 * [taylor]: Taking taylor expansion of +nan.0 in n 4.639 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.639 * [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 4.639 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.639 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.639 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.639 * [taylor]: Taking taylor expansion of 0.5 in n 4.639 * [backup-simplify]: Simplify 0.5 into 0.5 4.639 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.639 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.639 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.639 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.639 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.639 * [taylor]: Taking taylor expansion of 1.0 in n 4.639 * [backup-simplify]: Simplify 1.0 into 1.0 4.639 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.640 * [taylor]: Taking taylor expansion of 2.0 in n 4.640 * [backup-simplify]: Simplify 2.0 into 2.0 4.640 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.641 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.643 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.643 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.643 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.643 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.643 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.643 * [taylor]: Taking taylor expansion of 1.0 in n 4.643 * [backup-simplify]: Simplify 1.0 into 1.0 4.643 * [taylor]: Taking taylor expansion of (log PI) in n 4.643 * [taylor]: Taking taylor expansion of PI in n 4.643 * [backup-simplify]: Simplify PI into PI 4.643 * [backup-simplify]: Simplify (log PI) into (log PI) 4.644 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.646 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.646 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.646 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.646 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.646 * [taylor]: Taking taylor expansion of 1.0 in n 4.646 * [backup-simplify]: Simplify 1.0 into 1.0 4.646 * [taylor]: Taking taylor expansion of (log n) in n 4.646 * [taylor]: Taking taylor expansion of n in n 4.646 * [backup-simplify]: Simplify 0 into 0 4.646 * [backup-simplify]: Simplify 1 into 1 4.646 * [backup-simplify]: Simplify (log 1) into 0 4.647 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.647 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.647 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.648 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.649 * [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) 4.650 * [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)) 4.652 * [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))) 4.654 * [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) 4.654 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.654 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.654 * [taylor]: Taking taylor expansion of 2.0 in n 4.654 * [backup-simplify]: Simplify 2.0 into 2.0 4.654 * [taylor]: Taking taylor expansion of (* n PI) in n 4.654 * [taylor]: Taking taylor expansion of n in n 4.654 * [backup-simplify]: Simplify 0 into 0 4.654 * [backup-simplify]: Simplify 1 into 1 4.654 * [taylor]: Taking taylor expansion of PI in n 4.654 * [backup-simplify]: Simplify PI into PI 4.655 * [backup-simplify]: Simplify (* 0 PI) into 0 4.655 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.657 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.658 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.659 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.659 * [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 4.659 * [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 4.659 * [taylor]: Taking taylor expansion of +nan.0 in n 4.659 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.659 * [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 4.659 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.659 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.660 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.660 * [taylor]: Taking taylor expansion of 0.5 in n 4.660 * [backup-simplify]: Simplify 0.5 into 0.5 4.660 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.660 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.660 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.660 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.660 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.660 * [taylor]: Taking taylor expansion of 1.0 in n 4.660 * [backup-simplify]: Simplify 1.0 into 1.0 4.660 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.660 * [taylor]: Taking taylor expansion of 2.0 in n 4.660 * [backup-simplify]: Simplify 2.0 into 2.0 4.660 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.661 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.663 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.663 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.663 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.663 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.663 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.663 * [taylor]: Taking taylor expansion of 1.0 in n 4.663 * [backup-simplify]: Simplify 1.0 into 1.0 4.663 * [taylor]: Taking taylor expansion of (log PI) in n 4.663 * [taylor]: Taking taylor expansion of PI in n 4.663 * [backup-simplify]: Simplify PI into PI 4.664 * [backup-simplify]: Simplify (log PI) into (log PI) 4.665 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.666 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.666 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.666 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.666 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.666 * [taylor]: Taking taylor expansion of 1.0 in n 4.666 * [backup-simplify]: Simplify 1.0 into 1.0 4.666 * [taylor]: Taking taylor expansion of (log n) in n 4.666 * [taylor]: Taking taylor expansion of n in n 4.667 * [backup-simplify]: Simplify 0 into 0 4.667 * [backup-simplify]: Simplify 1 into 1 4.667 * [backup-simplify]: Simplify (log 1) into 0 4.667 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.667 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.668 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.668 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.670 * [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) 4.671 * [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)) 4.672 * [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))) 4.674 * [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) 4.674 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 4.674 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.674 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.674 * [taylor]: Taking taylor expansion of 2.0 in n 4.674 * [backup-simplify]: Simplify 2.0 into 2.0 4.674 * [taylor]: Taking taylor expansion of (* n PI) in n 4.674 * [taylor]: Taking taylor expansion of n in n 4.674 * [backup-simplify]: Simplify 0 into 0 4.674 * [backup-simplify]: Simplify 1 into 1 4.674 * [taylor]: Taking taylor expansion of PI in n 4.674 * [backup-simplify]: Simplify PI into PI 4.675 * [backup-simplify]: Simplify (* 0 PI) into 0 4.675 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.677 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.678 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.679 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.681 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.682 * [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)) 4.684 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.687 * [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)) 4.690 * [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))) 4.691 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.693 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.695 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 4.698 * [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)) 4.700 * [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))) 4.703 * [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)))))))) 4.714 * [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)))))))))))) 4.724 * [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)))))))))))) 4.733 * [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)))))))))))))) 4.743 * [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)))))))))))))) 4.764 * [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)))))))))))))) 4.787 * [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)))))))))))))))))))))) 4.787 * [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)))))) 4.787 * [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 4.787 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 4.787 * [taylor]: Taking taylor expansion of 1.0 in n 4.787 * [backup-simplify]: Simplify 1.0 into 1.0 4.787 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 4.787 * [taylor]: Taking taylor expansion of (sqrt k) in n 4.788 * [taylor]: Taking taylor expansion of k in n 4.788 * [backup-simplify]: Simplify k into k 4.788 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 4.788 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 4.788 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.788 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.788 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.788 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.788 * [taylor]: Taking taylor expansion of 0.5 in n 4.788 * [backup-simplify]: Simplify 0.5 into 0.5 4.788 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.788 * [taylor]: Taking taylor expansion of 1.0 in n 4.788 * [backup-simplify]: Simplify 1.0 into 1.0 4.788 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.788 * [taylor]: Taking taylor expansion of k in n 4.788 * [backup-simplify]: Simplify k into k 4.788 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.788 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.788 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.788 * [taylor]: Taking taylor expansion of 2.0 in n 4.788 * [backup-simplify]: Simplify 2.0 into 2.0 4.788 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.788 * [taylor]: Taking taylor expansion of PI in n 4.788 * [backup-simplify]: Simplify PI into PI 4.788 * [taylor]: Taking taylor expansion of n in n 4.788 * [backup-simplify]: Simplify 0 into 0 4.788 * [backup-simplify]: Simplify 1 into 1 4.788 * [backup-simplify]: Simplify (/ PI 1) into PI 4.789 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.789 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.789 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.790 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.790 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.790 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.791 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.792 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.792 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.792 * [taylor]: Taking taylor expansion of 1.0 in k 4.792 * [backup-simplify]: Simplify 1.0 into 1.0 4.792 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.792 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.792 * [taylor]: Taking taylor expansion of k in k 4.792 * [backup-simplify]: Simplify 0 into 0 4.792 * [backup-simplify]: Simplify 1 into 1 4.792 * [backup-simplify]: Simplify (sqrt 0) into 0 4.793 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.793 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.793 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.793 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.793 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.793 * [taylor]: Taking taylor expansion of 0.5 in k 4.793 * [backup-simplify]: Simplify 0.5 into 0.5 4.793 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.793 * [taylor]: Taking taylor expansion of 1.0 in k 4.793 * [backup-simplify]: Simplify 1.0 into 1.0 4.793 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.793 * [taylor]: Taking taylor expansion of k in k 4.793 * [backup-simplify]: Simplify 0 into 0 4.793 * [backup-simplify]: Simplify 1 into 1 4.794 * [backup-simplify]: Simplify (/ 1 1) into 1 4.794 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.794 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.794 * [taylor]: Taking taylor expansion of 2.0 in k 4.794 * [backup-simplify]: Simplify 2.0 into 2.0 4.794 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.794 * [taylor]: Taking taylor expansion of PI in k 4.794 * [backup-simplify]: Simplify PI into PI 4.794 * [taylor]: Taking taylor expansion of n in k 4.794 * [backup-simplify]: Simplify n into n 4.794 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.794 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.794 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.794 * [backup-simplify]: Simplify (- 1) into -1 4.795 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.795 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.795 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.795 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.795 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.795 * [taylor]: Taking taylor expansion of 1.0 in k 4.795 * [backup-simplify]: Simplify 1.0 into 1.0 4.795 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.795 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.795 * [taylor]: Taking taylor expansion of k in k 4.795 * [backup-simplify]: Simplify 0 into 0 4.795 * [backup-simplify]: Simplify 1 into 1 4.795 * [backup-simplify]: Simplify (sqrt 0) into 0 4.796 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.796 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.796 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.796 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.796 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.796 * [taylor]: Taking taylor expansion of 0.5 in k 4.796 * [backup-simplify]: Simplify 0.5 into 0.5 4.796 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.796 * [taylor]: Taking taylor expansion of 1.0 in k 4.796 * [backup-simplify]: Simplify 1.0 into 1.0 4.796 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.796 * [taylor]: Taking taylor expansion of k in k 4.797 * [backup-simplify]: Simplify 0 into 0 4.797 * [backup-simplify]: Simplify 1 into 1 4.797 * [backup-simplify]: Simplify (/ 1 1) into 1 4.797 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.797 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.797 * [taylor]: Taking taylor expansion of 2.0 in k 4.797 * [backup-simplify]: Simplify 2.0 into 2.0 4.797 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.797 * [taylor]: Taking taylor expansion of PI in k 4.797 * [backup-simplify]: Simplify PI into PI 4.797 * [taylor]: Taking taylor expansion of n in k 4.797 * [backup-simplify]: Simplify n into n 4.797 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.797 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.797 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.797 * [backup-simplify]: Simplify (- 1) into -1 4.798 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.798 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.798 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.798 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.798 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 4.799 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.799 * [taylor]: Taking taylor expansion of 0 in n 4.799 * [backup-simplify]: Simplify 0 into 0 4.799 * [backup-simplify]: Simplify 0 into 0 4.799 * [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))))))) 4.800 * [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))))))) 4.800 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.800 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.800 * [taylor]: Taking taylor expansion of +nan.0 in n 4.800 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.800 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.800 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.800 * [taylor]: Taking taylor expansion of 0.5 in n 4.800 * [backup-simplify]: Simplify 0.5 into 0.5 4.800 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.800 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.800 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.800 * [taylor]: Taking taylor expansion of 2.0 in n 4.800 * [backup-simplify]: Simplify 2.0 into 2.0 4.800 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.800 * [taylor]: Taking taylor expansion of PI in n 4.800 * [backup-simplify]: Simplify PI into PI 4.800 * [taylor]: Taking taylor expansion of n in n 4.800 * [backup-simplify]: Simplify 0 into 0 4.800 * [backup-simplify]: Simplify 1 into 1 4.800 * [backup-simplify]: Simplify (/ PI 1) into PI 4.801 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.801 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.801 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.801 * [taylor]: Taking taylor expansion of 1.0 in n 4.801 * [backup-simplify]: Simplify 1.0 into 1.0 4.801 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.802 * [taylor]: Taking taylor expansion of k in n 4.802 * [backup-simplify]: Simplify k into k 4.802 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.802 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.802 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.803 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.803 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.804 * [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)))) 4.805 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.806 * [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)))))) 4.806 * [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))))))) 4.807 * [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))))))) 4.807 * [backup-simplify]: Simplify 0 into 0 4.809 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.810 * [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))))))) 4.810 * [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))))))) 4.810 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.810 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.811 * [taylor]: Taking taylor expansion of +nan.0 in n 4.811 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.811 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.811 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.811 * [taylor]: Taking taylor expansion of 0.5 in n 4.811 * [backup-simplify]: Simplify 0.5 into 0.5 4.811 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.811 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.811 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.811 * [taylor]: Taking taylor expansion of 2.0 in n 4.811 * [backup-simplify]: Simplify 2.0 into 2.0 4.811 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.811 * [taylor]: Taking taylor expansion of PI in n 4.811 * [backup-simplify]: Simplify PI into PI 4.811 * [taylor]: Taking taylor expansion of n in n 4.811 * [backup-simplify]: Simplify 0 into 0 4.811 * [backup-simplify]: Simplify 1 into 1 4.811 * [backup-simplify]: Simplify (/ PI 1) into PI 4.811 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.812 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.812 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.812 * [taylor]: Taking taylor expansion of 1.0 in n 4.812 * [backup-simplify]: Simplify 1.0 into 1.0 4.812 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.812 * [taylor]: Taking taylor expansion of k in n 4.812 * [backup-simplify]: Simplify k into k 4.812 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.813 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.813 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.814 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.815 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.816 * [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)))) 4.817 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.818 * [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)))))) 4.820 * [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))))))) 4.821 * [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))))))) 4.822 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.823 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.823 * [backup-simplify]: Simplify (- 0) into 0 4.823 * [backup-simplify]: Simplify (+ 0 0) into 0 4.824 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.825 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.827 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.828 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.830 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 4.831 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.833 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 4.833 * [backup-simplify]: Simplify (- 0) into 0 4.834 * [backup-simplify]: Simplify 0 into 0 4.834 * [backup-simplify]: Simplify 0 into 0 4.837 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.839 * [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))))))) 4.840 * [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))))))) 4.840 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.840 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.841 * [taylor]: Taking taylor expansion of +nan.0 in n 4.841 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.841 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.841 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.841 * [taylor]: Taking taylor expansion of 0.5 in n 4.841 * [backup-simplify]: Simplify 0.5 into 0.5 4.841 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.841 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.841 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.841 * [taylor]: Taking taylor expansion of 2.0 in n 4.841 * [backup-simplify]: Simplify 2.0 into 2.0 4.841 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.841 * [taylor]: Taking taylor expansion of PI in n 4.841 * [backup-simplify]: Simplify PI into PI 4.841 * [taylor]: Taking taylor expansion of n in n 4.841 * [backup-simplify]: Simplify 0 into 0 4.841 * [backup-simplify]: Simplify 1 into 1 4.841 * [backup-simplify]: Simplify (/ PI 1) into PI 4.842 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.843 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.843 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.843 * [taylor]: Taking taylor expansion of 1.0 in n 4.843 * [backup-simplify]: Simplify 1.0 into 1.0 4.843 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.843 * [taylor]: Taking taylor expansion of k in n 4.843 * [backup-simplify]: Simplify k into k 4.843 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.845 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.845 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.845 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.846 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.847 * [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)))) 4.848 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.850 * [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)))))) 4.851 * [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))))))) 4.853 * [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))))))) 4.857 * [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)))))))) 4.858 * [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)))) 4.858 * [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 4.858 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 4.858 * [taylor]: Taking taylor expansion of 1.0 in n 4.859 * [backup-simplify]: Simplify 1.0 into 1.0 4.859 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 4.859 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.859 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.859 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.859 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.859 * [taylor]: Taking taylor expansion of 0.5 in n 4.859 * [backup-simplify]: Simplify 0.5 into 0.5 4.859 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.859 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.859 * [taylor]: Taking taylor expansion of k in n 4.859 * [backup-simplify]: Simplify k into k 4.859 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.859 * [taylor]: Taking taylor expansion of 1.0 in n 4.859 * [backup-simplify]: Simplify 1.0 into 1.0 4.859 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.859 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.859 * [taylor]: Taking taylor expansion of -2.0 in n 4.859 * [backup-simplify]: Simplify -2.0 into -2.0 4.859 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.859 * [taylor]: Taking taylor expansion of PI in n 4.859 * [backup-simplify]: Simplify PI into PI 4.859 * [taylor]: Taking taylor expansion of n in n 4.859 * [backup-simplify]: Simplify 0 into 0 4.859 * [backup-simplify]: Simplify 1 into 1 4.860 * [backup-simplify]: Simplify (/ PI 1) into PI 4.860 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.861 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.862 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.862 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.863 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.864 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.865 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.866 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 4.866 * [taylor]: Taking taylor expansion of (/ -1 k) in n 4.866 * [taylor]: Taking taylor expansion of -1 in n 4.866 * [backup-simplify]: Simplify -1 into -1 4.866 * [taylor]: Taking taylor expansion of k in n 4.866 * [backup-simplify]: Simplify k into k 4.866 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 4.866 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 4.866 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 4.866 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 4.867 * [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))) 4.867 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.867 * [taylor]: Taking taylor expansion of 1.0 in k 4.867 * [backup-simplify]: Simplify 1.0 into 1.0 4.868 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.868 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.868 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.868 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.868 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.868 * [taylor]: Taking taylor expansion of 0.5 in k 4.868 * [backup-simplify]: Simplify 0.5 into 0.5 4.868 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.868 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.868 * [taylor]: Taking taylor expansion of k in k 4.868 * [backup-simplify]: Simplify 0 into 0 4.868 * [backup-simplify]: Simplify 1 into 1 4.868 * [backup-simplify]: Simplify (/ 1 1) into 1 4.868 * [taylor]: Taking taylor expansion of 1.0 in k 4.868 * [backup-simplify]: Simplify 1.0 into 1.0 4.868 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.868 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.868 * [taylor]: Taking taylor expansion of -2.0 in k 4.868 * [backup-simplify]: Simplify -2.0 into -2.0 4.868 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.868 * [taylor]: Taking taylor expansion of PI in k 4.869 * [backup-simplify]: Simplify PI into PI 4.869 * [taylor]: Taking taylor expansion of n in k 4.869 * [backup-simplify]: Simplify n into n 4.869 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.869 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.869 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.869 * [backup-simplify]: Simplify (+ 1 0) into 1 4.870 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.870 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.870 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.870 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.870 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.870 * [taylor]: Taking taylor expansion of -1 in k 4.870 * [backup-simplify]: Simplify -1 into -1 4.870 * [taylor]: Taking taylor expansion of k in k 4.870 * [backup-simplify]: Simplify 0 into 0 4.870 * [backup-simplify]: Simplify 1 into 1 4.871 * [backup-simplify]: Simplify (/ -1 1) into -1 4.871 * [backup-simplify]: Simplify (sqrt 0) into 0 4.873 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.873 * [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))))))) 4.873 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.873 * [taylor]: Taking taylor expansion of 1.0 in k 4.873 * [backup-simplify]: Simplify 1.0 into 1.0 4.873 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.873 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.873 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.873 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.873 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.873 * [taylor]: Taking taylor expansion of 0.5 in k 4.873 * [backup-simplify]: Simplify 0.5 into 0.5 4.873 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.873 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.873 * [taylor]: Taking taylor expansion of k in k 4.873 * [backup-simplify]: Simplify 0 into 0 4.873 * [backup-simplify]: Simplify 1 into 1 4.874 * [backup-simplify]: Simplify (/ 1 1) into 1 4.874 * [taylor]: Taking taylor expansion of 1.0 in k 4.874 * [backup-simplify]: Simplify 1.0 into 1.0 4.874 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.874 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.874 * [taylor]: Taking taylor expansion of -2.0 in k 4.874 * [backup-simplify]: Simplify -2.0 into -2.0 4.874 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.874 * [taylor]: Taking taylor expansion of PI in k 4.874 * [backup-simplify]: Simplify PI into PI 4.874 * [taylor]: Taking taylor expansion of n in k 4.874 * [backup-simplify]: Simplify n into n 4.874 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.874 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.874 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.875 * [backup-simplify]: Simplify (+ 1 0) into 1 4.875 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.875 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.876 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.876 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.876 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.876 * [taylor]: Taking taylor expansion of -1 in k 4.876 * [backup-simplify]: Simplify -1 into -1 4.876 * [taylor]: Taking taylor expansion of k in k 4.876 * [backup-simplify]: Simplify 0 into 0 4.876 * [backup-simplify]: Simplify 1 into 1 4.876 * [backup-simplify]: Simplify (/ -1 1) into -1 4.877 * [backup-simplify]: Simplify (sqrt 0) into 0 4.882 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.883 * [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))))))) 4.883 * [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))))))) 4.883 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.883 * [taylor]: Taking taylor expansion of +nan.0 in n 4.883 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.883 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.883 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.883 * [taylor]: Taking taylor expansion of 0.5 in n 4.883 * [backup-simplify]: Simplify 0.5 into 0.5 4.883 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.883 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.883 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.883 * [taylor]: Taking taylor expansion of k in n 4.883 * [backup-simplify]: Simplify k into k 4.884 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.884 * [taylor]: Taking taylor expansion of 1.0 in n 4.884 * [backup-simplify]: Simplify 1.0 into 1.0 4.884 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.884 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.884 * [taylor]: Taking taylor expansion of -2.0 in n 4.884 * [backup-simplify]: Simplify -2.0 into -2.0 4.884 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.884 * [taylor]: Taking taylor expansion of PI in n 4.884 * [backup-simplify]: Simplify PI into PI 4.884 * [taylor]: Taking taylor expansion of n in n 4.884 * [backup-simplify]: Simplify 0 into 0 4.884 * [backup-simplify]: Simplify 1 into 1 4.884 * [backup-simplify]: Simplify (/ PI 1) into PI 4.885 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.886 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.886 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.887 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.888 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.890 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.891 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.892 * [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)))))) 4.894 * [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)))))) 4.894 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.897 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.898 * [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)))))))) 4.899 * [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)))))))) 4.899 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 4.899 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.899 * [taylor]: Taking taylor expansion of +nan.0 in n 4.899 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.899 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.899 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.899 * [taylor]: Taking taylor expansion of 0.5 in n 4.899 * [backup-simplify]: Simplify 0.5 into 0.5 4.899 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.900 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.900 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.900 * [taylor]: Taking taylor expansion of k in n 4.900 * [backup-simplify]: Simplify k into k 4.900 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.900 * [taylor]: Taking taylor expansion of 1.0 in n 4.900 * [backup-simplify]: Simplify 1.0 into 1.0 4.900 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.900 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.900 * [taylor]: Taking taylor expansion of -2.0 in n 4.900 * [backup-simplify]: Simplify -2.0 into -2.0 4.900 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.900 * [taylor]: Taking taylor expansion of PI in n 4.900 * [backup-simplify]: Simplify PI into PI 4.900 * [taylor]: Taking taylor expansion of n in n 4.900 * [backup-simplify]: Simplify 0 into 0 4.900 * [backup-simplify]: Simplify 1 into 1 4.901 * [backup-simplify]: Simplify (/ PI 1) into PI 4.902 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.903 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.903 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.904 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.905 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.907 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.908 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.909 * [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)))))) 4.910 * [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))))))) 4.912 * [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))))))) 4.913 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.913 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.915 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.915 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.916 * [backup-simplify]: Simplify (+ 0 0) into 0 4.917 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.918 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.920 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 4.922 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.924 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 4.924 * [backup-simplify]: Simplify 0 into 0 4.925 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.928 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.930 * [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)))))))) 4.931 * [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)))))))) 4.931 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 4.931 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.931 * [taylor]: Taking taylor expansion of +nan.0 in n 4.931 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.931 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.931 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.931 * [taylor]: Taking taylor expansion of 0.5 in n 4.931 * [backup-simplify]: Simplify 0.5 into 0.5 4.931 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.931 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.931 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.931 * [taylor]: Taking taylor expansion of k in n 4.931 * [backup-simplify]: Simplify k into k 4.931 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.931 * [taylor]: Taking taylor expansion of 1.0 in n 4.932 * [backup-simplify]: Simplify 1.0 into 1.0 4.932 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.932 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.932 * [taylor]: Taking taylor expansion of -2.0 in n 4.932 * [backup-simplify]: Simplify -2.0 into -2.0 4.932 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.932 * [taylor]: Taking taylor expansion of PI in n 4.932 * [backup-simplify]: Simplify PI into PI 4.932 * [taylor]: Taking taylor expansion of n in n 4.932 * [backup-simplify]: Simplify 0 into 0 4.932 * [backup-simplify]: Simplify 1 into 1 4.933 * [backup-simplify]: Simplify (/ PI 1) into PI 4.933 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.934 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.934 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.936 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.937 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.938 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.939 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.941 * [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)))))) 4.942 * [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))))))) 4.943 * [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))))))) 4.948 * [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)))))))))))) 4.948 * * * [progress]: simplifying candidates 4.953 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 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(log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 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(sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 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2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 4.962 * * [simplify]: Extracting # 0 : cost 0 4.963 * * [simplify]: Extracting # 1 : cost 0 4.963 * * [simplify]: Extracting # 2 : cost 0 4.964 * * [simplify]: Extracting # 3 : cost 0 4.965 * * [simplify]: Extracting # 4 : cost 0 4.966 * * [simplify]: Extracting # 5 : cost 0 4.966 * * [simplify]: Extracting # 6 : cost 0 4.967 * * [simplify]: Extracting # 7 : cost 0 4.968 * * [simplify]: Extracting # 8 : cost 0 4.969 * * [simplify]: Extracting # 9 : cost 0 4.970 * * [simplify]: Extracting # 10 : cost 0 4.971 * * [simplify]: Extracting # 11 : cost 0 4.972 * * [simplify]: Extracting # 12 : cost 0 4.973 * * [simplify]: Extracting # 13 : cost 0 4.974 * * [simplify]: Extracting # 14 : cost 0 4.976 * * [simplify]: Extracting # 15 : cost 0 4.977 * * [simplify]: Extracting # 16 : cost 0 4.978 * * [simplify]: Extracting # 17 : cost 0 4.979 * * [simplify]: Extracting # 18 : cost 0 4.980 * * [simplify]: Extracting # 19 : cost 0 4.981 * * [simplify]: Extracting # 20 : cost 0 4.982 * * [simplify]: Extracting # 21 : cost 0 4.983 * * [simplify]: Extracting # 22 : cost 0 4.984 * * [simplify]: Extracting # 23 : cost 0 4.985 * * [simplify]: Extracting # 24 : cost 0 4.986 * * [simplify]: Extracting # 25 : cost 0 4.988 * * [simplify]: Extracting # 26 : cost 0 4.989 * * [simplify]: Extracting # 27 : cost 0 4.989 * * [simplify]: Extracting # 28 : cost 0 4.990 * * [simplify]: Extracting # 29 : cost 0 4.990 * * [simplify]: Extracting # 30 : cost 0 4.991 * * [simplify]: Extracting # 31 : cost 0 4.991 * * [simplify]: Extracting # 32 : cost 0 4.992 * * [simplify]: iteration 0 : 369 enodes (cost 2880 ) 5.134 * * [simplify]: Extracting # 0 : cost 0 5.136 * * [simplify]: Extracting # 1 : cost 0 5.137 * * [simplify]: Extracting # 2 : cost 0 5.138 * * [simplify]: Extracting # 3 : cost 0 5.139 * * [simplify]: Extracting # 4 : cost 0 5.141 * * [simplify]: Extracting # 5 : cost 0 5.142 * * [simplify]: Extracting # 6 : cost 0 5.143 * * [simplify]: iteration 1 : 961 enodes (cost 2712 ) 5.705 * * [simplify]: Extracting # 0 : cost 0 5.711 * * [simplify]: Extracting # 1 : cost 0 5.718 * * [simplify]: Extracting # 2 : cost 0 5.726 * * [simplify]: Extracting # 3 : cost 0 5.734 * * [simplify]: Extracting # 4 : cost 0 5.742 * * [simplify]: Extracting # 5 : cost 0 5.750 * * [simplify]: iteration 2 : 3131 enodes (cost 2550 ) 7.175 * * [simplify]: Extracting # 0 : cost 0 7.182 * * [simplify]: Extracting # 1 : cost 0 7.189 * * [simplify]: Extracting # 2 : cost 0 7.195 * * [simplify]: Extracting # 3 : cost 0 7.206 * * [simplify]: Extracting # 4 : cost 0 7.218 * * [simplify]: iteration done: 5000 enodes (cost 2540 ) 7.221 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (pow (* n (* 2.0 PI)) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (pow 1.0 3) k) (sqrt k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (exp (* (* 2.0 PI) n)) (pow (* 2.0 (* n PI)) 3) (pow (* 2.0 (* n PI)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* 2.0 (* n PI)) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (/ (/ (pow 1.0 3) k) (sqrt k))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (fma (- 0.5) (* k (fma (log (* 2.0 PI)) (pow (* 2.0 (* n PI)) 0.5) (* (log n) (pow (* 2.0 (* n PI)) 0.5)))) (fma (* 0.125 (pow k 2)) (fma (pow (log (* 2.0 PI)) 2) (pow (* 2.0 (* n PI)) 0.5) (* (pow (* 2.0 (* n PI)) 0.5) (pow (log n) 2))) (fma 0.25 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* 2.0 (* n PI)) 0.5)) (pow (* 2.0 (* n PI)) 0.5)))) (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) (pow (exp (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))) 0.5) (- (- (fma k +nan.0 +nan.0) (* (* +nan.0 k) k))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3))))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) +nan.0))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (fma (* +nan.0 (* (pow k 2) (pow (log (* 2.0 PI)) 2))) (- (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (fma (* (pow k 2) (log (* 2.0 PI))) (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) +nan.0) (fma (- (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (log n))))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (fma (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) +nan.0 (fma +nan.0 (- (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (fma +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (fma (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) +nan.0 (- (* +nan.0 (- (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) (* (* +nan.0 (* k (log n))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) (fma +nan.0 (- (/ (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) k) (/ (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) (pow k 2))) (- (/ +nan.0 (/ (pow k 3) (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)))))) (fma (- +nan.0) (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k) (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) 7.230 * * * [progress]: adding candidates to table 7.864 * * [progress]: iteration 2 / 4 7.864 * * * [progress]: picking best candidate 7.925 * * * * [pick]: Picked # 7.925 * * * [progress]: localizing error 7.963 * * * [progress]: generating rewritten candidates 7.963 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 7.992 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 8.050 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 8.063 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 8.125 * * * [progress]: generating series expansions 8.125 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 8.126 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 8.126 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.126 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.126 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.127 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.127 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.127 * [taylor]: Taking taylor expansion of 0.25 in k 8.127 * [backup-simplify]: Simplify 0.25 into 0.25 8.127 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.127 * [taylor]: Taking taylor expansion of 1.0 in k 8.127 * [backup-simplify]: Simplify 1.0 into 1.0 8.127 * [taylor]: Taking taylor expansion of k in k 8.127 * [backup-simplify]: Simplify 0 into 0 8.127 * [backup-simplify]: Simplify 1 into 1 8.127 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.127 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.127 * [taylor]: Taking taylor expansion of 2.0 in k 8.127 * [backup-simplify]: Simplify 2.0 into 2.0 8.127 * [taylor]: Taking taylor expansion of (* n PI) in k 8.127 * [taylor]: Taking taylor expansion of n in k 8.127 * [backup-simplify]: Simplify n into n 8.127 * [taylor]: Taking taylor expansion of PI in k 8.127 * [backup-simplify]: Simplify PI into PI 8.127 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.127 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.127 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.128 * [backup-simplify]: Simplify (- 0) into 0 8.128 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.129 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.129 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.129 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.129 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.129 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.129 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.129 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.129 * [taylor]: Taking taylor expansion of 0.25 in n 8.129 * [backup-simplify]: Simplify 0.25 into 0.25 8.129 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.129 * [taylor]: Taking taylor expansion of 1.0 in n 8.129 * [backup-simplify]: Simplify 1.0 into 1.0 8.129 * [taylor]: Taking taylor expansion of k in n 8.129 * [backup-simplify]: Simplify k into k 8.129 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.129 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.130 * [taylor]: Taking taylor expansion of 2.0 in n 8.130 * [backup-simplify]: Simplify 2.0 into 2.0 8.130 * [taylor]: Taking taylor expansion of (* n PI) in n 8.130 * [taylor]: Taking taylor expansion of n in n 8.130 * [backup-simplify]: Simplify 0 into 0 8.130 * [backup-simplify]: Simplify 1 into 1 8.130 * [taylor]: Taking taylor expansion of PI in n 8.130 * [backup-simplify]: Simplify PI into PI 8.130 * [backup-simplify]: Simplify (* 0 PI) into 0 8.131 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.132 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.134 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.135 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.135 * [backup-simplify]: Simplify (- k) into (- k) 8.135 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.135 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.137 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.139 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.140 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.140 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.140 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.140 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.140 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.140 * [taylor]: Taking taylor expansion of 0.25 in n 8.140 * [backup-simplify]: Simplify 0.25 into 0.25 8.140 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.140 * [taylor]: Taking taylor expansion of 1.0 in n 8.140 * [backup-simplify]: Simplify 1.0 into 1.0 8.140 * [taylor]: Taking taylor expansion of k in n 8.140 * [backup-simplify]: Simplify k into k 8.140 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.140 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.140 * [taylor]: Taking taylor expansion of 2.0 in n 8.140 * [backup-simplify]: Simplify 2.0 into 2.0 8.140 * [taylor]: Taking taylor expansion of (* n PI) in n 8.140 * [taylor]: Taking taylor expansion of n in n 8.140 * [backup-simplify]: Simplify 0 into 0 8.140 * [backup-simplify]: Simplify 1 into 1 8.141 * [taylor]: Taking taylor expansion of PI in n 8.141 * [backup-simplify]: Simplify PI into PI 8.141 * [backup-simplify]: Simplify (* 0 PI) into 0 8.141 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.143 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.144 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.146 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.146 * [backup-simplify]: Simplify (- k) into (- k) 8.146 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.146 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.154 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.155 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.156 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.156 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.156 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.157 * [taylor]: Taking taylor expansion of 0.25 in k 8.157 * [backup-simplify]: Simplify 0.25 into 0.25 8.157 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.157 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.157 * [taylor]: Taking taylor expansion of 1.0 in k 8.157 * [backup-simplify]: Simplify 1.0 into 1.0 8.157 * [taylor]: Taking taylor expansion of k in k 8.157 * [backup-simplify]: Simplify 0 into 0 8.157 * [backup-simplify]: Simplify 1 into 1 8.157 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.157 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.157 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.157 * [taylor]: Taking taylor expansion of 2.0 in k 8.157 * [backup-simplify]: Simplify 2.0 into 2.0 8.157 * [taylor]: Taking taylor expansion of PI in k 8.157 * [backup-simplify]: Simplify PI into PI 8.158 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.159 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.159 * [taylor]: Taking taylor expansion of (log n) in k 8.159 * [taylor]: Taking taylor expansion of n in k 8.159 * [backup-simplify]: Simplify n into n 8.159 * [backup-simplify]: Simplify (log n) into (log n) 8.159 * [backup-simplify]: Simplify (- 0) into 0 8.160 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.161 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.162 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.163 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.165 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.166 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.167 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.168 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.170 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.170 * [backup-simplify]: Simplify (- 0) into 0 8.171 * [backup-simplify]: Simplify (+ 0 0) into 0 8.171 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 8.173 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.174 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.176 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.177 * [taylor]: Taking taylor expansion of 0 in k 8.177 * [backup-simplify]: Simplify 0 into 0 8.177 * [backup-simplify]: Simplify 0 into 0 8.178 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.180 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.181 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.181 * [backup-simplify]: Simplify (+ 0 0) into 0 8.181 * [backup-simplify]: Simplify (- 1) into -1 8.182 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.183 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.186 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 8.189 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.191 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.192 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.193 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.195 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.195 * [backup-simplify]: Simplify (- 0) into 0 8.195 * [backup-simplify]: Simplify (+ 0 0) into 0 8.196 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.197 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.198 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.200 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.200 * [taylor]: Taking taylor expansion of 0 in k 8.200 * [backup-simplify]: Simplify 0 into 0 8.200 * [backup-simplify]: Simplify 0 into 0 8.200 * [backup-simplify]: Simplify 0 into 0 8.200 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.202 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.203 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.204 * [backup-simplify]: Simplify (+ 0 0) into 0 8.204 * [backup-simplify]: Simplify (- 0) into 0 8.204 * [backup-simplify]: Simplify (+ 0 0) into 0 8.205 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.207 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.210 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.213 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.220 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 8.221 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 8.222 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 8.222 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 8.222 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.222 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.222 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 8.222 * [taylor]: Taking taylor expansion of 0.25 in k 8.222 * [backup-simplify]: Simplify 0.25 into 0.25 8.222 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.222 * [taylor]: Taking taylor expansion of 1.0 in k 8.222 * [backup-simplify]: Simplify 1.0 into 1.0 8.222 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.222 * [taylor]: Taking taylor expansion of k in k 8.222 * [backup-simplify]: Simplify 0 into 0 8.222 * [backup-simplify]: Simplify 1 into 1 8.222 * [backup-simplify]: Simplify (/ 1 1) into 1 8.222 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.222 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.222 * [taylor]: Taking taylor expansion of 2.0 in k 8.223 * [backup-simplify]: Simplify 2.0 into 2.0 8.223 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.223 * [taylor]: Taking taylor expansion of PI in k 8.223 * [backup-simplify]: Simplify PI into PI 8.223 * [taylor]: Taking taylor expansion of n in k 8.223 * [backup-simplify]: Simplify n into n 8.223 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.223 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.223 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.223 * [backup-simplify]: Simplify (- 1) into -1 8.224 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.224 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 8.224 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 8.225 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 8.225 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.225 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.225 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.225 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.225 * [taylor]: Taking taylor expansion of 0.25 in n 8.225 * [backup-simplify]: Simplify 0.25 into 0.25 8.225 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.225 * [taylor]: Taking taylor expansion of 1.0 in n 8.225 * [backup-simplify]: Simplify 1.0 into 1.0 8.225 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.225 * [taylor]: Taking taylor expansion of k in n 8.225 * [backup-simplify]: Simplify k into k 8.225 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.225 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.225 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.225 * [taylor]: Taking taylor expansion of 2.0 in n 8.225 * [backup-simplify]: Simplify 2.0 into 2.0 8.225 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.225 * [taylor]: Taking taylor expansion of PI in n 8.225 * [backup-simplify]: Simplify PI into PI 8.225 * [taylor]: Taking taylor expansion of n in n 8.225 * [backup-simplify]: Simplify 0 into 0 8.225 * [backup-simplify]: Simplify 1 into 1 8.226 * [backup-simplify]: Simplify (/ PI 1) into PI 8.227 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.228 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.228 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.228 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.228 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.230 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.231 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.232 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.232 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.232 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.232 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.232 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.232 * [taylor]: Taking taylor expansion of 0.25 in n 8.232 * [backup-simplify]: Simplify 0.25 into 0.25 8.232 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.232 * [taylor]: Taking taylor expansion of 1.0 in n 8.232 * [backup-simplify]: Simplify 1.0 into 1.0 8.232 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.232 * [taylor]: Taking taylor expansion of k in n 8.233 * [backup-simplify]: Simplify k into k 8.233 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.233 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.233 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.233 * [taylor]: Taking taylor expansion of 2.0 in n 8.233 * [backup-simplify]: Simplify 2.0 into 2.0 8.233 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.233 * [taylor]: Taking taylor expansion of PI in n 8.233 * [backup-simplify]: Simplify PI into PI 8.233 * [taylor]: Taking taylor expansion of n in n 8.233 * [backup-simplify]: Simplify 0 into 0 8.233 * [backup-simplify]: Simplify 1 into 1 8.233 * [backup-simplify]: Simplify (/ PI 1) into PI 8.234 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.235 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.235 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.235 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.235 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.237 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.238 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.240 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.240 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.240 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.240 * [taylor]: Taking taylor expansion of 0.25 in k 8.240 * [backup-simplify]: Simplify 0.25 into 0.25 8.240 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.240 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.240 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.240 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.240 * [taylor]: Taking taylor expansion of 2.0 in k 8.240 * [backup-simplify]: Simplify 2.0 into 2.0 8.240 * [taylor]: Taking taylor expansion of PI in k 8.240 * [backup-simplify]: Simplify PI into PI 8.241 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.242 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.242 * [taylor]: Taking taylor expansion of (log n) in k 8.242 * [taylor]: Taking taylor expansion of n in k 8.242 * [backup-simplify]: Simplify n into n 8.242 * [backup-simplify]: Simplify (log n) into (log n) 8.242 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.242 * [taylor]: Taking taylor expansion of 1.0 in k 8.242 * [backup-simplify]: Simplify 1.0 into 1.0 8.242 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.242 * [taylor]: Taking taylor expansion of k in k 8.242 * [backup-simplify]: Simplify 0 into 0 8.242 * [backup-simplify]: Simplify 1 into 1 8.243 * [backup-simplify]: Simplify (/ 1 1) into 1 8.243 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.244 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.244 * [backup-simplify]: Simplify (- 1) into -1 8.245 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.246 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.247 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 8.248 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.250 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.251 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.252 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.253 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.254 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.254 * [backup-simplify]: Simplify (- 0) into 0 8.254 * [backup-simplify]: Simplify (+ 0 0) into 0 8.255 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.256 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.258 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.260 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.260 * [taylor]: Taking taylor expansion of 0 in k 8.260 * [backup-simplify]: Simplify 0 into 0 8.260 * [backup-simplify]: Simplify 0 into 0 8.260 * [backup-simplify]: Simplify 0 into 0 8.261 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.262 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.265 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.266 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.266 * [backup-simplify]: Simplify (- 0) into 0 8.266 * [backup-simplify]: Simplify (+ 0 0) into 0 8.267 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.269 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.271 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.273 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.273 * [taylor]: Taking taylor expansion of 0 in k 8.273 * [backup-simplify]: Simplify 0 into 0 8.273 * [backup-simplify]: Simplify 0 into 0 8.273 * [backup-simplify]: Simplify 0 into 0 8.273 * [backup-simplify]: Simplify 0 into 0 8.275 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.276 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.282 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.282 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.283 * [backup-simplify]: Simplify (- 0) into 0 8.283 * [backup-simplify]: Simplify (+ 0 0) into 0 8.284 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.293 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.295 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.298 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.298 * [taylor]: Taking taylor expansion of 0 in k 8.298 * [backup-simplify]: Simplify 0 into 0 8.298 * [backup-simplify]: Simplify 0 into 0 8.299 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 8.300 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 8.300 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 8.300 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 8.300 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.300 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.300 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 8.300 * [taylor]: Taking taylor expansion of 0.25 in k 8.300 * [backup-simplify]: Simplify 0.25 into 0.25 8.300 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.300 * [taylor]: Taking taylor expansion of k in k 8.300 * [backup-simplify]: Simplify 0 into 0 8.300 * [backup-simplify]: Simplify 1 into 1 8.301 * [backup-simplify]: Simplify (/ 1 1) into 1 8.301 * [taylor]: Taking taylor expansion of 1.0 in k 8.301 * [backup-simplify]: Simplify 1.0 into 1.0 8.301 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.301 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.301 * [taylor]: Taking taylor expansion of -2.0 in k 8.301 * [backup-simplify]: Simplify -2.0 into -2.0 8.301 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.301 * [taylor]: Taking taylor expansion of PI in k 8.301 * [backup-simplify]: Simplify PI into PI 8.301 * [taylor]: Taking taylor expansion of n in k 8.301 * [backup-simplify]: Simplify n into n 8.301 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.301 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.301 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.302 * [backup-simplify]: Simplify (+ 1 0) into 1 8.302 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 8.302 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 8.303 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 8.303 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.303 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.303 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.303 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.303 * [taylor]: Taking taylor expansion of 0.25 in n 8.303 * [backup-simplify]: Simplify 0.25 into 0.25 8.303 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.303 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.303 * [taylor]: Taking taylor expansion of k in n 8.303 * [backup-simplify]: Simplify k into k 8.303 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.303 * [taylor]: Taking taylor expansion of 1.0 in n 8.303 * [backup-simplify]: Simplify 1.0 into 1.0 8.303 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.303 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.303 * [taylor]: Taking taylor expansion of -2.0 in n 8.303 * [backup-simplify]: Simplify -2.0 into -2.0 8.303 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.303 * [taylor]: Taking taylor expansion of PI in n 8.303 * [backup-simplify]: Simplify PI into PI 8.303 * [taylor]: Taking taylor expansion of n in n 8.303 * [backup-simplify]: Simplify 0 into 0 8.303 * [backup-simplify]: Simplify 1 into 1 8.304 * [backup-simplify]: Simplify (/ PI 1) into PI 8.304 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.305 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.305 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.306 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.308 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.309 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.309 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.309 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.309 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.310 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.310 * [taylor]: Taking taylor expansion of 0.25 in n 8.310 * [backup-simplify]: Simplify 0.25 into 0.25 8.310 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.310 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.310 * [taylor]: Taking taylor expansion of k in n 8.310 * [backup-simplify]: Simplify k into k 8.310 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.310 * [taylor]: Taking taylor expansion of 1.0 in n 8.310 * [backup-simplify]: Simplify 1.0 into 1.0 8.310 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.310 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.310 * [taylor]: Taking taylor expansion of -2.0 in n 8.310 * [backup-simplify]: Simplify -2.0 into -2.0 8.310 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.310 * [taylor]: Taking taylor expansion of PI in n 8.310 * [backup-simplify]: Simplify PI into PI 8.310 * [taylor]: Taking taylor expansion of n in n 8.310 * [backup-simplify]: Simplify 0 into 0 8.310 * [backup-simplify]: Simplify 1 into 1 8.311 * [backup-simplify]: Simplify (/ PI 1) into PI 8.311 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.312 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.312 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.312 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.314 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.315 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.316 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.316 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.316 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.317 * [taylor]: Taking taylor expansion of 0.25 in k 8.317 * [backup-simplify]: Simplify 0.25 into 0.25 8.317 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.317 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.317 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.317 * [taylor]: Taking taylor expansion of k in k 8.317 * [backup-simplify]: Simplify 0 into 0 8.317 * [backup-simplify]: Simplify 1 into 1 8.317 * [backup-simplify]: Simplify (/ 1 1) into 1 8.317 * [taylor]: Taking taylor expansion of 1.0 in k 8.317 * [backup-simplify]: Simplify 1.0 into 1.0 8.317 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.317 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.317 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.317 * [taylor]: Taking taylor expansion of -2.0 in k 8.317 * [backup-simplify]: Simplify -2.0 into -2.0 8.317 * [taylor]: Taking taylor expansion of PI in k 8.317 * [backup-simplify]: Simplify PI into PI 8.318 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.319 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.319 * [taylor]: Taking taylor expansion of (log n) in k 8.319 * [taylor]: Taking taylor expansion of n in k 8.319 * [backup-simplify]: Simplify n into n 8.319 * [backup-simplify]: Simplify (log n) into (log n) 8.319 * [backup-simplify]: Simplify (+ 1 0) into 1 8.319 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.321 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.322 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.323 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 8.324 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.325 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.326 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.327 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.329 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.329 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.329 * [backup-simplify]: Simplify (+ 0 0) into 0 8.330 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.331 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.332 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.334 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.334 * [taylor]: Taking taylor expansion of 0 in k 8.334 * [backup-simplify]: Simplify 0 into 0 8.334 * [backup-simplify]: Simplify 0 into 0 8.334 * [backup-simplify]: Simplify 0 into 0 8.335 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.336 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.340 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.340 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.341 * [backup-simplify]: Simplify (+ 0 0) into 0 8.341 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.342 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.343 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.345 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.345 * [taylor]: Taking taylor expansion of 0 in k 8.345 * [backup-simplify]: Simplify 0 into 0 8.345 * [backup-simplify]: Simplify 0 into 0 8.345 * [backup-simplify]: Simplify 0 into 0 8.345 * [backup-simplify]: Simplify 0 into 0 8.345 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.346 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.350 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 8.350 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.351 * [backup-simplify]: Simplify (+ 0 0) into 0 8.351 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.352 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.354 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.355 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.356 * [taylor]: Taking taylor expansion of 0 in k 8.356 * [backup-simplify]: Simplify 0 into 0 8.356 * [backup-simplify]: Simplify 0 into 0 8.356 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 8.357 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 8.357 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 8.357 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.357 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.357 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.357 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.357 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.357 * [taylor]: Taking taylor expansion of 0.25 in k 8.357 * [backup-simplify]: Simplify 0.25 into 0.25 8.357 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.357 * [taylor]: Taking taylor expansion of 1.0 in k 8.357 * [backup-simplify]: Simplify 1.0 into 1.0 8.357 * [taylor]: Taking taylor expansion of k in k 8.357 * [backup-simplify]: Simplify 0 into 0 8.357 * [backup-simplify]: Simplify 1 into 1 8.357 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.357 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.357 * [taylor]: Taking taylor expansion of 2.0 in k 8.357 * [backup-simplify]: Simplify 2.0 into 2.0 8.357 * [taylor]: Taking taylor expansion of (* n PI) in k 8.357 * [taylor]: Taking taylor expansion of n in k 8.357 * [backup-simplify]: Simplify n into n 8.357 * [taylor]: Taking taylor expansion of PI in k 8.357 * [backup-simplify]: Simplify PI into PI 8.358 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.358 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.358 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.358 * [backup-simplify]: Simplify (- 0) into 0 8.358 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.358 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.359 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.359 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.359 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.359 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.359 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.359 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.359 * [taylor]: Taking taylor expansion of 0.25 in n 8.359 * [backup-simplify]: Simplify 0.25 into 0.25 8.359 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.359 * [taylor]: Taking taylor expansion of 1.0 in n 8.359 * [backup-simplify]: Simplify 1.0 into 1.0 8.359 * [taylor]: Taking taylor expansion of k in n 8.359 * [backup-simplify]: Simplify k into k 8.359 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.359 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.359 * [taylor]: Taking taylor expansion of 2.0 in n 8.359 * [backup-simplify]: Simplify 2.0 into 2.0 8.359 * [taylor]: Taking taylor expansion of (* n PI) in n 8.359 * [taylor]: Taking taylor expansion of n in n 8.359 * [backup-simplify]: Simplify 0 into 0 8.359 * [backup-simplify]: Simplify 1 into 1 8.359 * [taylor]: Taking taylor expansion of PI in n 8.359 * [backup-simplify]: Simplify PI into PI 8.359 * [backup-simplify]: Simplify (* 0 PI) into 0 8.360 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.361 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.362 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.362 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.362 * [backup-simplify]: Simplify (- k) into (- k) 8.362 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.362 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.363 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.364 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.365 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.365 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.365 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.365 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.365 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.365 * [taylor]: Taking taylor expansion of 0.25 in n 8.365 * [backup-simplify]: Simplify 0.25 into 0.25 8.365 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.365 * [taylor]: Taking taylor expansion of 1.0 in n 8.365 * [backup-simplify]: Simplify 1.0 into 1.0 8.365 * [taylor]: Taking taylor expansion of k in n 8.365 * [backup-simplify]: Simplify k into k 8.365 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.365 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.365 * [taylor]: Taking taylor expansion of 2.0 in n 8.365 * [backup-simplify]: Simplify 2.0 into 2.0 8.365 * [taylor]: Taking taylor expansion of (* n PI) in n 8.365 * [taylor]: Taking taylor expansion of n in n 8.365 * [backup-simplify]: Simplify 0 into 0 8.365 * [backup-simplify]: Simplify 1 into 1 8.365 * [taylor]: Taking taylor expansion of PI in n 8.365 * [backup-simplify]: Simplify PI into PI 8.366 * [backup-simplify]: Simplify (* 0 PI) into 0 8.366 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.367 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.368 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.369 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.369 * [backup-simplify]: Simplify (- k) into (- k) 8.369 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.369 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.370 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.370 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.371 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.371 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.371 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.371 * [taylor]: Taking taylor expansion of 0.25 in k 8.371 * [backup-simplify]: Simplify 0.25 into 0.25 8.371 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.372 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.372 * [taylor]: Taking taylor expansion of 1.0 in k 8.372 * [backup-simplify]: Simplify 1.0 into 1.0 8.372 * [taylor]: Taking taylor expansion of k in k 8.372 * [backup-simplify]: Simplify 0 into 0 8.372 * [backup-simplify]: Simplify 1 into 1 8.372 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.372 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.372 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.372 * [taylor]: Taking taylor expansion of 2.0 in k 8.372 * [backup-simplify]: Simplify 2.0 into 2.0 8.372 * [taylor]: Taking taylor expansion of PI in k 8.372 * [backup-simplify]: Simplify PI into PI 8.372 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.373 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.373 * [taylor]: Taking taylor expansion of (log n) in k 8.373 * [taylor]: Taking taylor expansion of n in k 8.373 * [backup-simplify]: Simplify n into n 8.373 * [backup-simplify]: Simplify (log n) into (log n) 8.373 * [backup-simplify]: Simplify (- 0) into 0 8.374 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.375 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.376 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.378 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.380 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.381 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.383 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.384 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.386 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.386 * [backup-simplify]: Simplify (- 0) into 0 8.387 * [backup-simplify]: Simplify (+ 0 0) into 0 8.387 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 8.389 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.390 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.392 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.392 * [taylor]: Taking taylor expansion of 0 in k 8.392 * [backup-simplify]: Simplify 0 into 0 8.392 * [backup-simplify]: Simplify 0 into 0 8.393 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.395 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.396 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.397 * [backup-simplify]: Simplify (+ 0 0) into 0 8.397 * [backup-simplify]: Simplify (- 1) into -1 8.398 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.399 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.402 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 8.405 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.408 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.410 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.411 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.415 * [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 8.415 * [backup-simplify]: Simplify (- 0) into 0 8.416 * [backup-simplify]: Simplify (+ 0 0) into 0 8.417 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.418 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.420 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.423 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.423 * [taylor]: Taking taylor expansion of 0 in k 8.423 * [backup-simplify]: Simplify 0 into 0 8.423 * [backup-simplify]: Simplify 0 into 0 8.423 * [backup-simplify]: Simplify 0 into 0 8.424 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.435 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.437 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.438 * [backup-simplify]: Simplify (+ 0 0) into 0 8.438 * [backup-simplify]: Simplify (- 0) into 0 8.439 * [backup-simplify]: Simplify (+ 0 0) into 0 8.441 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.443 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.448 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.454 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.465 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 8.466 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 8.466 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 8.466 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 8.466 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.466 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.466 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 8.466 * [taylor]: Taking taylor expansion of 0.25 in k 8.466 * [backup-simplify]: Simplify 0.25 into 0.25 8.466 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.466 * [taylor]: Taking taylor expansion of 1.0 in k 8.466 * [backup-simplify]: Simplify 1.0 into 1.0 8.466 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.466 * [taylor]: Taking taylor expansion of k in k 8.466 * [backup-simplify]: Simplify 0 into 0 8.466 * [backup-simplify]: Simplify 1 into 1 8.467 * [backup-simplify]: Simplify (/ 1 1) into 1 8.467 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.467 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.467 * [taylor]: Taking taylor expansion of 2.0 in k 8.467 * [backup-simplify]: Simplify 2.0 into 2.0 8.467 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.467 * [taylor]: Taking taylor expansion of PI in k 8.467 * [backup-simplify]: Simplify PI into PI 8.467 * [taylor]: Taking taylor expansion of n in k 8.467 * [backup-simplify]: Simplify n into n 8.467 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.467 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.467 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.468 * [backup-simplify]: Simplify (- 1) into -1 8.468 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.469 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 8.469 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 8.469 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 8.469 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.469 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.469 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.469 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.469 * [taylor]: Taking taylor expansion of 0.25 in n 8.469 * [backup-simplify]: Simplify 0.25 into 0.25 8.469 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.469 * [taylor]: Taking taylor expansion of 1.0 in n 8.469 * [backup-simplify]: Simplify 1.0 into 1.0 8.469 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.469 * [taylor]: Taking taylor expansion of k in n 8.469 * [backup-simplify]: Simplify k into k 8.469 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.469 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.469 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.469 * [taylor]: Taking taylor expansion of 2.0 in n 8.469 * [backup-simplify]: Simplify 2.0 into 2.0 8.469 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.469 * [taylor]: Taking taylor expansion of PI in n 8.469 * [backup-simplify]: Simplify PI into PI 8.469 * [taylor]: Taking taylor expansion of n in n 8.469 * [backup-simplify]: Simplify 0 into 0 8.469 * [backup-simplify]: Simplify 1 into 1 8.470 * [backup-simplify]: Simplify (/ PI 1) into PI 8.470 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.471 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.471 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.471 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.471 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.472 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.473 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.473 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.473 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.473 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.473 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.473 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.473 * [taylor]: Taking taylor expansion of 0.25 in n 8.473 * [backup-simplify]: Simplify 0.25 into 0.25 8.474 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.474 * [taylor]: Taking taylor expansion of 1.0 in n 8.474 * [backup-simplify]: Simplify 1.0 into 1.0 8.474 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.474 * [taylor]: Taking taylor expansion of k in n 8.474 * [backup-simplify]: Simplify k into k 8.474 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.474 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.474 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.474 * [taylor]: Taking taylor expansion of 2.0 in n 8.474 * [backup-simplify]: Simplify 2.0 into 2.0 8.474 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.474 * [taylor]: Taking taylor expansion of PI in n 8.474 * [backup-simplify]: Simplify PI into PI 8.474 * [taylor]: Taking taylor expansion of n in n 8.474 * [backup-simplify]: Simplify 0 into 0 8.474 * [backup-simplify]: Simplify 1 into 1 8.474 * [backup-simplify]: Simplify (/ PI 1) into PI 8.474 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.475 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.475 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.475 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.475 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.476 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.477 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.478 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.478 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.478 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.478 * [taylor]: Taking taylor expansion of 0.25 in k 8.478 * [backup-simplify]: Simplify 0.25 into 0.25 8.478 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.478 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.478 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.478 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.478 * [taylor]: Taking taylor expansion of 2.0 in k 8.478 * [backup-simplify]: Simplify 2.0 into 2.0 8.478 * [taylor]: Taking taylor expansion of PI in k 8.478 * [backup-simplify]: Simplify PI into PI 8.478 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.479 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.479 * [taylor]: Taking taylor expansion of (log n) in k 8.479 * [taylor]: Taking taylor expansion of n in k 8.479 * [backup-simplify]: Simplify n into n 8.479 * [backup-simplify]: Simplify (log n) into (log n) 8.479 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.479 * [taylor]: Taking taylor expansion of 1.0 in k 8.479 * [backup-simplify]: Simplify 1.0 into 1.0 8.479 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.479 * [taylor]: Taking taylor expansion of k in k 8.479 * [backup-simplify]: Simplify 0 into 0 8.479 * [backup-simplify]: Simplify 1 into 1 8.479 * [backup-simplify]: Simplify (/ 1 1) into 1 8.480 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.480 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.480 * [backup-simplify]: Simplify (- 1) into -1 8.481 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.481 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.482 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 8.483 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.484 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.484 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.485 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.486 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.486 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.486 * [backup-simplify]: Simplify (- 0) into 0 8.486 * [backup-simplify]: Simplify (+ 0 0) into 0 8.487 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.488 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.488 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.490 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.490 * [taylor]: Taking taylor expansion of 0 in k 8.490 * [backup-simplify]: Simplify 0 into 0 8.490 * [backup-simplify]: Simplify 0 into 0 8.490 * [backup-simplify]: Simplify 0 into 0 8.490 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.491 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.493 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.493 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.493 * [backup-simplify]: Simplify (- 0) into 0 8.494 * [backup-simplify]: Simplify (+ 0 0) into 0 8.494 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.495 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.496 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.498 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.498 * [taylor]: Taking taylor expansion of 0 in k 8.498 * [backup-simplify]: Simplify 0 into 0 8.498 * [backup-simplify]: Simplify 0 into 0 8.498 * [backup-simplify]: Simplify 0 into 0 8.498 * [backup-simplify]: Simplify 0 into 0 8.499 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.501 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.508 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.508 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.508 * [backup-simplify]: Simplify (- 0) into 0 8.509 * [backup-simplify]: Simplify (+ 0 0) into 0 8.510 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.511 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.513 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.516 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.516 * [taylor]: Taking taylor expansion of 0 in k 8.516 * [backup-simplify]: Simplify 0 into 0 8.516 * [backup-simplify]: Simplify 0 into 0 8.517 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 8.518 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 8.518 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 8.518 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 8.518 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.518 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.518 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 8.518 * [taylor]: Taking taylor expansion of 0.25 in k 8.518 * [backup-simplify]: Simplify 0.25 into 0.25 8.518 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.518 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.518 * [taylor]: Taking taylor expansion of k in k 8.518 * [backup-simplify]: Simplify 0 into 0 8.518 * [backup-simplify]: Simplify 1 into 1 8.519 * [backup-simplify]: Simplify (/ 1 1) into 1 8.519 * [taylor]: Taking taylor expansion of 1.0 in k 8.519 * [backup-simplify]: Simplify 1.0 into 1.0 8.519 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.519 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.519 * [taylor]: Taking taylor expansion of -2.0 in k 8.519 * [backup-simplify]: Simplify -2.0 into -2.0 8.519 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.519 * [taylor]: Taking taylor expansion of PI in k 8.519 * [backup-simplify]: Simplify PI into PI 8.519 * [taylor]: Taking taylor expansion of n in k 8.519 * [backup-simplify]: Simplify n into n 8.519 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.519 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.519 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.520 * [backup-simplify]: Simplify (+ 1 0) into 1 8.520 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 8.520 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 8.521 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 8.521 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.521 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.521 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.521 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.521 * [taylor]: Taking taylor expansion of 0.25 in n 8.521 * [backup-simplify]: Simplify 0.25 into 0.25 8.521 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.521 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.521 * [taylor]: Taking taylor expansion of k in n 8.521 * [backup-simplify]: Simplify k into k 8.521 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.521 * [taylor]: Taking taylor expansion of 1.0 in n 8.521 * [backup-simplify]: Simplify 1.0 into 1.0 8.521 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.521 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.521 * [taylor]: Taking taylor expansion of -2.0 in n 8.521 * [backup-simplify]: Simplify -2.0 into -2.0 8.521 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.521 * [taylor]: Taking taylor expansion of PI in n 8.521 * [backup-simplify]: Simplify PI into PI 8.521 * [taylor]: Taking taylor expansion of n in n 8.521 * [backup-simplify]: Simplify 0 into 0 8.521 * [backup-simplify]: Simplify 1 into 1 8.522 * [backup-simplify]: Simplify (/ PI 1) into PI 8.522 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.523 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.523 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.524 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.525 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.526 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.527 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.527 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.527 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.527 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.527 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.527 * [taylor]: Taking taylor expansion of 0.25 in n 8.527 * [backup-simplify]: Simplify 0.25 into 0.25 8.528 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.528 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.528 * [taylor]: Taking taylor expansion of k in n 8.528 * [backup-simplify]: Simplify k into k 8.528 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.528 * [taylor]: Taking taylor expansion of 1.0 in n 8.528 * [backup-simplify]: Simplify 1.0 into 1.0 8.528 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.528 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.528 * [taylor]: Taking taylor expansion of -2.0 in n 8.528 * [backup-simplify]: Simplify -2.0 into -2.0 8.528 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.528 * [taylor]: Taking taylor expansion of PI in n 8.528 * [backup-simplify]: Simplify PI into PI 8.528 * [taylor]: Taking taylor expansion of n in n 8.528 * [backup-simplify]: Simplify 0 into 0 8.528 * [backup-simplify]: Simplify 1 into 1 8.529 * [backup-simplify]: Simplify (/ PI 1) into PI 8.529 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.530 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.530 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.531 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.532 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.533 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.534 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.534 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.534 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.534 * [taylor]: Taking taylor expansion of 0.25 in k 8.534 * [backup-simplify]: Simplify 0.25 into 0.25 8.534 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.535 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.535 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.535 * [taylor]: Taking taylor expansion of k in k 8.535 * [backup-simplify]: Simplify 0 into 0 8.535 * [backup-simplify]: Simplify 1 into 1 8.535 * [backup-simplify]: Simplify (/ 1 1) into 1 8.535 * [taylor]: Taking taylor expansion of 1.0 in k 8.535 * [backup-simplify]: Simplify 1.0 into 1.0 8.535 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.535 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.535 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.535 * [taylor]: Taking taylor expansion of -2.0 in k 8.535 * [backup-simplify]: Simplify -2.0 into -2.0 8.535 * [taylor]: Taking taylor expansion of PI in k 8.535 * [backup-simplify]: Simplify PI into PI 8.536 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.537 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.537 * [taylor]: Taking taylor expansion of (log n) in k 8.537 * [taylor]: Taking taylor expansion of n in k 8.537 * [backup-simplify]: Simplify n into n 8.537 * [backup-simplify]: Simplify (log n) into (log n) 8.537 * [backup-simplify]: Simplify (+ 1 0) into 1 8.537 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.538 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.539 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.539 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 8.540 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.541 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.541 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.542 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.543 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.543 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.543 * [backup-simplify]: Simplify (+ 0 0) into 0 8.544 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.545 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.545 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.547 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.547 * [taylor]: Taking taylor expansion of 0 in k 8.547 * [backup-simplify]: Simplify 0 into 0 8.547 * [backup-simplify]: Simplify 0 into 0 8.547 * [backup-simplify]: Simplify 0 into 0 8.547 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.548 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.550 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.550 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.550 * [backup-simplify]: Simplify (+ 0 0) into 0 8.551 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.552 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.553 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.554 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.554 * [taylor]: Taking taylor expansion of 0 in k 8.554 * [backup-simplify]: Simplify 0 into 0 8.554 * [backup-simplify]: Simplify 0 into 0 8.554 * [backup-simplify]: Simplify 0 into 0 8.554 * [backup-simplify]: Simplify 0 into 0 8.560 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.561 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.564 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 8.564 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.565 * [backup-simplify]: Simplify (+ 0 0) into 0 8.566 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.566 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.568 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.570 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.570 * [taylor]: Taking taylor expansion of 0 in k 8.570 * [backup-simplify]: Simplify 0 into 0 8.570 * [backup-simplify]: Simplify 0 into 0 8.571 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 8.571 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 8.572 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 8.572 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 8.572 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.572 * [taylor]: Taking taylor expansion of 1.0 in k 8.572 * [backup-simplify]: Simplify 1.0 into 1.0 8.572 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.572 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.572 * [taylor]: Taking taylor expansion of k in k 8.572 * [backup-simplify]: Simplify 0 into 0 8.572 * [backup-simplify]: Simplify 1 into 1 8.572 * [backup-simplify]: Simplify (/ 1 1) into 1 8.572 * [backup-simplify]: Simplify (sqrt 0) into 0 8.574 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.574 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.574 * [taylor]: Taking taylor expansion of 1.0 in k 8.574 * [backup-simplify]: Simplify 1.0 into 1.0 8.574 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.574 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.574 * [taylor]: Taking taylor expansion of k in k 8.574 * [backup-simplify]: Simplify 0 into 0 8.574 * [backup-simplify]: Simplify 1 into 1 8.574 * [backup-simplify]: Simplify (/ 1 1) into 1 8.575 * [backup-simplify]: Simplify (sqrt 0) into 0 8.576 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.577 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.577 * [backup-simplify]: Simplify 0 into 0 8.578 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.579 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.579 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.582 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.584 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.585 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.586 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.589 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.591 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.592 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.593 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 8.593 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 8.593 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 8.593 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.593 * [taylor]: Taking taylor expansion of 1.0 in k 8.594 * [backup-simplify]: Simplify 1.0 into 1.0 8.594 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.594 * [taylor]: Taking taylor expansion of k in k 8.594 * [backup-simplify]: Simplify 0 into 0 8.594 * [backup-simplify]: Simplify 1 into 1 8.594 * [backup-simplify]: Simplify (sqrt 0) into 0 8.595 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.595 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.595 * [taylor]: Taking taylor expansion of 1.0 in k 8.595 * [backup-simplify]: Simplify 1.0 into 1.0 8.595 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.595 * [taylor]: Taking taylor expansion of k in k 8.596 * [backup-simplify]: Simplify 0 into 0 8.596 * [backup-simplify]: Simplify 1 into 1 8.596 * [backup-simplify]: Simplify (sqrt 0) into 0 8.597 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.598 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.598 * [backup-simplify]: Simplify 0 into 0 8.599 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.600 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.603 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.605 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.605 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.609 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.611 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.612 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.613 * [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)))))))) 8.613 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 8.613 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 8.613 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.613 * [taylor]: Taking taylor expansion of 1.0 in k 8.613 * [backup-simplify]: Simplify 1.0 into 1.0 8.614 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.614 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.614 * [taylor]: Taking taylor expansion of -1 in k 8.614 * [backup-simplify]: Simplify -1 into -1 8.614 * [taylor]: Taking taylor expansion of k in k 8.614 * [backup-simplify]: Simplify 0 into 0 8.614 * [backup-simplify]: Simplify 1 into 1 8.614 * [backup-simplify]: Simplify (/ -1 1) into -1 8.615 * [backup-simplify]: Simplify (sqrt 0) into 0 8.616 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.616 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.616 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.616 * [taylor]: Taking taylor expansion of 1.0 in k 8.616 * [backup-simplify]: Simplify 1.0 into 1.0 8.616 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.616 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.616 * [taylor]: Taking taylor expansion of -1 in k 8.617 * [backup-simplify]: Simplify -1 into -1 8.617 * [taylor]: Taking taylor expansion of k in k 8.617 * [backup-simplify]: Simplify 0 into 0 8.617 * [backup-simplify]: Simplify 1 into 1 8.617 * [backup-simplify]: Simplify (/ -1 1) into -1 8.617 * [backup-simplify]: Simplify (sqrt 0) into 0 8.619 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.619 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.619 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.620 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.624 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.626 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 8.626 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.626 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.629 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.631 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 8.632 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.632 * [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))))) 8.633 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 8.633 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.633 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 8.633 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.633 * [taylor]: Taking taylor expansion of 2.0 in n 8.633 * [backup-simplify]: Simplify 2.0 into 2.0 8.633 * [taylor]: Taking taylor expansion of (* n PI) in n 8.633 * [taylor]: Taking taylor expansion of n in n 8.633 * [backup-simplify]: Simplify 0 into 0 8.633 * [backup-simplify]: Simplify 1 into 1 8.633 * [taylor]: Taking taylor expansion of PI in n 8.633 * [backup-simplify]: Simplify PI into PI 8.633 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.633 * [taylor]: Taking taylor expansion of 2.0 in n 8.633 * [backup-simplify]: Simplify 2.0 into 2.0 8.633 * [taylor]: Taking taylor expansion of (* n PI) in n 8.633 * [taylor]: Taking taylor expansion of n in n 8.633 * [backup-simplify]: Simplify 0 into 0 8.633 * [backup-simplify]: Simplify 1 into 1 8.633 * [taylor]: Taking taylor expansion of PI in n 8.633 * [backup-simplify]: Simplify PI into PI 8.634 * [backup-simplify]: Simplify (* 0 PI) into 0 8.634 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.634 * [backup-simplify]: Simplify 0 into 0 8.635 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.636 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.636 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.637 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.637 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.637 * [backup-simplify]: Simplify 0 into 0 8.638 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.639 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.639 * [backup-simplify]: Simplify 0 into 0 8.639 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.640 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 8.640 * [backup-simplify]: Simplify 0 into 0 8.641 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.642 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 8.642 * [backup-simplify]: Simplify 0 into 0 8.643 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.644 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 8.644 * [backup-simplify]: Simplify 0 into 0 8.645 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 8.646 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 8.646 * [backup-simplify]: Simplify 0 into 0 8.647 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.647 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 8.647 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 8.647 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.647 * [taylor]: Taking taylor expansion of 2.0 in n 8.647 * [backup-simplify]: Simplify 2.0 into 2.0 8.647 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.647 * [taylor]: Taking taylor expansion of PI in n 8.647 * [backup-simplify]: Simplify PI into PI 8.647 * [taylor]: Taking taylor expansion of n in n 8.647 * [backup-simplify]: Simplify 0 into 0 8.647 * [backup-simplify]: Simplify 1 into 1 8.647 * [backup-simplify]: Simplify (/ PI 1) into PI 8.647 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.647 * [taylor]: Taking taylor expansion of 2.0 in n 8.647 * [backup-simplify]: Simplify 2.0 into 2.0 8.648 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.648 * [taylor]: Taking taylor expansion of PI in n 8.648 * [backup-simplify]: Simplify PI into PI 8.648 * [taylor]: Taking taylor expansion of n in n 8.648 * [backup-simplify]: Simplify 0 into 0 8.648 * [backup-simplify]: Simplify 1 into 1 8.648 * [backup-simplify]: Simplify (/ PI 1) into PI 8.648 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.649 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.649 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.650 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.650 * [backup-simplify]: Simplify 0 into 0 8.650 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.651 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.651 * [backup-simplify]: Simplify 0 into 0 8.651 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.652 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.652 * [backup-simplify]: Simplify 0 into 0 8.653 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.654 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.654 * [backup-simplify]: Simplify 0 into 0 8.654 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.655 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.655 * [backup-simplify]: Simplify 0 into 0 8.656 * [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 8.657 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.657 * [backup-simplify]: Simplify 0 into 0 8.657 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 8.657 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 8.657 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 8.657 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.657 * [taylor]: Taking taylor expansion of -2.0 in n 8.657 * [backup-simplify]: Simplify -2.0 into -2.0 8.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.658 * [taylor]: Taking taylor expansion of PI in n 8.658 * [backup-simplify]: Simplify PI into PI 8.658 * [taylor]: Taking taylor expansion of n in n 8.658 * [backup-simplify]: Simplify 0 into 0 8.658 * [backup-simplify]: Simplify 1 into 1 8.658 * [backup-simplify]: Simplify (/ PI 1) into PI 8.658 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.658 * [taylor]: Taking taylor expansion of -2.0 in n 8.658 * [backup-simplify]: Simplify -2.0 into -2.0 8.658 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.658 * [taylor]: Taking taylor expansion of PI in n 8.658 * [backup-simplify]: Simplify PI into PI 8.658 * [taylor]: Taking taylor expansion of n in n 8.658 * [backup-simplify]: Simplify 0 into 0 8.658 * [backup-simplify]: Simplify 1 into 1 8.658 * [backup-simplify]: Simplify (/ PI 1) into PI 8.659 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.659 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.660 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.660 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.660 * [backup-simplify]: Simplify 0 into 0 8.661 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.661 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.661 * [backup-simplify]: Simplify 0 into 0 8.662 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.663 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.663 * [backup-simplify]: Simplify 0 into 0 8.663 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.664 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.664 * [backup-simplify]: Simplify 0 into 0 8.665 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.665 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.665 * [backup-simplify]: Simplify 0 into 0 8.666 * [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 8.667 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.667 * [backup-simplify]: Simplify 0 into 0 8.667 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 8.668 * * * [progress]: simplifying candidates 8.677 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* 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(* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 8.682 * * [simplify]: Extracting # 0 : cost 0 8.682 * * [simplify]: Extracting # 1 : cost 0 8.683 * * [simplify]: Extracting # 2 : cost 0 8.683 * * [simplify]: Extracting # 3 : cost 0 8.683 * * [simplify]: Extracting # 4 : cost 0 8.684 * * [simplify]: Extracting # 5 : cost 0 8.684 * * [simplify]: Extracting # 6 : cost 0 8.685 * * [simplify]: Extracting # 7 : cost 0 8.685 * * [simplify]: Extracting # 8 : cost 0 8.686 * * [simplify]: Extracting # 9 : cost 0 8.686 * * [simplify]: Extracting # 10 : cost 0 8.687 * * [simplify]: Extracting # 11 : cost 0 8.687 * * [simplify]: Extracting # 12 : cost 0 8.688 * * [simplify]: Extracting # 13 : cost 0 8.688 * * [simplify]: Extracting # 14 : cost 0 8.689 * * [simplify]: iteration 0 : 332 enodes (cost 3588 ) 8.835 * * [simplify]: Extracting # 0 : cost 0 8.836 * * [simplify]: Extracting # 1 : cost 0 8.838 * * [simplify]: Extracting # 2 : cost 0 8.839 * * [simplify]: Extracting # 3 : cost 0 8.840 * * [simplify]: Extracting # 4 : cost 0 8.841 * * [simplify]: Extracting # 5 : cost 0 8.842 * * [simplify]: Extracting # 6 : cost 0 8.843 * * [simplify]: Extracting # 7 : cost 0 8.844 * * [simplify]: iteration 1 : 854 enodes (cost 3308 ) 9.389 * * [simplify]: Extracting # 0 : cost 0 9.393 * * [simplify]: Extracting # 1 : cost 0 9.398 * * [simplify]: Extracting # 2 : cost 0 9.404 * * [simplify]: Extracting # 3 : cost 0 9.410 * * [simplify]: Extracting # 4 : cost 0 9.416 * * [simplify]: iteration 2 : 2490 enodes (cost 3202 ) 10.369 * * [simplify]: Extracting # 0 : cost 0 10.375 * * [simplify]: Extracting # 1 : cost 0 10.387 * * [simplify]: Extracting # 2 : cost 0 10.400 * * [simplify]: Extracting # 3 : cost 0 10.413 * * [simplify]: Extracting # 4 : cost 0 10.432 * * [simplify]: iteration done: 5002 enodes (cost 3197 ) 10.435 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* PI n) 2.0) (- 1.0 k)) (* (* PI n) 2.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* PI n) 2.0) (- 1.0 k)) (* (* PI n) 2.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* k (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* PI n) 2.0) (* (* PI n) 2.0) (log (* (* PI n) 2.0)) (log (* (* PI n) 2.0)) (log (* (* PI n) 2.0)) (exp (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (pow (* 2.0 (* PI n)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (fma (- 0.25) (* k (fma (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 PI)) (* (pow (* 2.0 (* PI n)) 0.25) (log n)))) (fma (* 0.03125 (pow k 2)) (* (pow (* 2.0 (* PI n)) 0.25) (pow (log (* 2.0 PI)) 2)) (fma (* 0.03125 (pow k 2)) (* (pow (log n) 2) (pow (* 2.0 (* PI n)) 0.25)) (fma (* 0.0625 (* (pow k 2) (log (* 2.0 PI)))) (* (pow (* 2.0 (* PI n)) 0.25) (log n)) (pow (* 2.0 (* PI n)) 0.25))))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- 0.25) (* k (fma (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 PI)) (* (pow (* 2.0 (* PI n)) 0.25) (log n)))) (fma (* 0.03125 (pow k 2)) (* (pow (* 2.0 (* PI n)) 0.25) (pow (log (* 2.0 PI)) 2)) (fma (* 0.03125 (pow k 2)) (* (pow (log n) 2) (pow (* 2.0 (* PI n)) 0.25)) (fma (* 0.0625 (* (pow k 2) (log (* 2.0 PI)))) (* (pow (* 2.0 (* PI n)) 0.25) (log n)) (pow (* 2.0 (* PI n)) 0.25))))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- k) +nan.0 (fma +nan.0 (pow k 2) (- +nan.0))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (- (+ (- (/ +nan.0 (pow k 2)) (/ +nan.0 k)) +nan.0)) (* (* PI n) 2.0) (* (* PI n) 2.0) (* (* PI n) 2.0) 10.438 * * * [progress]: adding candidates to table 11.821 * * [progress]: iteration 3 / 4 11.821 * * * [progress]: picking best candidate 11.853 * * * * [pick]: Picked # 11.853 * * * [progress]: localizing error 11.913 * * * [progress]: generating rewritten candidates 11.913 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 11.954 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 11.988 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 12.001 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 2) 12.031 * * * [progress]: generating series expansions 12.031 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 12.032 * [backup-simplify]: Simplify (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 12.032 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 12.032 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 12.032 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.032 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.032 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.032 * [taylor]: Taking taylor expansion of 0.5 in k 12.032 * [backup-simplify]: Simplify 0.5 into 0.5 12.032 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.032 * [taylor]: Taking taylor expansion of 1.0 in k 12.032 * [backup-simplify]: Simplify 1.0 into 1.0 12.032 * [taylor]: Taking taylor expansion of k in k 12.032 * [backup-simplify]: Simplify 0 into 0 12.032 * [backup-simplify]: Simplify 1 into 1 12.032 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.032 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.032 * [taylor]: Taking taylor expansion of 2.0 in k 12.032 * [backup-simplify]: Simplify 2.0 into 2.0 12.032 * [taylor]: Taking taylor expansion of (* n PI) in k 12.032 * [taylor]: Taking taylor expansion of n in k 12.032 * [backup-simplify]: Simplify n into n 12.032 * [taylor]: Taking taylor expansion of PI in k 12.032 * [backup-simplify]: Simplify PI into PI 12.032 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.032 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.032 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.033 * [backup-simplify]: Simplify (- 0) into 0 12.033 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.033 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.033 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 12.034 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 12.034 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.034 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.034 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.034 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.034 * [taylor]: Taking taylor expansion of 0.5 in n 12.034 * [backup-simplify]: Simplify 0.5 into 0.5 12.034 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.034 * [taylor]: Taking taylor expansion of 1.0 in n 12.034 * [backup-simplify]: Simplify 1.0 into 1.0 12.034 * [taylor]: Taking taylor expansion of k in n 12.034 * [backup-simplify]: Simplify k into k 12.034 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.034 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.034 * [taylor]: Taking taylor expansion of 2.0 in n 12.034 * [backup-simplify]: Simplify 2.0 into 2.0 12.034 * [taylor]: Taking taylor expansion of (* n PI) in n 12.034 * [taylor]: Taking taylor expansion of n in n 12.034 * [backup-simplify]: Simplify 0 into 0 12.034 * [backup-simplify]: Simplify 1 into 1 12.034 * [taylor]: Taking taylor expansion of PI in n 12.034 * [backup-simplify]: Simplify PI into PI 12.034 * [backup-simplify]: Simplify (* 0 PI) into 0 12.035 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.036 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.037 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.037 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.038 * [backup-simplify]: Simplify (- k) into (- k) 12.038 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.038 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.039 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.039 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.040 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.040 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.040 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.040 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.040 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.040 * [taylor]: Taking taylor expansion of 0.5 in n 12.040 * [backup-simplify]: Simplify 0.5 into 0.5 12.040 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.041 * [taylor]: Taking taylor expansion of 1.0 in n 12.041 * [backup-simplify]: Simplify 1.0 into 1.0 12.041 * [taylor]: Taking taylor expansion of k in n 12.041 * [backup-simplify]: Simplify k into k 12.041 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.041 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.041 * [taylor]: Taking taylor expansion of 2.0 in n 12.041 * [backup-simplify]: Simplify 2.0 into 2.0 12.041 * [taylor]: Taking taylor expansion of (* n PI) in n 12.041 * [taylor]: Taking taylor expansion of n in n 12.041 * [backup-simplify]: Simplify 0 into 0 12.041 * [backup-simplify]: Simplify 1 into 1 12.041 * [taylor]: Taking taylor expansion of PI in n 12.041 * [backup-simplify]: Simplify PI into PI 12.041 * [backup-simplify]: Simplify (* 0 PI) into 0 12.041 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.042 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.043 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.044 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.044 * [backup-simplify]: Simplify (- k) into (- k) 12.044 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.044 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.045 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.046 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.047 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.047 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.047 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.047 * [taylor]: Taking taylor expansion of 0.5 in k 12.047 * [backup-simplify]: Simplify 0.5 into 0.5 12.047 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.047 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.047 * [taylor]: Taking taylor expansion of 1.0 in k 12.047 * [backup-simplify]: Simplify 1.0 into 1.0 12.047 * [taylor]: Taking taylor expansion of k in k 12.047 * [backup-simplify]: Simplify 0 into 0 12.047 * [backup-simplify]: Simplify 1 into 1 12.047 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.047 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.047 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.047 * [taylor]: Taking taylor expansion of 2.0 in k 12.047 * [backup-simplify]: Simplify 2.0 into 2.0 12.047 * [taylor]: Taking taylor expansion of PI in k 12.047 * [backup-simplify]: Simplify PI into PI 12.047 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.048 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.048 * [taylor]: Taking taylor expansion of (log n) in k 12.048 * [taylor]: Taking taylor expansion of n in k 12.048 * [backup-simplify]: Simplify n into n 12.048 * [backup-simplify]: Simplify (log n) into (log n) 12.053 * [backup-simplify]: Simplify (- 0) into 0 12.054 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.055 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.055 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.056 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 12.057 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.058 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.059 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.060 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.061 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.061 * [backup-simplify]: Simplify (- 0) into 0 12.061 * [backup-simplify]: Simplify (+ 0 0) into 0 12.062 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 12.063 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.063 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.065 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.065 * [taylor]: Taking taylor expansion of 0 in k 12.065 * [backup-simplify]: Simplify 0 into 0 12.065 * [backup-simplify]: Simplify 0 into 0 12.065 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.066 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.067 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.067 * [backup-simplify]: Simplify (+ 0 0) into 0 12.067 * [backup-simplify]: Simplify (- 1) into -1 12.068 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.069 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.070 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 12.072 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.075 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.076 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.077 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.081 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.081 * [backup-simplify]: Simplify (- 0) into 0 12.082 * [backup-simplify]: Simplify (+ 0 0) into 0 12.082 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.084 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.085 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.088 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.088 * [taylor]: Taking taylor expansion of 0 in k 12.088 * [backup-simplify]: Simplify 0 into 0 12.088 * [backup-simplify]: Simplify 0 into 0 12.088 * [backup-simplify]: Simplify 0 into 0 12.089 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.093 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.094 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.095 * [backup-simplify]: Simplify (+ 0 0) into 0 12.095 * [backup-simplify]: Simplify (- 0) into 0 12.096 * [backup-simplify]: Simplify (+ 0 0) into 0 12.098 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.100 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.105 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.110 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.119 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 12.119 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 n) PI)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 12.119 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 12.119 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 12.119 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.119 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.119 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.119 * [taylor]: Taking taylor expansion of 0.5 in k 12.119 * [backup-simplify]: Simplify 0.5 into 0.5 12.119 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.119 * [taylor]: Taking taylor expansion of 1.0 in k 12.120 * [backup-simplify]: Simplify 1.0 into 1.0 12.120 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.120 * [taylor]: Taking taylor expansion of k in k 12.120 * [backup-simplify]: Simplify 0 into 0 12.120 * [backup-simplify]: Simplify 1 into 1 12.120 * [backup-simplify]: Simplify (/ 1 1) into 1 12.120 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.120 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.120 * [taylor]: Taking taylor expansion of 2.0 in k 12.120 * [backup-simplify]: Simplify 2.0 into 2.0 12.120 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.120 * [taylor]: Taking taylor expansion of PI in k 12.120 * [backup-simplify]: Simplify PI into PI 12.120 * [taylor]: Taking taylor expansion of n in k 12.120 * [backup-simplify]: Simplify n into n 12.120 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.120 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.120 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.120 * [backup-simplify]: Simplify (- 1) into -1 12.121 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.121 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.121 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 12.121 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 12.121 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.121 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.121 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.121 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.121 * [taylor]: Taking taylor expansion of 0.5 in n 12.121 * [backup-simplify]: Simplify 0.5 into 0.5 12.121 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.121 * [taylor]: Taking taylor expansion of 1.0 in n 12.121 * [backup-simplify]: Simplify 1.0 into 1.0 12.121 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.121 * [taylor]: Taking taylor expansion of k in n 12.121 * [backup-simplify]: Simplify k into k 12.121 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.122 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.122 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.122 * [taylor]: Taking taylor expansion of 2.0 in n 12.122 * [backup-simplify]: Simplify 2.0 into 2.0 12.122 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.122 * [taylor]: Taking taylor expansion of PI in n 12.122 * [backup-simplify]: Simplify PI into PI 12.122 * [taylor]: Taking taylor expansion of n in n 12.122 * [backup-simplify]: Simplify 0 into 0 12.122 * [backup-simplify]: Simplify 1 into 1 12.122 * [backup-simplify]: Simplify (/ PI 1) into PI 12.122 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.123 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.123 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.123 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.123 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.124 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.125 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.126 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.126 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.126 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.126 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.126 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.126 * [taylor]: Taking taylor expansion of 0.5 in n 12.126 * [backup-simplify]: Simplify 0.5 into 0.5 12.126 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.126 * [taylor]: Taking taylor expansion of 1.0 in n 12.126 * [backup-simplify]: Simplify 1.0 into 1.0 12.126 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.126 * [taylor]: Taking taylor expansion of k in n 12.126 * [backup-simplify]: Simplify k into k 12.126 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.126 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.126 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.126 * [taylor]: Taking taylor expansion of 2.0 in n 12.126 * [backup-simplify]: Simplify 2.0 into 2.0 12.126 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.126 * [taylor]: Taking taylor expansion of PI in n 12.126 * [backup-simplify]: Simplify PI into PI 12.126 * [taylor]: Taking taylor expansion of n in n 12.126 * [backup-simplify]: Simplify 0 into 0 12.126 * [backup-simplify]: Simplify 1 into 1 12.127 * [backup-simplify]: Simplify (/ PI 1) into PI 12.127 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.128 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.128 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.128 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.128 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.129 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.130 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.130 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.130 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.130 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.130 * [taylor]: Taking taylor expansion of 0.5 in k 12.130 * [backup-simplify]: Simplify 0.5 into 0.5 12.130 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.131 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.131 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.131 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.131 * [taylor]: Taking taylor expansion of 2.0 in k 12.131 * [backup-simplify]: Simplify 2.0 into 2.0 12.131 * [taylor]: Taking taylor expansion of PI in k 12.131 * [backup-simplify]: Simplify PI into PI 12.131 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.132 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.132 * [taylor]: Taking taylor expansion of (log n) in k 12.132 * [taylor]: Taking taylor expansion of n in k 12.132 * [backup-simplify]: Simplify n into n 12.132 * [backup-simplify]: Simplify (log n) into (log n) 12.132 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.132 * [taylor]: Taking taylor expansion of 1.0 in k 12.132 * [backup-simplify]: Simplify 1.0 into 1.0 12.132 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.132 * [taylor]: Taking taylor expansion of k in k 12.132 * [backup-simplify]: Simplify 0 into 0 12.132 * [backup-simplify]: Simplify 1 into 1 12.132 * [backup-simplify]: Simplify (/ 1 1) into 1 12.132 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.133 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.133 * [backup-simplify]: Simplify (- 1) into -1 12.134 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.134 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.135 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 12.136 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.137 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.137 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.138 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.139 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.139 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.139 * [backup-simplify]: Simplify (- 0) into 0 12.140 * [backup-simplify]: Simplify (+ 0 0) into 0 12.140 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.141 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.142 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.143 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.143 * [taylor]: Taking taylor expansion of 0 in k 12.143 * [backup-simplify]: Simplify 0 into 0 12.143 * [backup-simplify]: Simplify 0 into 0 12.143 * [backup-simplify]: Simplify 0 into 0 12.144 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.144 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.147 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.147 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.148 * [backup-simplify]: Simplify (- 0) into 0 12.148 * [backup-simplify]: Simplify (+ 0 0) into 0 12.149 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.151 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.152 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.154 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.155 * [taylor]: Taking taylor expansion of 0 in k 12.155 * [backup-simplify]: Simplify 0 into 0 12.155 * [backup-simplify]: Simplify 0 into 0 12.155 * [backup-simplify]: Simplify 0 into 0 12.155 * [backup-simplify]: Simplify 0 into 0 12.156 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.157 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.163 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 12.163 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.164 * [backup-simplify]: Simplify (- 0) into 0 12.164 * [backup-simplify]: Simplify (+ 0 0) into 0 12.166 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.167 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.169 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.172 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.172 * [taylor]: Taking taylor expansion of 0 in k 12.172 * [backup-simplify]: Simplify 0 into 0 12.172 * [backup-simplify]: Simplify 0 into 0 12.181 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 12.181 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 (- n)) PI)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 12.181 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 12.181 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 12.181 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.181 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.182 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.182 * [taylor]: Taking taylor expansion of 0.5 in k 12.182 * [backup-simplify]: Simplify 0.5 into 0.5 12.182 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.182 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.182 * [taylor]: Taking taylor expansion of k in k 12.182 * [backup-simplify]: Simplify 0 into 0 12.182 * [backup-simplify]: Simplify 1 into 1 12.183 * [backup-simplify]: Simplify (/ 1 1) into 1 12.183 * [taylor]: Taking taylor expansion of 1.0 in k 12.183 * [backup-simplify]: Simplify 1.0 into 1.0 12.183 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.183 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.183 * [taylor]: Taking taylor expansion of -2.0 in k 12.183 * [backup-simplify]: Simplify -2.0 into -2.0 12.183 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.183 * [taylor]: Taking taylor expansion of PI in k 12.183 * [backup-simplify]: Simplify PI into PI 12.183 * [taylor]: Taking taylor expansion of n in k 12.183 * [backup-simplify]: Simplify n into n 12.183 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.183 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.183 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.184 * [backup-simplify]: Simplify (+ 1 0) into 1 12.184 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.184 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 12.185 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 12.185 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.185 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.185 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.185 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.185 * [taylor]: Taking taylor expansion of 0.5 in n 12.185 * [backup-simplify]: Simplify 0.5 into 0.5 12.185 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.185 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.185 * [taylor]: Taking taylor expansion of k in n 12.185 * [backup-simplify]: Simplify k into k 12.185 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.185 * [taylor]: Taking taylor expansion of 1.0 in n 12.185 * [backup-simplify]: Simplify 1.0 into 1.0 12.185 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.186 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.186 * [taylor]: Taking taylor expansion of -2.0 in n 12.186 * [backup-simplify]: Simplify -2.0 into -2.0 12.186 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.186 * [taylor]: Taking taylor expansion of PI in n 12.186 * [backup-simplify]: Simplify PI into PI 12.186 * [taylor]: Taking taylor expansion of n in n 12.186 * [backup-simplify]: Simplify 0 into 0 12.186 * [backup-simplify]: Simplify 1 into 1 12.186 * [backup-simplify]: Simplify (/ PI 1) into PI 12.187 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.188 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.188 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.188 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.190 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.191 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.192 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.192 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.192 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.192 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.193 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.193 * [taylor]: Taking taylor expansion of 0.5 in n 12.193 * [backup-simplify]: Simplify 0.5 into 0.5 12.193 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.193 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.193 * [taylor]: Taking taylor expansion of k in n 12.193 * [backup-simplify]: Simplify k into k 12.193 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.193 * [taylor]: Taking taylor expansion of 1.0 in n 12.193 * [backup-simplify]: Simplify 1.0 into 1.0 12.193 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.193 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.193 * [taylor]: Taking taylor expansion of -2.0 in n 12.193 * [backup-simplify]: Simplify -2.0 into -2.0 12.193 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.193 * [taylor]: Taking taylor expansion of PI in n 12.193 * [backup-simplify]: Simplify PI into PI 12.193 * [taylor]: Taking taylor expansion of n in n 12.193 * [backup-simplify]: Simplify 0 into 0 12.193 * [backup-simplify]: Simplify 1 into 1 12.194 * [backup-simplify]: Simplify (/ PI 1) into PI 12.194 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.195 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.195 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.195 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.197 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.198 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.199 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.199 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.199 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.200 * [taylor]: Taking taylor expansion of 0.5 in k 12.200 * [backup-simplify]: Simplify 0.5 into 0.5 12.200 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.200 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.200 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.200 * [taylor]: Taking taylor expansion of k in k 12.200 * [backup-simplify]: Simplify 0 into 0 12.200 * [backup-simplify]: Simplify 1 into 1 12.200 * [backup-simplify]: Simplify (/ 1 1) into 1 12.200 * [taylor]: Taking taylor expansion of 1.0 in k 12.200 * [backup-simplify]: Simplify 1.0 into 1.0 12.200 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.200 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.200 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.200 * [taylor]: Taking taylor expansion of -2.0 in k 12.200 * [backup-simplify]: Simplify -2.0 into -2.0 12.200 * [taylor]: Taking taylor expansion of PI in k 12.200 * [backup-simplify]: Simplify PI into PI 12.201 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.202 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.202 * [taylor]: Taking taylor expansion of (log n) in k 12.202 * [taylor]: Taking taylor expansion of n in k 12.202 * [backup-simplify]: Simplify n into n 12.202 * [backup-simplify]: Simplify (log n) into (log n) 12.202 * [backup-simplify]: Simplify (+ 1 0) into 1 12.203 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.204 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.205 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.206 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 12.207 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.208 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.209 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.210 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.212 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.212 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.212 * [backup-simplify]: Simplify (+ 0 0) into 0 12.213 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.214 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.215 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.217 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.217 * [taylor]: Taking taylor expansion of 0 in k 12.217 * [backup-simplify]: Simplify 0 into 0 12.217 * [backup-simplify]: Simplify 0 into 0 12.217 * [backup-simplify]: Simplify 0 into 0 12.218 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.219 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.222 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 12.223 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.223 * [backup-simplify]: Simplify (+ 0 0) into 0 12.224 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.226 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.227 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.230 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.230 * [taylor]: Taking taylor expansion of 0 in k 12.230 * [backup-simplify]: Simplify 0 into 0 12.230 * [backup-simplify]: Simplify 0 into 0 12.230 * [backup-simplify]: Simplify 0 into 0 12.230 * [backup-simplify]: Simplify 0 into 0 12.231 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.232 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.239 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 12.239 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.239 * [backup-simplify]: Simplify (+ 0 0) into 0 12.241 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.242 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.244 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.247 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.248 * [taylor]: Taking taylor expansion of 0 in k 12.248 * [backup-simplify]: Simplify 0 into 0 12.248 * [backup-simplify]: Simplify 0 into 0 12.249 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 12.249 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 12.250 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 12.250 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 12.250 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 12.250 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.250 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.250 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 12.250 * [taylor]: Taking taylor expansion of 0.25 in k 12.250 * [backup-simplify]: Simplify 0.25 into 0.25 12.250 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.250 * [taylor]: Taking taylor expansion of 1.0 in k 12.250 * [backup-simplify]: Simplify 1.0 into 1.0 12.250 * [taylor]: Taking taylor expansion of k in k 12.250 * [backup-simplify]: Simplify 0 into 0 12.250 * [backup-simplify]: Simplify 1 into 1 12.250 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.251 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.251 * [taylor]: Taking taylor expansion of 2.0 in k 12.251 * [backup-simplify]: Simplify 2.0 into 2.0 12.251 * [taylor]: Taking taylor expansion of (* n PI) in k 12.251 * [taylor]: Taking taylor expansion of n in k 12.251 * [backup-simplify]: Simplify n into n 12.251 * [taylor]: Taking taylor expansion of PI in k 12.251 * [backup-simplify]: Simplify PI into PI 12.251 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.251 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.251 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.251 * [backup-simplify]: Simplify (- 0) into 0 12.252 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.252 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 12.253 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 12.253 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 12.253 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.253 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.253 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.253 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.253 * [taylor]: Taking taylor expansion of 0.25 in n 12.253 * [backup-simplify]: Simplify 0.25 into 0.25 12.253 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.253 * [taylor]: Taking taylor expansion of 1.0 in n 12.253 * [backup-simplify]: Simplify 1.0 into 1.0 12.253 * [taylor]: Taking taylor expansion of k in n 12.253 * [backup-simplify]: Simplify k into k 12.253 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.253 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.253 * [taylor]: Taking taylor expansion of 2.0 in n 12.253 * [backup-simplify]: Simplify 2.0 into 2.0 12.253 * [taylor]: Taking taylor expansion of (* n PI) in n 12.253 * [taylor]: Taking taylor expansion of n in n 12.253 * [backup-simplify]: Simplify 0 into 0 12.253 * [backup-simplify]: Simplify 1 into 1 12.253 * [taylor]: Taking taylor expansion of PI in n 12.253 * [backup-simplify]: Simplify PI into PI 12.254 * [backup-simplify]: Simplify (* 0 PI) into 0 12.254 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.256 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.257 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.259 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.259 * [backup-simplify]: Simplify (- k) into (- k) 12.259 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.259 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.260 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.261 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.263 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.263 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.263 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.263 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.263 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.263 * [taylor]: Taking taylor expansion of 0.25 in n 12.263 * [backup-simplify]: Simplify 0.25 into 0.25 12.263 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.263 * [taylor]: Taking taylor expansion of 1.0 in n 12.263 * [backup-simplify]: Simplify 1.0 into 1.0 12.263 * [taylor]: Taking taylor expansion of k in n 12.263 * [backup-simplify]: Simplify k into k 12.263 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.263 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.263 * [taylor]: Taking taylor expansion of 2.0 in n 12.263 * [backup-simplify]: Simplify 2.0 into 2.0 12.263 * [taylor]: Taking taylor expansion of (* n PI) in n 12.263 * [taylor]: Taking taylor expansion of n in n 12.263 * [backup-simplify]: Simplify 0 into 0 12.263 * [backup-simplify]: Simplify 1 into 1 12.263 * [taylor]: Taking taylor expansion of PI in n 12.263 * [backup-simplify]: Simplify PI into PI 12.264 * [backup-simplify]: Simplify (* 0 PI) into 0 12.264 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.266 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.267 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.268 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.268 * [backup-simplify]: Simplify (- k) into (- k) 12.268 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.268 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.270 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.271 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.273 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.273 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.273 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.273 * [taylor]: Taking taylor expansion of 0.25 in k 12.273 * [backup-simplify]: Simplify 0.25 into 0.25 12.273 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.273 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.273 * [taylor]: Taking taylor expansion of 1.0 in k 12.273 * [backup-simplify]: Simplify 1.0 into 1.0 12.273 * [taylor]: Taking taylor expansion of k in k 12.273 * [backup-simplify]: Simplify 0 into 0 12.274 * [backup-simplify]: Simplify 1 into 1 12.274 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.274 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.274 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.274 * [taylor]: Taking taylor expansion of 2.0 in k 12.274 * [backup-simplify]: Simplify 2.0 into 2.0 12.274 * [taylor]: Taking taylor expansion of PI in k 12.274 * [backup-simplify]: Simplify PI into PI 12.274 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.275 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.275 * [taylor]: Taking taylor expansion of (log n) in k 12.276 * [taylor]: Taking taylor expansion of n in k 12.276 * [backup-simplify]: Simplify n into n 12.276 * [backup-simplify]: Simplify (log n) into (log n) 12.276 * [backup-simplify]: Simplify (- 0) into 0 12.276 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.278 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.279 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.280 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 12.281 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.282 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.284 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.285 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.287 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.287 * [backup-simplify]: Simplify (- 0) into 0 12.287 * [backup-simplify]: Simplify (+ 0 0) into 0 12.288 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 12.289 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.291 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.293 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.293 * [taylor]: Taking taylor expansion of 0 in k 12.293 * [backup-simplify]: Simplify 0 into 0 12.293 * [backup-simplify]: Simplify 0 into 0 12.294 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.296 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.297 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.297 * [backup-simplify]: Simplify (+ 0 0) into 0 12.298 * [backup-simplify]: Simplify (- 1) into -1 12.298 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.300 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.302 * [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)))) 12.304 * [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)))))) 12.306 * [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)))))) 12.306 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.307 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.309 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.309 * [backup-simplify]: Simplify (- 0) into 0 12.310 * [backup-simplify]: Simplify (+ 0 0) into 0 12.310 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.311 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.312 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.314 * [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 12.314 * [taylor]: Taking taylor expansion of 0 in k 12.314 * [backup-simplify]: Simplify 0 into 0 12.314 * [backup-simplify]: Simplify 0 into 0 12.314 * [backup-simplify]: Simplify 0 into 0 12.314 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.317 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.318 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.318 * [backup-simplify]: Simplify (+ 0 0) into 0 12.318 * [backup-simplify]: Simplify (- 0) into 0 12.319 * [backup-simplify]: Simplify (+ 0 0) into 0 12.320 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.328 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.332 * [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))))) 12.337 * [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))))) 12.348 * [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)))))) 12.349 * [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)))) 12.349 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 12.349 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 12.349 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.349 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.349 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 12.349 * [taylor]: Taking taylor expansion of 0.25 in k 12.349 * [backup-simplify]: Simplify 0.25 into 0.25 12.349 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.349 * [taylor]: Taking taylor expansion of 1.0 in k 12.349 * [backup-simplify]: Simplify 1.0 into 1.0 12.349 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.349 * [taylor]: Taking taylor expansion of k in k 12.349 * [backup-simplify]: Simplify 0 into 0 12.349 * [backup-simplify]: Simplify 1 into 1 12.350 * [backup-simplify]: Simplify (/ 1 1) into 1 12.350 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.350 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.350 * [taylor]: Taking taylor expansion of 2.0 in k 12.350 * [backup-simplify]: Simplify 2.0 into 2.0 12.350 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.350 * [taylor]: Taking taylor expansion of PI in k 12.350 * [backup-simplify]: Simplify PI into PI 12.350 * [taylor]: Taking taylor expansion of n in k 12.350 * [backup-simplify]: Simplify n into n 12.350 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.350 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.350 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.351 * [backup-simplify]: Simplify (- 1) into -1 12.351 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.351 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 12.351 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 12.352 * [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))))) 12.352 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.352 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.352 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.352 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.352 * [taylor]: Taking taylor expansion of 0.25 in n 12.352 * [backup-simplify]: Simplify 0.25 into 0.25 12.352 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.352 * [taylor]: Taking taylor expansion of 1.0 in n 12.352 * [backup-simplify]: Simplify 1.0 into 1.0 12.352 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.352 * [taylor]: Taking taylor expansion of k in n 12.352 * [backup-simplify]: Simplify k into k 12.352 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.352 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.352 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.352 * [taylor]: Taking taylor expansion of 2.0 in n 12.352 * [backup-simplify]: Simplify 2.0 into 2.0 12.352 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.352 * [taylor]: Taking taylor expansion of PI in n 12.352 * [backup-simplify]: Simplify PI into PI 12.352 * [taylor]: Taking taylor expansion of n in n 12.352 * [backup-simplify]: Simplify 0 into 0 12.352 * [backup-simplify]: Simplify 1 into 1 12.353 * [backup-simplify]: Simplify (/ PI 1) into PI 12.354 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.355 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.355 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.355 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.355 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.356 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.358 * [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)))) 12.359 * [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))))) 12.359 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.359 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.359 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.359 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.359 * [taylor]: Taking taylor expansion of 0.25 in n 12.359 * [backup-simplify]: Simplify 0.25 into 0.25 12.359 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.359 * [taylor]: Taking taylor expansion of 1.0 in n 12.359 * [backup-simplify]: Simplify 1.0 into 1.0 12.359 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.359 * [taylor]: Taking taylor expansion of k in n 12.359 * [backup-simplify]: Simplify k into k 12.359 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.359 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.359 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.359 * [taylor]: Taking taylor expansion of 2.0 in n 12.359 * [backup-simplify]: Simplify 2.0 into 2.0 12.359 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.359 * [taylor]: Taking taylor expansion of PI in n 12.359 * [backup-simplify]: Simplify PI into PI 12.360 * [taylor]: Taking taylor expansion of n in n 12.360 * [backup-simplify]: Simplify 0 into 0 12.360 * [backup-simplify]: Simplify 1 into 1 12.360 * [backup-simplify]: Simplify (/ PI 1) into PI 12.361 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.362 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.362 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.362 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.362 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.363 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.365 * [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)))) 12.366 * [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))))) 12.366 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.366 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.366 * [taylor]: Taking taylor expansion of 0.25 in k 12.366 * [backup-simplify]: Simplify 0.25 into 0.25 12.366 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.366 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.366 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.366 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.366 * [taylor]: Taking taylor expansion of 2.0 in k 12.366 * [backup-simplify]: Simplify 2.0 into 2.0 12.366 * [taylor]: Taking taylor expansion of PI in k 12.366 * [backup-simplify]: Simplify PI into PI 12.367 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.368 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.368 * [taylor]: Taking taylor expansion of (log n) in k 12.368 * [taylor]: Taking taylor expansion of n in k 12.368 * [backup-simplify]: Simplify n into n 12.368 * [backup-simplify]: Simplify (log n) into (log n) 12.368 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.368 * [taylor]: Taking taylor expansion of 1.0 in k 12.368 * [backup-simplify]: Simplify 1.0 into 1.0 12.368 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.368 * [taylor]: Taking taylor expansion of k in k 12.368 * [backup-simplify]: Simplify 0 into 0 12.368 * [backup-simplify]: Simplify 1 into 1 12.369 * [backup-simplify]: Simplify (/ 1 1) into 1 12.369 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.370 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.370 * [backup-simplify]: Simplify (- 1) into -1 12.370 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.372 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.373 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 12.374 * [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))))) 12.376 * [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))))) 12.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.377 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.379 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.379 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.380 * [backup-simplify]: Simplify (- 0) into 0 12.380 * [backup-simplify]: Simplify (+ 0 0) into 0 12.381 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.382 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.383 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.386 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.386 * [taylor]: Taking taylor expansion of 0 in k 12.386 * [backup-simplify]: Simplify 0 into 0 12.386 * [backup-simplify]: Simplify 0 into 0 12.386 * [backup-simplify]: Simplify 0 into 0 12.387 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.388 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.391 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.392 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.392 * [backup-simplify]: Simplify (- 0) into 0 12.392 * [backup-simplify]: Simplify (+ 0 0) into 0 12.393 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.395 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.396 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.399 * [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 12.399 * [taylor]: Taking taylor expansion of 0 in k 12.399 * [backup-simplify]: Simplify 0 into 0 12.399 * [backup-simplify]: Simplify 0 into 0 12.399 * [backup-simplify]: Simplify 0 into 0 12.399 * [backup-simplify]: Simplify 0 into 0 12.400 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.402 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.408 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 12.408 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.409 * [backup-simplify]: Simplify (- 0) into 0 12.409 * [backup-simplify]: Simplify (+ 0 0) into 0 12.410 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.411 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.412 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.413 * [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 12.413 * [taylor]: Taking taylor expansion of 0 in k 12.413 * [backup-simplify]: Simplify 0 into 0 12.413 * [backup-simplify]: Simplify 0 into 0 12.414 * [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)))) 12.415 * [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))) 12.415 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 12.415 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 12.415 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.415 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.415 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 12.415 * [taylor]: Taking taylor expansion of 0.25 in k 12.415 * [backup-simplify]: Simplify 0.25 into 0.25 12.415 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.415 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.415 * [taylor]: Taking taylor expansion of k in k 12.415 * [backup-simplify]: Simplify 0 into 0 12.415 * [backup-simplify]: Simplify 1 into 1 12.415 * [backup-simplify]: Simplify (/ 1 1) into 1 12.415 * [taylor]: Taking taylor expansion of 1.0 in k 12.415 * [backup-simplify]: Simplify 1.0 into 1.0 12.415 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.415 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.415 * [taylor]: Taking taylor expansion of -2.0 in k 12.415 * [backup-simplify]: Simplify -2.0 into -2.0 12.415 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.415 * [taylor]: Taking taylor expansion of PI in k 12.416 * [backup-simplify]: Simplify PI into PI 12.416 * [taylor]: Taking taylor expansion of n in k 12.416 * [backup-simplify]: Simplify n into n 12.416 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.416 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.416 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.416 * [backup-simplify]: Simplify (+ 1 0) into 1 12.416 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 12.416 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 12.417 * [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)))))) 12.417 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.417 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.417 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.417 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.417 * [taylor]: Taking taylor expansion of 0.25 in n 12.417 * [backup-simplify]: Simplify 0.25 into 0.25 12.417 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.417 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.417 * [taylor]: Taking taylor expansion of k in n 12.417 * [backup-simplify]: Simplify k into k 12.417 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.417 * [taylor]: Taking taylor expansion of 1.0 in n 12.417 * [backup-simplify]: Simplify 1.0 into 1.0 12.417 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.417 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.417 * [taylor]: Taking taylor expansion of -2.0 in n 12.417 * [backup-simplify]: Simplify -2.0 into -2.0 12.417 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.417 * [taylor]: Taking taylor expansion of PI in n 12.417 * [backup-simplify]: Simplify PI into PI 12.417 * [taylor]: Taking taylor expansion of n in n 12.417 * [backup-simplify]: Simplify 0 into 0 12.417 * [backup-simplify]: Simplify 1 into 1 12.417 * [backup-simplify]: Simplify (/ PI 1) into PI 12.418 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.418 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.418 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.418 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.419 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.420 * [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)))) 12.421 * [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))))) 12.421 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.421 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.421 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.421 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.421 * [taylor]: Taking taylor expansion of 0.25 in n 12.421 * [backup-simplify]: Simplify 0.25 into 0.25 12.421 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.421 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.421 * [taylor]: Taking taylor expansion of k in n 12.421 * [backup-simplify]: Simplify k into k 12.421 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.421 * [taylor]: Taking taylor expansion of 1.0 in n 12.421 * [backup-simplify]: Simplify 1.0 into 1.0 12.421 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.421 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.421 * [taylor]: Taking taylor expansion of -2.0 in n 12.421 * [backup-simplify]: Simplify -2.0 into -2.0 12.421 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.421 * [taylor]: Taking taylor expansion of PI in n 12.421 * [backup-simplify]: Simplify PI into PI 12.421 * [taylor]: Taking taylor expansion of n in n 12.421 * [backup-simplify]: Simplify 0 into 0 12.421 * [backup-simplify]: Simplify 1 into 1 12.422 * [backup-simplify]: Simplify (/ PI 1) into PI 12.422 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.422 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.423 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.423 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.424 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.424 * [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)))) 12.425 * [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))))) 12.425 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.425 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.425 * [taylor]: Taking taylor expansion of 0.25 in k 12.425 * [backup-simplify]: Simplify 0.25 into 0.25 12.425 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.425 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.425 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.425 * [taylor]: Taking taylor expansion of k in k 12.425 * [backup-simplify]: Simplify 0 into 0 12.425 * [backup-simplify]: Simplify 1 into 1 12.426 * [backup-simplify]: Simplify (/ 1 1) into 1 12.426 * [taylor]: Taking taylor expansion of 1.0 in k 12.426 * [backup-simplify]: Simplify 1.0 into 1.0 12.426 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.426 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.426 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.426 * [taylor]: Taking taylor expansion of -2.0 in k 12.426 * [backup-simplify]: Simplify -2.0 into -2.0 12.426 * [taylor]: Taking taylor expansion of PI in k 12.426 * [backup-simplify]: Simplify PI into PI 12.426 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.427 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.427 * [taylor]: Taking taylor expansion of (log n) in k 12.427 * [taylor]: Taking taylor expansion of n in k 12.427 * [backup-simplify]: Simplify n into n 12.427 * [backup-simplify]: Simplify (log n) into (log n) 12.427 * [backup-simplify]: Simplify (+ 1 0) into 1 12.427 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.428 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.429 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.429 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 12.430 * [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))))) 12.431 * [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))))) 12.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.432 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.433 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.433 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.433 * [backup-simplify]: Simplify (+ 0 0) into 0 12.434 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.435 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.436 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.437 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.437 * [taylor]: Taking taylor expansion of 0 in k 12.437 * [backup-simplify]: Simplify 0 into 0 12.437 * [backup-simplify]: Simplify 0 into 0 12.437 * [backup-simplify]: Simplify 0 into 0 12.438 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.439 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.443 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 12.443 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.443 * [backup-simplify]: Simplify (+ 0 0) into 0 12.444 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.445 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.447 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.450 * [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 12.450 * [taylor]: Taking taylor expansion of 0 in k 12.450 * [backup-simplify]: Simplify 0 into 0 12.450 * [backup-simplify]: Simplify 0 into 0 12.450 * [backup-simplify]: Simplify 0 into 0 12.450 * [backup-simplify]: Simplify 0 into 0 12.451 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.452 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.465 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 12.466 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.466 * [backup-simplify]: Simplify (+ 0 0) into 0 12.467 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.468 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.469 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.471 * [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 12.471 * [taylor]: Taking taylor expansion of 0 in k 12.471 * [backup-simplify]: Simplify 0 into 0 12.471 * [backup-simplify]: Simplify 0 into 0 12.472 * [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)))))) 12.472 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 12.472 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 12.472 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 12.472 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.472 * [taylor]: Taking taylor expansion of 1.0 in k 12.472 * [backup-simplify]: Simplify 1.0 into 1.0 12.472 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.472 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.472 * [taylor]: Taking taylor expansion of k in k 12.472 * [backup-simplify]: Simplify 0 into 0 12.472 * [backup-simplify]: Simplify 1 into 1 12.472 * [backup-simplify]: Simplify (/ 1 1) into 1 12.472 * [backup-simplify]: Simplify (sqrt 0) into 0 12.473 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.473 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.473 * [taylor]: Taking taylor expansion of 1.0 in k 12.473 * [backup-simplify]: Simplify 1.0 into 1.0 12.473 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.474 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.474 * [taylor]: Taking taylor expansion of k in k 12.474 * [backup-simplify]: Simplify 0 into 0 12.474 * [backup-simplify]: Simplify 1 into 1 12.474 * [backup-simplify]: Simplify (/ 1 1) into 1 12.474 * [backup-simplify]: Simplify (sqrt 0) into 0 12.475 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.475 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.475 * [backup-simplify]: Simplify 0 into 0 12.476 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.476 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.477 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.479 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.480 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.480 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.481 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.483 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.484 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.485 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.485 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 12.486 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 12.486 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 12.486 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.486 * [taylor]: Taking taylor expansion of 1.0 in k 12.486 * [backup-simplify]: Simplify 1.0 into 1.0 12.486 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.486 * [taylor]: Taking taylor expansion of k in k 12.486 * [backup-simplify]: Simplify 0 into 0 12.486 * [backup-simplify]: Simplify 1 into 1 12.486 * [backup-simplify]: Simplify (sqrt 0) into 0 12.487 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.487 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.487 * [taylor]: Taking taylor expansion of 1.0 in k 12.487 * [backup-simplify]: Simplify 1.0 into 1.0 12.487 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.487 * [taylor]: Taking taylor expansion of k in k 12.487 * [backup-simplify]: Simplify 0 into 0 12.487 * [backup-simplify]: Simplify 1 into 1 12.487 * [backup-simplify]: Simplify (sqrt 0) into 0 12.488 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.488 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.488 * [backup-simplify]: Simplify 0 into 0 12.489 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.489 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.491 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.493 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.493 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.495 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.497 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.497 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.498 * [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)))))))) 12.498 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 12.498 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 12.498 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.498 * [taylor]: Taking taylor expansion of 1.0 in k 12.498 * [backup-simplify]: Simplify 1.0 into 1.0 12.498 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.498 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.498 * [taylor]: Taking taylor expansion of -1 in k 12.498 * [backup-simplify]: Simplify -1 into -1 12.498 * [taylor]: Taking taylor expansion of k in k 12.498 * [backup-simplify]: Simplify 0 into 0 12.498 * [backup-simplify]: Simplify 1 into 1 12.499 * [backup-simplify]: Simplify (/ -1 1) into -1 12.499 * [backup-simplify]: Simplify (sqrt 0) into 0 12.500 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.500 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.500 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.500 * [taylor]: Taking taylor expansion of 1.0 in k 12.500 * [backup-simplify]: Simplify 1.0 into 1.0 12.500 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.500 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.500 * [taylor]: Taking taylor expansion of -1 in k 12.500 * [backup-simplify]: Simplify -1 into -1 12.500 * [taylor]: Taking taylor expansion of k in k 12.500 * [backup-simplify]: Simplify 0 into 0 12.500 * [backup-simplify]: Simplify 1 into 1 12.500 * [backup-simplify]: Simplify (/ -1 1) into -1 12.500 * [backup-simplify]: Simplify (sqrt 0) into 0 12.501 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.502 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.502 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.502 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.504 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.505 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 12.506 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.506 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.509 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.511 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 12.511 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.512 * [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))))) 12.512 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 2) 12.512 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.512 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 12.512 * [taylor]: Taking taylor expansion of (* n PI) in n 12.512 * [taylor]: Taking taylor expansion of n in n 12.512 * [backup-simplify]: Simplify 0 into 0 12.512 * [backup-simplify]: Simplify 1 into 1 12.512 * [taylor]: Taking taylor expansion of PI in n 12.512 * [backup-simplify]: Simplify PI into PI 12.512 * [taylor]: Taking taylor expansion of (* n PI) in n 12.512 * [taylor]: Taking taylor expansion of n in n 12.512 * [backup-simplify]: Simplify 0 into 0 12.512 * [backup-simplify]: Simplify 1 into 1 12.512 * [taylor]: Taking taylor expansion of PI in n 12.512 * [backup-simplify]: Simplify PI into PI 12.513 * [backup-simplify]: Simplify (* 0 PI) into 0 12.513 * [backup-simplify]: Simplify 0 into 0 12.514 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.514 * [backup-simplify]: Simplify PI into PI 12.514 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.514 * [backup-simplify]: Simplify 0 into 0 12.515 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.515 * [backup-simplify]: Simplify 0 into 0 12.516 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.516 * [backup-simplify]: Simplify 0 into 0 12.517 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.517 * [backup-simplify]: Simplify 0 into 0 12.518 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.518 * [backup-simplify]: Simplify 0 into 0 12.519 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 12.519 * [backup-simplify]: Simplify 0 into 0 12.519 * [backup-simplify]: Simplify (* PI n) into (* n PI) 12.519 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 12.519 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 12.519 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.519 * [taylor]: Taking taylor expansion of PI in n 12.519 * [backup-simplify]: Simplify PI into PI 12.519 * [taylor]: Taking taylor expansion of n in n 12.519 * [backup-simplify]: Simplify 0 into 0 12.519 * [backup-simplify]: Simplify 1 into 1 12.519 * [backup-simplify]: Simplify (/ PI 1) into PI 12.519 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.519 * [taylor]: Taking taylor expansion of PI in n 12.519 * [backup-simplify]: Simplify PI into PI 12.519 * [taylor]: Taking taylor expansion of n in n 12.519 * [backup-simplify]: Simplify 0 into 0 12.519 * [backup-simplify]: Simplify 1 into 1 12.520 * [backup-simplify]: Simplify (/ PI 1) into PI 12.520 * [backup-simplify]: Simplify PI into PI 12.520 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.520 * [backup-simplify]: Simplify 0 into 0 12.521 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.521 * [backup-simplify]: Simplify 0 into 0 12.521 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.521 * [backup-simplify]: Simplify 0 into 0 12.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.522 * [backup-simplify]: Simplify 0 into 0 12.523 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.523 * [backup-simplify]: Simplify 0 into 0 12.523 * [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 12.523 * [backup-simplify]: Simplify 0 into 0 12.523 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 12.524 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 12.524 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 12.524 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.524 * [taylor]: Taking taylor expansion of -1 in n 12.524 * [backup-simplify]: Simplify -1 into -1 12.524 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.524 * [taylor]: Taking taylor expansion of PI in n 12.524 * [backup-simplify]: Simplify PI into PI 12.524 * [taylor]: Taking taylor expansion of n in n 12.524 * [backup-simplify]: Simplify 0 into 0 12.524 * [backup-simplify]: Simplify 1 into 1 12.524 * [backup-simplify]: Simplify (/ PI 1) into PI 12.524 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.524 * [taylor]: Taking taylor expansion of -1 in n 12.524 * [backup-simplify]: Simplify -1 into -1 12.524 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.524 * [taylor]: Taking taylor expansion of PI in n 12.524 * [backup-simplify]: Simplify PI into PI 12.524 * [taylor]: Taking taylor expansion of n in n 12.524 * [backup-simplify]: Simplify 0 into 0 12.524 * [backup-simplify]: Simplify 1 into 1 12.525 * [backup-simplify]: Simplify (/ PI 1) into PI 12.525 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.525 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.526 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.526 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 12.526 * [backup-simplify]: Simplify 0 into 0 12.527 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.527 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 12.527 * [backup-simplify]: Simplify 0 into 0 12.528 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.529 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.529 * [backup-simplify]: Simplify 0 into 0 12.529 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.530 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.530 * [backup-simplify]: Simplify 0 into 0 12.531 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.532 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.532 * [backup-simplify]: Simplify 0 into 0 12.532 * [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 12.533 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.533 * [backup-simplify]: Simplify 0 into 0 12.534 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 12.534 * * * [progress]: simplifying candidates 12.537 * [simplify]: Simplifying: (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (+ (log 2.0) (+ (log n) (log PI))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (pow (* 2.0 (* n PI)) (/ k 2.0)) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) 1) (pow (* 2.0 (* n PI)) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt 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(* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* n PI) (* n PI) (* n PI) 12.542 * * [simplify]: Extracting # 0 : cost 0 12.542 * * [simplify]: Extracting # 1 : cost 0 12.542 * * [simplify]: Extracting # 2 : cost 0 12.543 * * [simplify]: Extracting # 3 : cost 0 12.543 * * [simplify]: Extracting # 4 : cost 0 12.544 * * [simplify]: Extracting # 5 : cost 0 12.545 * * [simplify]: Extracting # 6 : cost 0 12.545 * * [simplify]: Extracting # 7 : cost 0 12.546 * * [simplify]: Extracting # 8 : cost 0 12.546 * * [simplify]: Extracting # 9 : cost 0 12.547 * * [simplify]: Extracting # 10 : cost 0 12.547 * * [simplify]: Extracting # 11 : cost 0 12.555 * * [simplify]: Extracting # 12 : cost 0 12.555 * * [simplify]: Extracting # 13 : cost 0 12.556 * * [simplify]: iteration 0 : 398 enodes (cost 2712 ) 12.694 * * [simplify]: Extracting # 0 : cost 0 12.696 * * [simplify]: Extracting # 1 : cost 0 12.697 * * [simplify]: Extracting # 2 : cost 0 12.700 * * [simplify]: Extracting # 3 : cost 0 12.703 * * [simplify]: Extracting # 4 : cost 0 12.706 * * [simplify]: Extracting # 5 : cost 0 12.709 * * [simplify]: Extracting # 6 : cost 0 12.719 * * [simplify]: iteration 1 : 1018 enodes (cost 2503 ) 13.225 * * [simplify]: Extracting # 0 : cost 0 13.228 * * [simplify]: Extracting # 1 : cost 0 13.233 * * [simplify]: Extracting # 2 : cost 0 13.236 * * [simplify]: Extracting # 3 : cost 0 13.243 * * [simplify]: Extracting # 4 : cost 0 13.251 * * [simplify]: iteration 2 : 2797 enodes (cost 2409 ) 14.701 * * [simplify]: Extracting # 0 : cost 0 14.707 * * [simplify]: Extracting # 1 : cost 0 14.714 * * [simplify]: Extracting # 2 : cost 0 14.720 * * [simplify]: Extracting # 3 : cost 0 14.726 * * [simplify]: Extracting # 4 : cost 0 14.738 * * [simplify]: iteration done: 5001 enodes (cost 2403 ) 14.739 * [simplify]: Simplified to: (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 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2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* n (* 2.0 PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* PI (* 2.0 n)) (- 1.0 k)) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* (sqrt k) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* n PI)) (log1p (* n PI)) (* n PI) (log (* n PI)) (log (* n PI)) (exp (* n PI)) (pow (* n PI) 3) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (pow (* n PI) 3) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) n (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (- (fma (* 0.125 (pow k 2)) (fma (pow (* n (* 2.0 PI)) 0.5) (pow (log (* 2.0 PI)) 2) (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.5))) (fma (* 0.25 (pow k 2)) (* (* (log (* 2.0 PI)) (log n)) (pow (* n (* 2.0 PI)) 0.5)) (pow (* n (* 2.0 PI)) 0.5))) (* (* 0.5 k) (fma (pow (* n (* 2.0 PI)) 0.5) (log n) (* (pow (* n (* 2.0 PI)) 0.5) (log (* 2.0 PI)))))) (pow (pow (* n (* 2.0 PI)) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (fma (* (* 0.03125 (pow k 2)) (pow (* n (* 2.0 PI)) 0.25)) (pow (log (* 2.0 PI)) 2) (fma (* (* (pow (* n (* 2.0 PI)) 0.25) (log n)) (* (pow k 2) (log (* 2.0 PI)))) 0.0625 (fma (pow k 2) (* (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.25)) 0.03125) (pow (* n (* 2.0 PI)) 0.25)))) (* (* 0.25 k) (fma (pow (* n (* 2.0 PI)) 0.25) (log n) (* (log (* 2.0 PI)) (pow (* n (* 2.0 PI)) 0.25))))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- k) +nan.0 (- (* +nan.0 (pow k 2)) +nan.0)) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) +nan.0)) (* n PI) (* n PI) (* n PI) 14.741 * * * [progress]: adding candidates to table 15.840 * * [progress]: iteration 4 / 4 15.840 * * * [progress]: picking best candidate 15.871 * * * * [pick]: Picked # 15.871 * * * [progress]: localizing error 15.903 * * * [progress]: generating rewritten candidates 15.903 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2) 15.922 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 15.986 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 15.999 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 2 1) 16.026 * * * [progress]: generating series expansions 16.026 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2) 16.026 * [backup-simplify]: Simplify (pow (* n PI) (/ (- 1.0 k) 2.0)) into (pow (* n PI) (* 0.5 (- 1.0 k))) 16.026 * [approximate]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in (n k) around 0 16.026 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in k 16.026 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in k 16.026 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in k 16.026 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 16.026 * [taylor]: Taking taylor expansion of 0.5 in k 16.026 * [backup-simplify]: Simplify 0.5 into 0.5 16.026 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.026 * [taylor]: Taking taylor expansion of 1.0 in k 16.026 * [backup-simplify]: Simplify 1.0 into 1.0 16.026 * [taylor]: Taking taylor expansion of k in k 16.026 * [backup-simplify]: Simplify 0 into 0 16.026 * [backup-simplify]: Simplify 1 into 1 16.026 * [taylor]: Taking taylor expansion of (log (* n PI)) in k 16.026 * [taylor]: Taking taylor expansion of (* n PI) in k 16.026 * [taylor]: Taking taylor expansion of n in k 16.026 * [backup-simplify]: Simplify n into n 16.026 * [taylor]: Taking taylor expansion of PI in k 16.026 * [backup-simplify]: Simplify PI into PI 16.026 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.026 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI)) 16.027 * [backup-simplify]: Simplify (- 0) into 0 16.027 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.028 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 16.028 * [backup-simplify]: Simplify (* 0.5 (log (* n PI))) into (* 0.5 (log (* n PI))) 16.028 * [backup-simplify]: Simplify (exp (* 0.5 (log (* n PI)))) into (pow (* n PI) 0.5) 16.028 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 16.028 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 16.028 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 16.028 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 16.028 * [taylor]: Taking taylor expansion of 0.5 in n 16.028 * [backup-simplify]: Simplify 0.5 into 0.5 16.028 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.028 * [taylor]: Taking taylor expansion of 1.0 in n 16.028 * [backup-simplify]: Simplify 1.0 into 1.0 16.028 * [taylor]: Taking taylor expansion of k in n 16.028 * [backup-simplify]: Simplify k into k 16.028 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 16.028 * [taylor]: Taking taylor expansion of (* n PI) in n 16.028 * [taylor]: Taking taylor expansion of n in n 16.028 * [backup-simplify]: Simplify 0 into 0 16.028 * [backup-simplify]: Simplify 1 into 1 16.028 * [taylor]: Taking taylor expansion of PI in n 16.028 * [backup-simplify]: Simplify PI into PI 16.028 * [backup-simplify]: Simplify (* 0 PI) into 0 16.029 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.030 * [backup-simplify]: Simplify (log PI) into (log PI) 16.030 * [backup-simplify]: Simplify (- k) into (- k) 16.030 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.030 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 16.030 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 16.031 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log n) (log PI))) into (* 0.5 (* (- 1.0 k) (+ (log n) (log PI)))) 16.031 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) 16.031 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 16.031 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 16.031 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 16.031 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 16.031 * [taylor]: Taking taylor expansion of 0.5 in n 16.031 * [backup-simplify]: Simplify 0.5 into 0.5 16.031 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.031 * [taylor]: Taking taylor expansion of 1.0 in n 16.031 * [backup-simplify]: Simplify 1.0 into 1.0 16.031 * [taylor]: Taking taylor expansion of k in n 16.031 * [backup-simplify]: Simplify k into k 16.031 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 16.031 * [taylor]: Taking taylor expansion of (* n PI) in n 16.031 * [taylor]: Taking taylor expansion of n in n 16.031 * [backup-simplify]: Simplify 0 into 0 16.031 * [backup-simplify]: Simplify 1 into 1 16.031 * [taylor]: Taking taylor expansion of PI in n 16.031 * [backup-simplify]: Simplify PI into PI 16.032 * [backup-simplify]: Simplify (* 0 PI) into 0 16.033 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.033 * [backup-simplify]: Simplify (log PI) into (log PI) 16.033 * [backup-simplify]: Simplify (- k) into (- k) 16.033 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.033 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 16.034 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 16.034 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log n) (log PI))) into (* 0.5 (* (- 1.0 k) (+ (log n) (log PI)))) 16.034 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) 16.034 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) in k 16.034 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log n) (log PI)))) in k 16.034 * [taylor]: Taking taylor expansion of 0.5 in k 16.034 * [backup-simplify]: Simplify 0.5 into 0.5 16.035 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log n) (log PI))) in k 16.035 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.035 * [taylor]: Taking taylor expansion of 1.0 in k 16.035 * [backup-simplify]: Simplify 1.0 into 1.0 16.035 * [taylor]: Taking taylor expansion of k in k 16.035 * [backup-simplify]: Simplify 0 into 0 16.035 * [backup-simplify]: Simplify 1 into 1 16.035 * [taylor]: Taking taylor expansion of (+ (log n) (log PI)) in k 16.035 * [taylor]: Taking taylor expansion of (log n) in k 16.035 * [taylor]: Taking taylor expansion of n in k 16.035 * [backup-simplify]: Simplify n into n 16.035 * [backup-simplify]: Simplify (log n) into (log n) 16.035 * [taylor]: Taking taylor expansion of (log PI) in k 16.035 * [taylor]: Taking taylor expansion of PI in k 16.035 * [backup-simplify]: Simplify PI into PI 16.035 * [backup-simplify]: Simplify (log PI) into (log PI) 16.035 * [backup-simplify]: Simplify (- 0) into 0 16.036 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.036 * [backup-simplify]: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) 16.036 * [backup-simplify]: Simplify (* 1.0 (+ (log n) (log PI))) into (* 1.0 (+ (log n) (log PI))) 16.037 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log n) (log PI)))) into (* 0.5 (+ (log n) (log PI))) 16.037 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log n) (log PI)))) into (exp (* 0.5 (+ (log n) (log PI)))) 16.037 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log n) (log PI)))) into (exp (* 0.5 (+ (log n) (log PI)))) 16.038 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.039 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 16.039 * [backup-simplify]: Simplify (- 0) into 0 16.040 * [backup-simplify]: Simplify (+ 0 0) into 0 16.040 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 16.040 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 16.041 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log n) (log PI)))) into 0 16.042 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.042 * [taylor]: Taking taylor expansion of 0 in k 16.042 * [backup-simplify]: Simplify 0 into 0 16.042 * [backup-simplify]: Simplify 0 into 0 16.042 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 16.043 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 16.043 * [backup-simplify]: Simplify (+ 0 0) into 0 16.043 * [backup-simplify]: Simplify (- 1) into -1 16.044 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.044 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log n) (log PI)))) into (- (+ (log PI) (log n))) 16.045 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log PI) (log n)))) (* 0 (* 1.0 (+ (log n) (log PI))))) into (- (+ (* 0.5 (log n)) (* 0.5 (log PI)))) 16.046 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 0.5 (log n)) (* 0.5 (log PI)))) 1) 1)))) into (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) 16.047 * [backup-simplify]: Simplify (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) into (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) 16.048 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 16.050 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 16.050 * [backup-simplify]: Simplify (- 0) into 0 16.050 * [backup-simplify]: Simplify (+ 0 0) into 0 16.051 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 16.051 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 16.052 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log PI))))) into 0 16.053 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.053 * [taylor]: Taking taylor expansion of 0 in k 16.053 * [backup-simplify]: Simplify 0 into 0 16.053 * [backup-simplify]: Simplify 0 into 0 16.053 * [backup-simplify]: Simplify 0 into 0 16.055 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 16.058 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 16.058 * [backup-simplify]: Simplify (+ 0 0) into 0 16.059 * [backup-simplify]: Simplify (- 0) into 0 16.059 * [backup-simplify]: Simplify (+ 0 0) into 0 16.061 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log n) (log PI))))) into 0 16.063 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log PI) (log n)))) (* 0 (* 1.0 (+ (log n) (log PI)))))) into 0 16.065 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 0.5 (log n)) (* 0.5 (log PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.125 (pow (log PI) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) 16.069 * [backup-simplify]: Simplify (* (+ (* 0.125 (pow (log PI) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) into (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) 16.075 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) (* k 1)) (exp (* 0.5 (+ (log n) (log PI)))))) into (- (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log n) 2)))) (* 0.25 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (* (log n) (log PI)))))))) (+ (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log PI)))) (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log n)))))) 16.075 * [backup-simplify]: Simplify (pow (* (/ 1 n) PI) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) 16.075 * [approximate]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 16.075 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in k 16.075 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in k 16.075 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in k 16.076 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 16.076 * [taylor]: Taking taylor expansion of 0.5 in k 16.076 * [backup-simplify]: Simplify 0.5 into 0.5 16.076 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.076 * [taylor]: Taking taylor expansion of 1.0 in k 16.076 * [backup-simplify]: Simplify 1.0 into 1.0 16.076 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.076 * [taylor]: Taking taylor expansion of k in k 16.076 * [backup-simplify]: Simplify 0 into 0 16.076 * [backup-simplify]: Simplify 1 into 1 16.076 * [backup-simplify]: Simplify (/ 1 1) into 1 16.076 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k 16.076 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.076 * [taylor]: Taking taylor expansion of PI in k 16.076 * [backup-simplify]: Simplify PI into PI 16.076 * [taylor]: Taking taylor expansion of n in k 16.076 * [backup-simplify]: Simplify n into n 16.076 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.077 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n)) 16.077 * [backup-simplify]: Simplify (- 1) into -1 16.077 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.078 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 16.078 * [backup-simplify]: Simplify (* -0.5 (log (/ PI n))) into (* -0.5 (log (/ PI n))) 16.078 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) into (exp (* 0.5 (* (log (/ PI n)) (- 1.0 (/ 1 k))))) 16.078 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 16.078 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 16.078 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 16.078 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 16.078 * [taylor]: Taking taylor expansion of 0.5 in n 16.078 * [backup-simplify]: Simplify 0.5 into 0.5 16.078 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.078 * [taylor]: Taking taylor expansion of 1.0 in n 16.078 * [backup-simplify]: Simplify 1.0 into 1.0 16.078 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.078 * [taylor]: Taking taylor expansion of k in n 16.078 * [backup-simplify]: Simplify k into k 16.079 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.079 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 16.079 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.079 * [taylor]: Taking taylor expansion of PI in n 16.079 * [backup-simplify]: Simplify PI into PI 16.079 * [taylor]: Taking taylor expansion of n in n 16.079 * [backup-simplify]: Simplify 0 into 0 16.079 * [backup-simplify]: Simplify 1 into 1 16.079 * [backup-simplify]: Simplify (/ PI 1) into PI 16.080 * [backup-simplify]: Simplify (log PI) into (log PI) 16.080 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.080 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.080 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 16.081 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 16.081 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k)))) 16.082 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 16.082 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 16.082 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 16.082 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 16.082 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 16.082 * [taylor]: Taking taylor expansion of 0.5 in n 16.082 * [backup-simplify]: Simplify 0.5 into 0.5 16.082 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.082 * [taylor]: Taking taylor expansion of 1.0 in n 16.082 * [backup-simplify]: Simplify 1.0 into 1.0 16.082 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.082 * [taylor]: Taking taylor expansion of k in n 16.083 * [backup-simplify]: Simplify k into k 16.083 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.083 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 16.083 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.083 * [taylor]: Taking taylor expansion of PI in n 16.083 * [backup-simplify]: Simplify PI into PI 16.083 * [taylor]: Taking taylor expansion of n in n 16.083 * [backup-simplify]: Simplify 0 into 0 16.083 * [backup-simplify]: Simplify 1 into 1 16.083 * [backup-simplify]: Simplify (/ PI 1) into PI 16.084 * [backup-simplify]: Simplify (log PI) into (log PI) 16.084 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.084 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.084 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 16.085 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 16.086 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k)))) 16.086 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 16.086 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) in k 16.087 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k)))) in k 16.087 * [taylor]: Taking taylor expansion of 0.5 in k 16.087 * [backup-simplify]: Simplify 0.5 into 0.5 16.087 * [taylor]: Taking taylor expansion of (* (- (log PI) (log n)) (- 1.0 (/ 1 k))) in k 16.087 * [taylor]: Taking taylor expansion of (- (log PI) (log n)) in k 16.087 * [taylor]: Taking taylor expansion of (log PI) in k 16.087 * [taylor]: Taking taylor expansion of PI in k 16.087 * [backup-simplify]: Simplify PI into PI 16.087 * [backup-simplify]: Simplify (log PI) into (log PI) 16.088 * [taylor]: Taking taylor expansion of (log n) in k 16.088 * [taylor]: Taking taylor expansion of n in k 16.088 * [backup-simplify]: Simplify n into n 16.088 * [backup-simplify]: Simplify (log n) into (log n) 16.088 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.088 * [taylor]: Taking taylor expansion of 1.0 in k 16.088 * [backup-simplify]: Simplify 1.0 into 1.0 16.088 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.088 * [taylor]: Taking taylor expansion of k in k 16.088 * [backup-simplify]: Simplify 0 into 0 16.088 * [backup-simplify]: Simplify 1 into 1 16.088 * [backup-simplify]: Simplify (/ 1 1) into 1 16.088 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.089 * [backup-simplify]: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n)) 16.089 * [backup-simplify]: Simplify (- 1) into -1 16.090 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.090 * [backup-simplify]: Simplify (* (- (log PI) (log n)) -1) into (* -1 (- (log PI) (log n))) 16.091 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log PI) (log n)))) into (* -0.5 (- (log PI) (log n))) 16.091 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 16.092 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 16.093 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.094 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 16.095 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.095 * [backup-simplify]: Simplify (- 0) into 0 16.095 * [backup-simplify]: Simplify (+ 0 0) into 0 16.096 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 16.097 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 16.098 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0 16.106 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.106 * [taylor]: Taking taylor expansion of 0 in k 16.106 * [backup-simplify]: Simplify 0 into 0 16.106 * [backup-simplify]: Simplify 0 into 0 16.106 * [backup-simplify]: Simplify 0 into 0 16.108 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.111 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 16.111 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.111 * [backup-simplify]: Simplify (- 0) into 0 16.112 * [backup-simplify]: Simplify (+ 0 0) into 0 16.113 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 16.114 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 16.115 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0 16.117 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.117 * [taylor]: Taking taylor expansion of 0 in k 16.117 * [backup-simplify]: Simplify 0 into 0 16.117 * [backup-simplify]: Simplify 0 into 0 16.117 * [backup-simplify]: Simplify 0 into 0 16.117 * [backup-simplify]: Simplify 0 into 0 16.118 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.124 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 16.124 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.125 * [backup-simplify]: Simplify (- 0) into 0 16.125 * [backup-simplify]: Simplify (+ 0 0) into 0 16.126 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 16.127 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 16.128 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0 16.131 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.131 * [taylor]: Taking taylor expansion of 0 in k 16.131 * [backup-simplify]: Simplify 0 into 0 16.131 * [backup-simplify]: Simplify 0 into 0 16.131 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n)))))) 16.132 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) PI) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 16.132 * [approximate]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 16.132 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 16.132 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in k 16.132 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in k 16.132 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 16.132 * [taylor]: Taking taylor expansion of 0.5 in k 16.132 * [backup-simplify]: Simplify 0.5 into 0.5 16.132 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 16.132 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.132 * [taylor]: Taking taylor expansion of k in k 16.132 * [backup-simplify]: Simplify 0 into 0 16.132 * [backup-simplify]: Simplify 1 into 1 16.133 * [backup-simplify]: Simplify (/ 1 1) into 1 16.133 * [taylor]: Taking taylor expansion of 1.0 in k 16.133 * [backup-simplify]: Simplify 1.0 into 1.0 16.133 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k 16.133 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k 16.133 * [taylor]: Taking taylor expansion of -1 in k 16.133 * [backup-simplify]: Simplify -1 into -1 16.133 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.133 * [taylor]: Taking taylor expansion of PI in k 16.133 * [backup-simplify]: Simplify PI into PI 16.133 * [taylor]: Taking taylor expansion of n in k 16.133 * [backup-simplify]: Simplify n into n 16.133 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.133 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 16.133 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 16.134 * [backup-simplify]: Simplify (+ 1 0) into 1 16.134 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 16.134 * [backup-simplify]: Simplify (* 0.5 (log (* -1 (/ PI n)))) into (* 0.5 (log (* -1 (/ PI n)))) 16.135 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -1 (/ PI n)))))) 16.135 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 16.135 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 16.135 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 16.135 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 16.135 * [taylor]: Taking taylor expansion of 0.5 in n 16.135 * [backup-simplify]: Simplify 0.5 into 0.5 16.135 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 16.135 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.135 * [taylor]: Taking taylor expansion of k in n 16.135 * [backup-simplify]: Simplify k into k 16.135 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.135 * [taylor]: Taking taylor expansion of 1.0 in n 16.135 * [backup-simplify]: Simplify 1.0 into 1.0 16.135 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 16.135 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 16.135 * [taylor]: Taking taylor expansion of -1 in n 16.135 * [backup-simplify]: Simplify -1 into -1 16.135 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.135 * [taylor]: Taking taylor expansion of PI in n 16.135 * [backup-simplify]: Simplify PI into PI 16.135 * [taylor]: Taking taylor expansion of n in n 16.135 * [backup-simplify]: Simplify 0 into 0 16.135 * [backup-simplify]: Simplify 1 into 1 16.136 * [backup-simplify]: Simplify (/ PI 1) into PI 16.136 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 16.138 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 16.138 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 16.138 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 16.140 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 16.141 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 16.142 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 16.142 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 16.142 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 16.142 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 16.142 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 16.142 * [taylor]: Taking taylor expansion of 0.5 in n 16.142 * [backup-simplify]: Simplify 0.5 into 0.5 16.142 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 16.143 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.143 * [taylor]: Taking taylor expansion of k in n 16.143 * [backup-simplify]: Simplify k into k 16.143 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.143 * [taylor]: Taking taylor expansion of 1.0 in n 16.143 * [backup-simplify]: Simplify 1.0 into 1.0 16.143 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 16.143 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 16.143 * [taylor]: Taking taylor expansion of -1 in n 16.143 * [backup-simplify]: Simplify -1 into -1 16.143 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.143 * [taylor]: Taking taylor expansion of PI in n 16.143 * [backup-simplify]: Simplify PI into PI 16.143 * [taylor]: Taking taylor expansion of n in n 16.143 * [backup-simplify]: Simplify 0 into 0 16.143 * [backup-simplify]: Simplify 1 into 1 16.143 * [backup-simplify]: Simplify (/ PI 1) into PI 16.144 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 16.145 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 16.145 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 16.145 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 16.147 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 16.148 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 16.149 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 16.149 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 16.150 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 16.150 * [taylor]: Taking taylor expansion of 0.5 in k 16.150 * [backup-simplify]: Simplify 0.5 into 0.5 16.150 * [taylor]: Taking taylor expansion of (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 16.150 * [taylor]: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k 16.150 * [taylor]: Taking taylor expansion of (log (* -1 PI)) in k 16.150 * [taylor]: Taking taylor expansion of (* -1 PI) in k 16.150 * [taylor]: Taking taylor expansion of -1 in k 16.150 * [backup-simplify]: Simplify -1 into -1 16.150 * [taylor]: Taking taylor expansion of PI in k 16.150 * [backup-simplify]: Simplify PI into PI 16.150 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 16.151 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 16.151 * [taylor]: Taking taylor expansion of (log n) in k 16.151 * [taylor]: Taking taylor expansion of n in k 16.151 * [backup-simplify]: Simplify n into n 16.151 * [backup-simplify]: Simplify (log n) into (log n) 16.152 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 16.152 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.152 * [taylor]: Taking taylor expansion of k in k 16.152 * [backup-simplify]: Simplify 0 into 0 16.152 * [backup-simplify]: Simplify 1 into 1 16.152 * [backup-simplify]: Simplify (/ 1 1) into 1 16.152 * [taylor]: Taking taylor expansion of 1.0 in k 16.152 * [backup-simplify]: Simplify 1.0 into 1.0 16.152 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.153 * [backup-simplify]: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n)) 16.154 * [backup-simplify]: Simplify (+ 1 0) into 1 16.155 * [backup-simplify]: Simplify (* (- (log (* -1 PI)) (log n)) 1) into (- (log (* -1 PI)) (log n)) 16.156 * [backup-simplify]: Simplify (* 0.5 (- (log (* -1 PI)) (log n))) into (* 0.5 (- (log (* -1 PI)) (log n))) 16.157 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 16.159 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 16.160 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.160 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 16.162 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 16.162 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.163 * [backup-simplify]: Simplify (+ 0 0) into 0 16.163 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 16.165 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 16.166 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0 16.168 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 16.168 * [taylor]: Taking taylor expansion of 0 in k 16.168 * [backup-simplify]: Simplify 0 into 0 16.168 * [backup-simplify]: Simplify 0 into 0 16.168 * [backup-simplify]: Simplify 0 into 0 16.169 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.171 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 16.174 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0 16.174 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.175 * [backup-simplify]: Simplify (+ 0 0) into 0 16.176 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 16.177 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 16.179 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0 16.181 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.181 * [taylor]: Taking taylor expansion of 0 in k 16.181 * [backup-simplify]: Simplify 0 into 0 16.181 * [backup-simplify]: Simplify 0 into 0 16.181 * [backup-simplify]: Simplify 0 into 0 16.181 * [backup-simplify]: Simplify 0 into 0 16.182 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.183 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.186 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -1 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -1 PI) 1)))) 6) into 0 16.187 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.187 * [backup-simplify]: Simplify (+ 0 0) into 0 16.188 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 16.189 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 16.190 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0 16.191 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.191 * [taylor]: Taking taylor expansion of 0 in k 16.191 * [backup-simplify]: Simplify 0 into 0 16.192 * [backup-simplify]: Simplify 0 into 0 16.192 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -1 PI)) (log (/ -1 n)))))) 16.192 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 16.193 * [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))) 16.193 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 16.193 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 16.193 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 16.193 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 16.193 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 16.193 * [taylor]: Taking taylor expansion of 0.25 in k 16.193 * [backup-simplify]: Simplify 0.25 into 0.25 16.193 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.193 * [taylor]: Taking taylor expansion of 1.0 in k 16.193 * [backup-simplify]: Simplify 1.0 into 1.0 16.193 * [taylor]: Taking taylor expansion of k in k 16.193 * [backup-simplify]: Simplify 0 into 0 16.193 * [backup-simplify]: Simplify 1 into 1 16.193 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 16.193 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 16.193 * [taylor]: Taking taylor expansion of 2.0 in k 16.193 * [backup-simplify]: Simplify 2.0 into 2.0 16.193 * [taylor]: Taking taylor expansion of (* n PI) in k 16.193 * [taylor]: Taking taylor expansion of n in k 16.193 * [backup-simplify]: Simplify n into n 16.193 * [taylor]: Taking taylor expansion of PI in k 16.193 * [backup-simplify]: Simplify PI into PI 16.193 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.193 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 16.193 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 16.194 * [backup-simplify]: Simplify (- 0) into 0 16.194 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.194 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 16.194 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 16.194 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 16.194 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 16.194 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 16.194 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 16.194 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 16.194 * [taylor]: Taking taylor expansion of 0.25 in n 16.195 * [backup-simplify]: Simplify 0.25 into 0.25 16.195 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.195 * [taylor]: Taking taylor expansion of 1.0 in n 16.195 * [backup-simplify]: Simplify 1.0 into 1.0 16.195 * [taylor]: Taking taylor expansion of k in n 16.195 * [backup-simplify]: Simplify k into k 16.195 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 16.195 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 16.195 * [taylor]: Taking taylor expansion of 2.0 in n 16.195 * [backup-simplify]: Simplify 2.0 into 2.0 16.195 * [taylor]: Taking taylor expansion of (* n PI) in n 16.195 * [taylor]: Taking taylor expansion of n in n 16.195 * [backup-simplify]: Simplify 0 into 0 16.195 * [backup-simplify]: Simplify 1 into 1 16.195 * [taylor]: Taking taylor expansion of PI in n 16.195 * [backup-simplify]: Simplify PI into PI 16.195 * [backup-simplify]: Simplify (* 0 PI) into 0 16.195 * [backup-simplify]: Simplify (* 2.0 0) into 0 16.196 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.197 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 16.198 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.198 * [backup-simplify]: Simplify (- k) into (- k) 16.198 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.198 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 16.199 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.200 * [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)))) 16.201 * [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))))) 16.201 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 16.201 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 16.201 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 16.201 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 16.201 * [taylor]: Taking taylor expansion of 0.25 in n 16.201 * [backup-simplify]: Simplify 0.25 into 0.25 16.201 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.201 * [taylor]: Taking taylor expansion of 1.0 in n 16.201 * [backup-simplify]: Simplify 1.0 into 1.0 16.201 * [taylor]: Taking taylor expansion of k in n 16.201 * [backup-simplify]: Simplify k into k 16.201 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 16.201 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 16.201 * [taylor]: Taking taylor expansion of 2.0 in n 16.201 * [backup-simplify]: Simplify 2.0 into 2.0 16.201 * [taylor]: Taking taylor expansion of (* n PI) in n 16.201 * [taylor]: Taking taylor expansion of n in n 16.201 * [backup-simplify]: Simplify 0 into 0 16.201 * [backup-simplify]: Simplify 1 into 1 16.201 * [taylor]: Taking taylor expansion of PI in n 16.201 * [backup-simplify]: Simplify PI into PI 16.201 * [backup-simplify]: Simplify (* 0 PI) into 0 16.202 * [backup-simplify]: Simplify (* 2.0 0) into 0 16.202 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.203 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 16.204 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.204 * [backup-simplify]: Simplify (- k) into (- k) 16.204 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.204 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 16.205 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.206 * [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)))) 16.207 * [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))))) 16.207 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 16.207 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 16.207 * [taylor]: Taking taylor expansion of 0.25 in k 16.207 * [backup-simplify]: Simplify 0.25 into 0.25 16.207 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 16.207 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.207 * [taylor]: Taking taylor expansion of 1.0 in k 16.207 * [backup-simplify]: Simplify 1.0 into 1.0 16.207 * [taylor]: Taking taylor expansion of k in k 16.207 * [backup-simplify]: Simplify 0 into 0 16.207 * [backup-simplify]: Simplify 1 into 1 16.207 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 16.207 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 16.207 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 16.207 * [taylor]: Taking taylor expansion of 2.0 in k 16.207 * [backup-simplify]: Simplify 2.0 into 2.0 16.207 * [taylor]: Taking taylor expansion of PI in k 16.207 * [backup-simplify]: Simplify PI into PI 16.207 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.208 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.208 * [taylor]: Taking taylor expansion of (log n) in k 16.208 * [taylor]: Taking taylor expansion of n in k 16.208 * [backup-simplify]: Simplify n into n 16.208 * [backup-simplify]: Simplify (log n) into (log n) 16.208 * [backup-simplify]: Simplify (- 0) into 0 16.209 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.210 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 16.211 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 16.212 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 16.213 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 16.214 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 16.216 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.217 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 16.219 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.219 * [backup-simplify]: Simplify (- 0) into 0 16.219 * [backup-simplify]: Simplify (+ 0 0) into 0 16.220 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 16.221 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.223 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 16.225 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.225 * [taylor]: Taking taylor expansion of 0 in k 16.225 * [backup-simplify]: Simplify 0 into 0 16.225 * [backup-simplify]: Simplify 0 into 0 16.226 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 16.228 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.229 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 16.229 * [backup-simplify]: Simplify (+ 0 0) into 0 16.229 * [backup-simplify]: Simplify (- 1) into -1 16.230 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.231 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 16.234 * [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)))) 16.237 * [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)))))) 16.245 * [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)))))) 16.246 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 16.247 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 16.252 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 16.252 * [backup-simplify]: Simplify (- 0) into 0 16.252 * [backup-simplify]: Simplify (+ 0 0) into 0 16.253 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 16.255 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.256 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 16.259 * [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 16.259 * [taylor]: Taking taylor expansion of 0 in k 16.259 * [backup-simplify]: Simplify 0 into 0 16.259 * [backup-simplify]: Simplify 0 into 0 16.259 * [backup-simplify]: Simplify 0 into 0 16.260 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.264 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 16.266 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 16.266 * [backup-simplify]: Simplify (+ 0 0) into 0 16.266 * [backup-simplify]: Simplify (- 0) into 0 16.267 * [backup-simplify]: Simplify (+ 0 0) into 0 16.269 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 16.271 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 16.275 * [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))))) 16.281 * [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))))) 16.291 * [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)))))) 16.292 * [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)))) 16.292 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 16.292 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 16.292 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 16.292 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 16.292 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 16.292 * [taylor]: Taking taylor expansion of 0.25 in k 16.292 * [backup-simplify]: Simplify 0.25 into 0.25 16.292 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.292 * [taylor]: Taking taylor expansion of 1.0 in k 16.292 * [backup-simplify]: Simplify 1.0 into 1.0 16.292 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.292 * [taylor]: Taking taylor expansion of k in k 16.292 * [backup-simplify]: Simplify 0 into 0 16.292 * [backup-simplify]: Simplify 1 into 1 16.293 * [backup-simplify]: Simplify (/ 1 1) into 1 16.293 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 16.293 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 16.293 * [taylor]: Taking taylor expansion of 2.0 in k 16.293 * [backup-simplify]: Simplify 2.0 into 2.0 16.293 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.293 * [taylor]: Taking taylor expansion of PI in k 16.293 * [backup-simplify]: Simplify PI into PI 16.293 * [taylor]: Taking taylor expansion of n in k 16.293 * [backup-simplify]: Simplify n into n 16.293 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.293 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 16.293 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 16.294 * [backup-simplify]: Simplify (- 1) into -1 16.294 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.295 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 16.295 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 16.295 * [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))))) 16.295 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 16.295 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 16.295 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 16.295 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 16.295 * [taylor]: Taking taylor expansion of 0.25 in n 16.295 * [backup-simplify]: Simplify 0.25 into 0.25 16.295 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.295 * [taylor]: Taking taylor expansion of 1.0 in n 16.295 * [backup-simplify]: Simplify 1.0 into 1.0 16.295 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.295 * [taylor]: Taking taylor expansion of k in n 16.295 * [backup-simplify]: Simplify k into k 16.296 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.296 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 16.296 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 16.296 * [taylor]: Taking taylor expansion of 2.0 in n 16.296 * [backup-simplify]: Simplify 2.0 into 2.0 16.296 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.296 * [taylor]: Taking taylor expansion of PI in n 16.296 * [backup-simplify]: Simplify PI into PI 16.296 * [taylor]: Taking taylor expansion of n in n 16.296 * [backup-simplify]: Simplify 0 into 0 16.296 * [backup-simplify]: Simplify 1 into 1 16.296 * [backup-simplify]: Simplify (/ PI 1) into PI 16.297 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.298 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.298 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.298 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.298 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 16.300 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.301 * [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)))) 16.302 * [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))))) 16.302 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 16.302 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 16.302 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 16.303 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 16.303 * [taylor]: Taking taylor expansion of 0.25 in n 16.303 * [backup-simplify]: Simplify 0.25 into 0.25 16.303 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.303 * [taylor]: Taking taylor expansion of 1.0 in n 16.303 * [backup-simplify]: Simplify 1.0 into 1.0 16.303 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.303 * [taylor]: Taking taylor expansion of k in n 16.303 * [backup-simplify]: Simplify k into k 16.303 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.303 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 16.303 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 16.303 * [taylor]: Taking taylor expansion of 2.0 in n 16.303 * [backup-simplify]: Simplify 2.0 into 2.0 16.303 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.303 * [taylor]: Taking taylor expansion of PI in n 16.303 * [backup-simplify]: Simplify PI into PI 16.303 * [taylor]: Taking taylor expansion of n in n 16.303 * [backup-simplify]: Simplify 0 into 0 16.303 * [backup-simplify]: Simplify 1 into 1 16.304 * [backup-simplify]: Simplify (/ PI 1) into PI 16.304 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.305 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.305 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.305 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.306 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 16.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.309 * [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)))) 16.310 * [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))))) 16.310 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 16.310 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 16.310 * [taylor]: Taking taylor expansion of 0.25 in k 16.310 * [backup-simplify]: Simplify 0.25 into 0.25 16.310 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 16.310 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 16.310 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 16.310 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 16.310 * [taylor]: Taking taylor expansion of 2.0 in k 16.310 * [backup-simplify]: Simplify 2.0 into 2.0 16.310 * [taylor]: Taking taylor expansion of PI in k 16.310 * [backup-simplify]: Simplify PI into PI 16.311 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.312 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.312 * [taylor]: Taking taylor expansion of (log n) in k 16.312 * [taylor]: Taking taylor expansion of n in k 16.312 * [backup-simplify]: Simplify n into n 16.312 * [backup-simplify]: Simplify (log n) into (log n) 16.312 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.312 * [taylor]: Taking taylor expansion of 1.0 in k 16.312 * [backup-simplify]: Simplify 1.0 into 1.0 16.312 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.312 * [taylor]: Taking taylor expansion of k in k 16.312 * [backup-simplify]: Simplify 0 into 0 16.312 * [backup-simplify]: Simplify 1 into 1 16.313 * [backup-simplify]: Simplify (/ 1 1) into 1 16.313 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.314 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 16.314 * [backup-simplify]: Simplify (- 1) into -1 16.315 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.316 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 16.317 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 16.318 * [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))))) 16.320 * [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))))) 16.321 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.321 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 16.323 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.324 * [backup-simplify]: Simplify (- 0) into 0 16.324 * [backup-simplify]: Simplify (+ 0 0) into 0 16.325 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 16.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.328 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 16.330 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.330 * [taylor]: Taking taylor expansion of 0 in k 16.330 * [backup-simplify]: Simplify 0 into 0 16.330 * [backup-simplify]: Simplify 0 into 0 16.330 * [backup-simplify]: Simplify 0 into 0 16.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.332 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.335 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 16.336 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.336 * [backup-simplify]: Simplify (- 0) into 0 16.337 * [backup-simplify]: Simplify (+ 0 0) into 0 16.337 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 16.339 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.340 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 16.343 * [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 16.343 * [taylor]: Taking taylor expansion of 0 in k 16.343 * [backup-simplify]: Simplify 0 into 0 16.343 * [backup-simplify]: Simplify 0 into 0 16.343 * [backup-simplify]: Simplify 0 into 0 16.343 * [backup-simplify]: Simplify 0 into 0 16.344 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.346 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.352 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 16.352 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.353 * [backup-simplify]: Simplify (- 0) into 0 16.353 * [backup-simplify]: Simplify (+ 0 0) into 0 16.354 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 16.356 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.358 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 16.361 * [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 16.361 * [taylor]: Taking taylor expansion of 0 in k 16.361 * [backup-simplify]: Simplify 0 into 0 16.361 * [backup-simplify]: Simplify 0 into 0 16.363 * [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)))) 16.364 * [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))) 16.364 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 16.364 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 16.364 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 16.364 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 16.364 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 16.364 * [taylor]: Taking taylor expansion of 0.25 in k 16.364 * [backup-simplify]: Simplify 0.25 into 0.25 16.364 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 16.364 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.364 * [taylor]: Taking taylor expansion of k in k 16.364 * [backup-simplify]: Simplify 0 into 0 16.364 * [backup-simplify]: Simplify 1 into 1 16.364 * [backup-simplify]: Simplify (/ 1 1) into 1 16.365 * [taylor]: Taking taylor expansion of 1.0 in k 16.365 * [backup-simplify]: Simplify 1.0 into 1.0 16.365 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 16.365 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 16.365 * [taylor]: Taking taylor expansion of -2.0 in k 16.365 * [backup-simplify]: Simplify -2.0 into -2.0 16.365 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.365 * [taylor]: Taking taylor expansion of PI in k 16.365 * [backup-simplify]: Simplify PI into PI 16.365 * [taylor]: Taking taylor expansion of n in k 16.365 * [backup-simplify]: Simplify n into n 16.365 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.365 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 16.365 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 16.366 * [backup-simplify]: Simplify (+ 1 0) into 1 16.366 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 16.366 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 16.366 * [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)))))) 16.366 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 16.366 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 16.367 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 16.367 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 16.367 * [taylor]: Taking taylor expansion of 0.25 in n 16.367 * [backup-simplify]: Simplify 0.25 into 0.25 16.367 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 16.367 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.367 * [taylor]: Taking taylor expansion of k in n 16.367 * [backup-simplify]: Simplify k into k 16.367 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.367 * [taylor]: Taking taylor expansion of 1.0 in n 16.367 * [backup-simplify]: Simplify 1.0 into 1.0 16.367 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 16.367 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 16.367 * [taylor]: Taking taylor expansion of -2.0 in n 16.367 * [backup-simplify]: Simplify -2.0 into -2.0 16.367 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.367 * [taylor]: Taking taylor expansion of PI in n 16.367 * [backup-simplify]: Simplify PI into PI 16.367 * [taylor]: Taking taylor expansion of n in n 16.367 * [backup-simplify]: Simplify 0 into 0 16.367 * [backup-simplify]: Simplify 1 into 1 16.368 * [backup-simplify]: Simplify (/ PI 1) into PI 16.368 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 16.369 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 16.369 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 16.369 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 16.371 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.372 * [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)))) 16.374 * [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))))) 16.374 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 16.374 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 16.374 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 16.374 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 16.374 * [taylor]: Taking taylor expansion of 0.25 in n 16.374 * [backup-simplify]: Simplify 0.25 into 0.25 16.374 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 16.374 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.374 * [taylor]: Taking taylor expansion of k in n 16.374 * [backup-simplify]: Simplify k into k 16.374 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.374 * [taylor]: Taking taylor expansion of 1.0 in n 16.374 * [backup-simplify]: Simplify 1.0 into 1.0 16.374 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 16.374 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 16.374 * [taylor]: Taking taylor expansion of -2.0 in n 16.374 * [backup-simplify]: Simplify -2.0 into -2.0 16.374 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.374 * [taylor]: Taking taylor expansion of PI in n 16.374 * [backup-simplify]: Simplify PI into PI 16.374 * [taylor]: Taking taylor expansion of n in n 16.374 * [backup-simplify]: Simplify 0 into 0 16.374 * [backup-simplify]: Simplify 1 into 1 16.375 * [backup-simplify]: Simplify (/ PI 1) into PI 16.376 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 16.377 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 16.377 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 16.377 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 16.378 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.380 * [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)))) 16.381 * [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))))) 16.381 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 16.381 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 16.381 * [taylor]: Taking taylor expansion of 0.25 in k 16.381 * [backup-simplify]: Simplify 0.25 into 0.25 16.381 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 16.381 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 16.381 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.381 * [taylor]: Taking taylor expansion of k in k 16.381 * [backup-simplify]: Simplify 0 into 0 16.381 * [backup-simplify]: Simplify 1 into 1 16.382 * [backup-simplify]: Simplify (/ 1 1) into 1 16.382 * [taylor]: Taking taylor expansion of 1.0 in k 16.382 * [backup-simplify]: Simplify 1.0 into 1.0 16.382 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 16.382 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 16.382 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 16.382 * [taylor]: Taking taylor expansion of -2.0 in k 16.382 * [backup-simplify]: Simplify -2.0 into -2.0 16.382 * [taylor]: Taking taylor expansion of PI in k 16.382 * [backup-simplify]: Simplify PI into PI 16.382 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 16.383 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 16.383 * [taylor]: Taking taylor expansion of (log n) in k 16.384 * [taylor]: Taking taylor expansion of n in k 16.384 * [backup-simplify]: Simplify n into n 16.384 * [backup-simplify]: Simplify (log n) into (log n) 16.384 * [backup-simplify]: Simplify (+ 1 0) into 1 16.384 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.385 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 16.386 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 16.388 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 16.389 * [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))))) 16.390 * [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))))) 16.391 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.392 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 16.394 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 16.394 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.394 * [backup-simplify]: Simplify (+ 0 0) into 0 16.399 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 16.401 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.402 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 16.404 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.405 * [taylor]: Taking taylor expansion of 0 in k 16.405 * [backup-simplify]: Simplify 0 into 0 16.405 * [backup-simplify]: Simplify 0 into 0 16.405 * [backup-simplify]: Simplify 0 into 0 16.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.407 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.411 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 16.411 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.412 * [backup-simplify]: Simplify (+ 0 0) into 0 16.413 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 16.414 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.415 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 16.416 * [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 16.416 * [taylor]: Taking taylor expansion of 0 in k 16.416 * [backup-simplify]: Simplify 0 into 0 16.416 * [backup-simplify]: Simplify 0 into 0 16.416 * [backup-simplify]: Simplify 0 into 0 16.416 * [backup-simplify]: Simplify 0 into 0 16.417 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.417 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.421 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 16.421 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.421 * [backup-simplify]: Simplify (+ 0 0) into 0 16.422 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 16.423 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.424 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 16.426 * [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 16.426 * [taylor]: Taking taylor expansion of 0 in k 16.426 * [backup-simplify]: Simplify 0 into 0 16.426 * [backup-simplify]: Simplify 0 into 0 16.427 * [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)))))) 16.427 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 16.427 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 16.427 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 16.427 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 16.427 * [taylor]: Taking taylor expansion of 1.0 in k 16.427 * [backup-simplify]: Simplify 1.0 into 1.0 16.427 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 16.427 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.427 * [taylor]: Taking taylor expansion of k in k 16.427 * [backup-simplify]: Simplify 0 into 0 16.427 * [backup-simplify]: Simplify 1 into 1 16.427 * [backup-simplify]: Simplify (/ 1 1) into 1 16.428 * [backup-simplify]: Simplify (sqrt 0) into 0 16.428 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.428 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 16.428 * [taylor]: Taking taylor expansion of 1.0 in k 16.429 * [backup-simplify]: Simplify 1.0 into 1.0 16.429 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 16.429 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.429 * [taylor]: Taking taylor expansion of k in k 16.429 * [backup-simplify]: Simplify 0 into 0 16.429 * [backup-simplify]: Simplify 1 into 1 16.429 * [backup-simplify]: Simplify (/ 1 1) into 1 16.429 * [backup-simplify]: Simplify (sqrt 0) into 0 16.430 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.430 * [backup-simplify]: Simplify (* 1.0 0) into 0 16.430 * [backup-simplify]: Simplify 0 into 0 16.431 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 16.431 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.432 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 16.433 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 16.435 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 16.435 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.435 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.438 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 16.439 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 16.439 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.440 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 16.440 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 16.440 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 16.440 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 16.440 * [taylor]: Taking taylor expansion of 1.0 in k 16.440 * [backup-simplify]: Simplify 1.0 into 1.0 16.440 * [taylor]: Taking taylor expansion of (sqrt k) in k 16.440 * [taylor]: Taking taylor expansion of k in k 16.440 * [backup-simplify]: Simplify 0 into 0 16.440 * [backup-simplify]: Simplify 1 into 1 16.441 * [backup-simplify]: Simplify (sqrt 0) into 0 16.441 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.442 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 16.442 * [taylor]: Taking taylor expansion of 1.0 in k 16.442 * [backup-simplify]: Simplify 1.0 into 1.0 16.442 * [taylor]: Taking taylor expansion of (sqrt k) in k 16.442 * [taylor]: Taking taylor expansion of k in k 16.442 * [backup-simplify]: Simplify 0 into 0 16.442 * [backup-simplify]: Simplify 1 into 1 16.442 * [backup-simplify]: Simplify (sqrt 0) into 0 16.443 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.443 * [backup-simplify]: Simplify (* 1.0 0) into 0 16.443 * [backup-simplify]: Simplify 0 into 0 16.444 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 16.444 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.446 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 16.447 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 16.447 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.449 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 16.451 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 16.451 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.452 * [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)))))))) 16.452 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 16.452 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 16.452 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 16.452 * [taylor]: Taking taylor expansion of 1.0 in k 16.452 * [backup-simplify]: Simplify 1.0 into 1.0 16.452 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 16.452 * [taylor]: Taking taylor expansion of (/ -1 k) in k 16.452 * [taylor]: Taking taylor expansion of -1 in k 16.452 * [backup-simplify]: Simplify -1 into -1 16.452 * [taylor]: Taking taylor expansion of k in k 16.452 * [backup-simplify]: Simplify 0 into 0 16.452 * [backup-simplify]: Simplify 1 into 1 16.453 * [backup-simplify]: Simplify (/ -1 1) into -1 16.453 * [backup-simplify]: Simplify (sqrt 0) into 0 16.454 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 16.454 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 16.454 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 16.454 * [taylor]: Taking taylor expansion of 1.0 in k 16.454 * [backup-simplify]: Simplify 1.0 into 1.0 16.454 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 16.454 * [taylor]: Taking taylor expansion of (/ -1 k) in k 16.454 * [taylor]: Taking taylor expansion of -1 in k 16.454 * [backup-simplify]: Simplify -1 into -1 16.454 * [taylor]: Taking taylor expansion of k in k 16.454 * [backup-simplify]: Simplify 0 into 0 16.454 * [backup-simplify]: Simplify 1 into 1 16.454 * [backup-simplify]: Simplify (/ -1 1) into -1 16.455 * [backup-simplify]: Simplify (sqrt 0) into 0 16.455 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 16.456 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 16.456 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.456 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 16.458 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 16.459 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 16.460 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.460 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.463 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 16.465 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 16.465 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.466 * [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))))) 16.466 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 2 1) 16.466 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.466 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 16.466 * [taylor]: Taking taylor expansion of (* n PI) in n 16.466 * [taylor]: Taking taylor expansion of n in n 16.466 * [backup-simplify]: Simplify 0 into 0 16.466 * [backup-simplify]: Simplify 1 into 1 16.466 * [taylor]: Taking taylor expansion of PI in n 16.466 * [backup-simplify]: Simplify PI into PI 16.466 * [taylor]: Taking taylor expansion of (* n PI) in n 16.466 * [taylor]: Taking taylor expansion of n in n 16.466 * [backup-simplify]: Simplify 0 into 0 16.466 * [backup-simplify]: Simplify 1 into 1 16.466 * [taylor]: Taking taylor expansion of PI in n 16.466 * [backup-simplify]: Simplify PI into PI 16.467 * [backup-simplify]: Simplify (* 0 PI) into 0 16.467 * [backup-simplify]: Simplify 0 into 0 16.468 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.468 * [backup-simplify]: Simplify PI into PI 16.468 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.468 * [backup-simplify]: Simplify 0 into 0 16.469 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 16.469 * [backup-simplify]: Simplify 0 into 0 16.470 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 16.471 * [backup-simplify]: Simplify 0 into 0 16.472 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 16.472 * [backup-simplify]: Simplify 0 into 0 16.474 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 16.474 * [backup-simplify]: Simplify 0 into 0 16.476 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 16.476 * [backup-simplify]: Simplify 0 into 0 16.476 * [backup-simplify]: Simplify (* PI n) into (* n PI) 16.476 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 16.476 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 16.476 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.476 * [taylor]: Taking taylor expansion of PI in n 16.476 * [backup-simplify]: Simplify PI into PI 16.476 * [taylor]: Taking taylor expansion of n in n 16.476 * [backup-simplify]: Simplify 0 into 0 16.476 * [backup-simplify]: Simplify 1 into 1 16.477 * [backup-simplify]: Simplify (/ PI 1) into PI 16.477 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.477 * [taylor]: Taking taylor expansion of PI in n 16.477 * [backup-simplify]: Simplify PI into PI 16.477 * [taylor]: Taking taylor expansion of n in n 16.477 * [backup-simplify]: Simplify 0 into 0 16.477 * [backup-simplify]: Simplify 1 into 1 16.477 * [backup-simplify]: Simplify (/ PI 1) into PI 16.478 * [backup-simplify]: Simplify PI into PI 16.478 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.478 * [backup-simplify]: Simplify 0 into 0 16.480 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.480 * [backup-simplify]: Simplify 0 into 0 16.481 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.481 * [backup-simplify]: Simplify 0 into 0 16.482 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.482 * [backup-simplify]: Simplify 0 into 0 16.483 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.483 * [backup-simplify]: Simplify 0 into 0 16.484 * [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 16.484 * [backup-simplify]: Simplify 0 into 0 16.484 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 16.484 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 16.484 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 16.484 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 16.484 * [taylor]: Taking taylor expansion of -1 in n 16.484 * [backup-simplify]: Simplify -1 into -1 16.484 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.484 * [taylor]: Taking taylor expansion of PI in n 16.484 * [backup-simplify]: Simplify PI into PI 16.484 * [taylor]: Taking taylor expansion of n in n 16.484 * [backup-simplify]: Simplify 0 into 0 16.485 * [backup-simplify]: Simplify 1 into 1 16.485 * [backup-simplify]: Simplify (/ PI 1) into PI 16.485 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 16.485 * [taylor]: Taking taylor expansion of -1 in n 16.485 * [backup-simplify]: Simplify -1 into -1 16.485 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.485 * [taylor]: Taking taylor expansion of PI in n 16.485 * [backup-simplify]: Simplify PI into PI 16.485 * [taylor]: Taking taylor expansion of n in n 16.485 * [backup-simplify]: Simplify 0 into 0 16.485 * [backup-simplify]: Simplify 1 into 1 16.486 * [backup-simplify]: Simplify (/ PI 1) into PI 16.486 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 16.487 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 16.488 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.488 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 16.488 * [backup-simplify]: Simplify 0 into 0 16.489 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.490 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 16.491 * [backup-simplify]: Simplify 0 into 0 16.492 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.493 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.493 * [backup-simplify]: Simplify 0 into 0 16.494 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.495 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 16.495 * [backup-simplify]: Simplify 0 into 0 16.496 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.498 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 16.498 * [backup-simplify]: Simplify 0 into 0 16.499 * [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 16.501 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 16.501 * [backup-simplify]: Simplify 0 into 0 16.501 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 16.502 * * * [progress]: simplifying candidates 16.512 * [simplify]: Simplifying: (expm1 (pow (* n PI) (/ (- 1.0 k) 2.0))) (log1p (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (+ (log n) (log PI)) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ 1.0 2.0)) (pow (* n PI) (/ k 2.0)) (pow (* n PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* n PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n PI) (/ (sqrt (- 1.0 k)) 1)) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (pow (* n PI) (/ 1 1)) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (pow (* n PI) (/ 1 1)) (pow (* n PI) 1) (pow (* n PI) (- 1.0 k)) (pow n (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (exp (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* n PI)) (log1p (* n PI)) (* n PI) (+ (log n) (log PI)) (log (* n PI)) (exp (* n PI)) (* (* (* n n) n) (* (* PI PI) PI)) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (* (* (* n PI) (* n PI)) (* n PI)) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) (* n 1) (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (- (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log n) 2)))) (* 0.25 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (* (log n) (log PI)))))))) (+ (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log PI)))) (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -1 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* n PI) (* n PI) (* n PI) 16.522 * * [simplify]: Extracting # 0 : cost 0 16.522 * * [simplify]: Extracting # 1 : cost 0 16.522 * * [simplify]: Extracting # 2 : cost 0 16.523 * * [simplify]: Extracting # 3 : cost 0 16.524 * * [simplify]: Extracting # 4 : cost 0 16.524 * * [simplify]: Extracting # 5 : cost 0 16.525 * * [simplify]: Extracting # 6 : cost 0 16.525 * * [simplify]: Extracting # 7 : cost 0 16.526 * * [simplify]: Extracting # 8 : cost 0 16.527 * * [simplify]: Extracting # 9 : cost 0 16.527 * * [simplify]: Extracting # 10 : cost 0 16.528 * * [simplify]: Extracting # 11 : cost 0 16.528 * * [simplify]: Extracting # 12 : cost 0 16.529 * * [simplify]: Extracting # 13 : cost 0 16.530 * * [simplify]: iteration 0 : 401 enodes (cost 2593 ) 16.723 * * [simplify]: Extracting # 0 : cost 0 16.725 * * [simplify]: Extracting # 1 : cost 0 16.733 * * [simplify]: Extracting # 2 : cost 0 16.735 * * [simplify]: Extracting # 3 : cost 0 16.736 * * [simplify]: Extracting # 4 : cost 0 16.738 * * [simplify]: Extracting # 5 : cost 0 16.739 * * [simplify]: Extracting # 6 : cost 0 16.741 * * [simplify]: iteration 1 : 1023 enodes (cost 2390 ) 17.383 * * [simplify]: Extracting # 0 : cost 0 17.389 * * [simplify]: Extracting # 1 : cost 0 17.397 * * [simplify]: Extracting # 2 : cost 0 17.405 * * [simplify]: Extracting # 3 : cost 0 17.412 * * [simplify]: Extracting # 4 : cost 0 17.421 * * [simplify]: iteration 2 : 2853 enodes (cost 2297 ) 18.578 * * [simplify]: Extracting # 0 : cost 0 18.585 * * [simplify]: Extracting # 1 : cost 0 18.593 * * [simplify]: Extracting # 2 : cost 0 18.601 * * [simplify]: Extracting # 3 : cost 0 18.610 * * [simplify]: Extracting # 4 : cost 0 18.623 * * [simplify]: iteration done: 5000 enodes (cost 2291 ) 18.634 * [simplify]: Simplified to: (expm1 (pow (* n PI) (/ (- 1.0 k) 2.0))) (log1p (pow (* n PI) (/ (- 1.0 k) 2.0))) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* n PI) (/ 1.0 2.0)) (pow (* n PI) (/ k 2.0)) (pow (* n PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n PI) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n PI) (sqrt (- 1.0 k))) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (* PI n) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* PI n) (+ (sqrt 1.0) (sqrt k))) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (* PI n) (* PI n) (pow (* PI n) (- 1.0 k)) (pow n (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (exp (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (pow (* n PI) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (- 1.0 k) (* 2 2.0)) (/ (- 1.0 k) (* 2 2.0)) (/ (- 1.0 k) (* 2 2.0)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* n (* 2.0 PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (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)) (* (* 2.0 PI) n) (pow (* n (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (pow 1.0 3) k) (sqrt k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* n PI)) (log1p (* n PI)) (* PI n) (log (* PI n)) (log (* PI n)) (exp (* n PI)) (pow (* PI n) 3) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (pow (* PI n) 3) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) n (* (cbrt n) PI) (* (sqrt n) PI) (* PI n) (- (fma (pow k 2) (* (* (pow (log PI) 2) (pow (* PI n) 0.5)) 0.125) (fma (* 0.125 (* (pow (log n) 2) (pow (* PI n) 0.5))) (pow k 2) (fma (* 0.25 (* k (* (pow (* PI n) 0.5) k))) (* (log n) (log PI)) (pow (* PI n) 0.5)))) (* 0.5 (* (* (pow (* PI n) 0.5) k) (log (* PI n))))) (pow (pow (* PI n) 0.5) (- 1.0 k)) (pow (exp 0.5) (* (- (log (- PI)) (log (/ -1 n))) (- 1.0 k))) (fma (pow k 2) (* (* (pow (* n (* 2.0 PI)) 0.25) (pow (log (* 2.0 PI)) 2)) 0.03125) (- (fma (* 0.0625 (* (log (* 2.0 PI)) (* (pow (* n (* 2.0 PI)) 0.25) (log n)))) (pow k 2) (fma 0.03125 (* (* (pow k 2) (pow (* n (* 2.0 PI)) 0.25)) (pow (log n) 2)) (pow (* n (* 2.0 PI)) 0.25))) (* (* 0.25 k) (fma (pow (* n (* 2.0 PI)) 0.25) (log n) (* (log (* 2.0 PI)) (pow (* n (* 2.0 PI)) 0.25)))))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma +nan.0 (- k) (- (* +nan.0 (pow k 2)) +nan.0)) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) +nan.0)) (* PI n) (* PI n) (* PI n) 18.635 * * * [progress]: adding candidates to table 19.970 * [progress]: [Phase 3 of 3] Extracting. 19.970 * * [regime]: Finding splitpoints for: (# # # # # # #)