61.271 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.144 * * * [progress]: [2/2] Setting up program. 0.147 * [progress]: [Phase 2 of 3] Improving. 0.147 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.147 * * [simplify]: Extracting # 0 : cost 0 0.147 * * [simplify]: Extracting # 1 : cost 0 0.147 * * [simplify]: Extracting # 2 : cost 0 0.147 * * [simplify]: Extracting # 3 : cost 0 0.147 * * [simplify]: Extracting # 4 : cost 0 0.147 * * [simplify]: Extracting # 5 : cost 0 0.147 * * [simplify]: Extracting # 6 : cost 0 0.147 * * [simplify]: Extracting # 7 : cost 0 0.147 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.151 * * [simplify]: Extracting # 0 : cost 0 0.151 * * [simplify]: Extracting # 1 : cost 0 0.151 * * [simplify]: Extracting # 2 : cost 0 0.151 * * [simplify]: Extracting # 3 : cost 0 0.151 * * [simplify]: Extracting # 4 : cost 0 0.151 * * [simplify]: Extracting # 5 : cost 0 0.151 * * [simplify]: iteration 1 : 41 enodes (cost 16 ) 0.196 * * [simplify]: Extracting # 0 : cost 0 0.196 * * [simplify]: Extracting # 1 : cost 0 0.196 * * [simplify]: Extracting # 2 : cost 0 0.196 * * [simplify]: Extracting # 3 : cost 0 0.196 * * [simplify]: Extracting # 4 : cost 0 0.196 * * [simplify]: Extracting # 5 : cost 0 0.196 * * [simplify]: iteration 2 : 145 enodes (cost 16 ) 0.521 * * [simplify]: Extracting # 0 : cost 0 0.523 * * [simplify]: Extracting # 1 : cost 0 0.524 * * [simplify]: Extracting # 2 : cost 0 0.526 * * [simplify]: Extracting # 3 : cost 0 0.527 * * [simplify]: Extracting # 4 : cost 0 0.528 * * [simplify]: Extracting # 5 : cost 0 0.530 * * [simplify]: Extracting # 6 : cost 0 0.531 * * [simplify]: iteration 3 : 1125 enodes (cost 16 ) 8.004 * * [simplify]: Extracting # 0 : cost 0 8.017 * * [simplify]: Extracting # 1 : cost 0 8.025 * * [simplify]: Extracting # 2 : cost 0 8.031 * * [simplify]: Extracting # 3 : cost 0 8.040 * * [simplify]: Extracting # 4 : cost 0 8.049 * * [simplify]: Extracting # 5 : cost 0 8.058 * * [simplify]: iteration done: 5000 enodes (cost 16 ) 8.058 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 8.059 * * [progress]: iteration 1 / 4 8.059 * * * [progress]: picking best candidate 8.063 * * * * [pick]: Picked # 8.063 * * * [progress]: localizing error 8.092 * * * [progress]: generating rewritten candidates 8.092 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 8.138 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 8.150 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 8.181 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 8.247 * * * [progress]: generating series expansions 8.247 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 8.249 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 8.249 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 8.249 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 8.249 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.249 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.249 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.249 * [taylor]: Taking taylor expansion of 0.5 in k 8.249 * [backup-simplify]: Simplify 0.5 into 0.5 8.249 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.249 * [taylor]: Taking taylor expansion of 1.0 in k 8.249 * [backup-simplify]: Simplify 1.0 into 1.0 8.249 * [taylor]: Taking taylor expansion of k in k 8.249 * [backup-simplify]: Simplify 0 into 0 8.249 * [backup-simplify]: Simplify 1 into 1 8.249 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.249 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.249 * [taylor]: Taking taylor expansion of 2.0 in k 8.249 * [backup-simplify]: Simplify 2.0 into 2.0 8.249 * [taylor]: Taking taylor expansion of (* n PI) in k 8.249 * [taylor]: Taking taylor expansion of n in k 8.249 * [backup-simplify]: Simplify n into n 8.249 * [taylor]: Taking taylor expansion of PI in k 8.249 * [backup-simplify]: Simplify PI into PI 8.249 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.249 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.250 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.250 * [backup-simplify]: Simplify (- 0) into 0 8.251 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.251 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.251 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 8.251 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 8.251 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.251 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.251 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.251 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.251 * [taylor]: Taking taylor expansion of 0.5 in n 8.251 * [backup-simplify]: Simplify 0.5 into 0.5 8.252 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.252 * [taylor]: Taking taylor expansion of 1.0 in n 8.252 * [backup-simplify]: Simplify 1.0 into 1.0 8.252 * [taylor]: Taking taylor expansion of k in n 8.252 * [backup-simplify]: Simplify k into k 8.252 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.252 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.252 * [taylor]: Taking taylor expansion of 2.0 in n 8.252 * [backup-simplify]: Simplify 2.0 into 2.0 8.252 * [taylor]: Taking taylor expansion of (* n PI) in n 8.252 * [taylor]: Taking taylor expansion of n in n 8.252 * [backup-simplify]: Simplify 0 into 0 8.252 * [backup-simplify]: Simplify 1 into 1 8.252 * [taylor]: Taking taylor expansion of PI in n 8.252 * [backup-simplify]: Simplify PI into PI 8.252 * [backup-simplify]: Simplify (* 0 PI) into 0 8.253 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.254 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.256 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.257 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.257 * [backup-simplify]: Simplify (- k) into (- k) 8.257 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.257 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.258 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.260 * [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)))) 8.261 * [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))))) 8.261 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.261 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.261 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.261 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.261 * [taylor]: Taking taylor expansion of 0.5 in n 8.261 * [backup-simplify]: Simplify 0.5 into 0.5 8.261 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.261 * [taylor]: Taking taylor expansion of 1.0 in n 8.261 * [backup-simplify]: Simplify 1.0 into 1.0 8.261 * [taylor]: Taking taylor expansion of k in n 8.261 * [backup-simplify]: Simplify k into k 8.261 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.261 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.261 * [taylor]: Taking taylor expansion of 2.0 in n 8.261 * [backup-simplify]: Simplify 2.0 into 2.0 8.261 * [taylor]: Taking taylor expansion of (* n PI) in n 8.261 * [taylor]: Taking taylor expansion of n in n 8.261 * [backup-simplify]: Simplify 0 into 0 8.261 * [backup-simplify]: Simplify 1 into 1 8.262 * [taylor]: Taking taylor expansion of PI in n 8.262 * [backup-simplify]: Simplify PI into PI 8.262 * [backup-simplify]: Simplify (* 0 PI) into 0 8.263 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.264 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.266 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.267 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.267 * [backup-simplify]: Simplify (- k) into (- k) 8.267 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.267 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.269 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.270 * [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)))) 8.271 * [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))))) 8.272 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.272 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.272 * [taylor]: Taking taylor expansion of 0.5 in k 8.272 * [backup-simplify]: Simplify 0.5 into 0.5 8.272 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.272 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.272 * [taylor]: Taking taylor expansion of 1.0 in k 8.272 * [backup-simplify]: Simplify 1.0 into 1.0 8.272 * [taylor]: Taking taylor expansion of k in k 8.272 * [backup-simplify]: Simplify 0 into 0 8.272 * [backup-simplify]: Simplify 1 into 1 8.272 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.272 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.272 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.272 * [taylor]: Taking taylor expansion of 2.0 in k 8.272 * [backup-simplify]: Simplify 2.0 into 2.0 8.272 * [taylor]: Taking taylor expansion of PI in k 8.272 * [backup-simplify]: Simplify PI into PI 8.273 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.274 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.274 * [taylor]: Taking taylor expansion of (log n) in k 8.274 * [taylor]: Taking taylor expansion of n in k 8.274 * [backup-simplify]: Simplify n into n 8.274 * [backup-simplify]: Simplify (log n) into (log n) 8.274 * [backup-simplify]: Simplify (- 0) into 0 8.275 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.276 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.277 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.278 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 8.279 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 8.279 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 8.280 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.281 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.282 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.282 * [backup-simplify]: Simplify (- 0) into 0 8.282 * [backup-simplify]: Simplify (+ 0 0) into 0 8.283 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 8.284 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.284 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.285 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.286 * [taylor]: Taking taylor expansion of 0 in k 8.286 * [backup-simplify]: Simplify 0 into 0 8.286 * [backup-simplify]: Simplify 0 into 0 8.286 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.287 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.288 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.288 * [backup-simplify]: Simplify (+ 0 0) into 0 8.288 * [backup-simplify]: Simplify (- 1) into -1 8.288 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.289 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.291 * [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)))) 8.293 * [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)))))) 8.295 * [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)))))) 8.296 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.296 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.299 * [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 8.299 * [backup-simplify]: Simplify (- 0) into 0 8.299 * [backup-simplify]: Simplify (+ 0 0) into 0 8.300 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.301 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.302 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.304 * [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 8.304 * [taylor]: Taking taylor expansion of 0 in k 8.304 * [backup-simplify]: Simplify 0 into 0 8.304 * [backup-simplify]: Simplify 0 into 0 8.304 * [backup-simplify]: Simplify 0 into 0 8.304 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.307 * [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 8.310 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.310 * [backup-simplify]: Simplify (+ 0 0) into 0 8.310 * [backup-simplify]: Simplify (- 0) into 0 8.311 * [backup-simplify]: Simplify (+ 0 0) into 0 8.313 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.316 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.321 * [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)))))) 8.326 * [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)))))) 8.337 * [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)))))) 8.338 * [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)))) 8.339 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 8.339 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.339 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.339 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.339 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.339 * [taylor]: Taking taylor expansion of 0.5 in k 8.339 * [backup-simplify]: Simplify 0.5 into 0.5 8.339 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.339 * [taylor]: Taking taylor expansion of 1.0 in k 8.339 * [backup-simplify]: Simplify 1.0 into 1.0 8.339 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.339 * [taylor]: Taking taylor expansion of k in k 8.339 * [backup-simplify]: Simplify 0 into 0 8.339 * [backup-simplify]: Simplify 1 into 1 8.339 * [backup-simplify]: Simplify (/ 1 1) into 1 8.339 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.339 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.339 * [taylor]: Taking taylor expansion of 2.0 in k 8.339 * [backup-simplify]: Simplify 2.0 into 2.0 8.340 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.340 * [taylor]: Taking taylor expansion of PI in k 8.340 * [backup-simplify]: Simplify PI into PI 8.340 * [taylor]: Taking taylor expansion of n in k 8.340 * [backup-simplify]: Simplify n into n 8.340 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.340 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.340 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.341 * [backup-simplify]: Simplify (- 1) into -1 8.341 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.342 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.342 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 8.342 * [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))))) 8.342 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.342 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.342 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.342 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.342 * [taylor]: Taking taylor expansion of 0.5 in n 8.342 * [backup-simplify]: Simplify 0.5 into 0.5 8.342 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.342 * [taylor]: Taking taylor expansion of 1.0 in n 8.342 * [backup-simplify]: Simplify 1.0 into 1.0 8.343 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.343 * [taylor]: Taking taylor expansion of k in n 8.343 * [backup-simplify]: Simplify k into k 8.343 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.343 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.343 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.343 * [taylor]: Taking taylor expansion of 2.0 in n 8.343 * [backup-simplify]: Simplify 2.0 into 2.0 8.343 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.343 * [taylor]: Taking taylor expansion of PI in n 8.343 * [backup-simplify]: Simplify PI into PI 8.343 * [taylor]: Taking taylor expansion of n in n 8.343 * [backup-simplify]: Simplify 0 into 0 8.343 * [backup-simplify]: Simplify 1 into 1 8.343 * [backup-simplify]: Simplify (/ PI 1) into PI 8.344 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.345 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.345 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.345 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.345 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.351 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.351 * [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)))) 8.352 * [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))))) 8.352 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.352 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.352 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.352 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.352 * [taylor]: Taking taylor expansion of 0.5 in n 8.352 * [backup-simplify]: Simplify 0.5 into 0.5 8.352 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.352 * [taylor]: Taking taylor expansion of 1.0 in n 8.352 * [backup-simplify]: Simplify 1.0 into 1.0 8.352 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.352 * [taylor]: Taking taylor expansion of k in n 8.352 * [backup-simplify]: Simplify k into k 8.353 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.353 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.353 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.353 * [taylor]: Taking taylor expansion of 2.0 in n 8.353 * [backup-simplify]: Simplify 2.0 into 2.0 8.353 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.353 * [taylor]: Taking taylor expansion of PI in n 8.353 * [backup-simplify]: Simplify PI into PI 8.353 * [taylor]: Taking taylor expansion of n in n 8.353 * [backup-simplify]: Simplify 0 into 0 8.353 * [backup-simplify]: Simplify 1 into 1 8.353 * [backup-simplify]: Simplify (/ PI 1) into PI 8.353 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.354 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.354 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.354 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.354 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.355 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.356 * [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)))) 8.357 * [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))))) 8.357 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.357 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.357 * [taylor]: Taking taylor expansion of 0.5 in k 8.357 * [backup-simplify]: Simplify 0.5 into 0.5 8.357 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.357 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.357 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.357 * [taylor]: Taking taylor expansion of (* 2.0 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 PI in k 8.357 * [backup-simplify]: Simplify PI into PI 8.357 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.358 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.358 * [taylor]: Taking taylor expansion of (log n) in k 8.358 * [taylor]: Taking taylor expansion of n in k 8.358 * [backup-simplify]: Simplify n into n 8.358 * [backup-simplify]: Simplify (log n) into (log n) 8.358 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.358 * [taylor]: Taking taylor expansion of 1.0 in k 8.358 * [backup-simplify]: Simplify 1.0 into 1.0 8.358 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.358 * [taylor]: Taking taylor expansion of k in k 8.358 * [backup-simplify]: Simplify 0 into 0 8.358 * [backup-simplify]: Simplify 1 into 1 8.358 * [backup-simplify]: Simplify (/ 1 1) into 1 8.359 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.359 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.359 * [backup-simplify]: Simplify (- 1) into -1 8.360 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.360 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.361 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 8.362 * [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))))) 8.363 * [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))))) 8.363 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.364 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.365 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.365 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.365 * [backup-simplify]: Simplify (- 0) into 0 8.365 * [backup-simplify]: Simplify (+ 0 0) into 0 8.366 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.367 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.367 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.369 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.369 * [taylor]: Taking taylor expansion of 0 in k 8.369 * [backup-simplify]: Simplify 0 into 0 8.369 * [backup-simplify]: Simplify 0 into 0 8.369 * [backup-simplify]: Simplify 0 into 0 8.369 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.370 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.372 * [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 8.372 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.372 * [backup-simplify]: Simplify (- 0) into 0 8.373 * [backup-simplify]: Simplify (+ 0 0) into 0 8.373 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.375 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.376 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.379 * [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 8.379 * [taylor]: Taking taylor expansion of 0 in k 8.379 * [backup-simplify]: Simplify 0 into 0 8.379 * [backup-simplify]: Simplify 0 into 0 8.379 * [backup-simplify]: Simplify 0 into 0 8.379 * [backup-simplify]: Simplify 0 into 0 8.380 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.382 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.388 * [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 8.388 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.389 * [backup-simplify]: Simplify (- 0) into 0 8.389 * [backup-simplify]: Simplify (+ 0 0) into 0 8.390 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.391 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.392 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.394 * [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 8.394 * [taylor]: Taking taylor expansion of 0 in k 8.395 * [backup-simplify]: Simplify 0 into 0 8.395 * [backup-simplify]: Simplify 0 into 0 8.395 * [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)))) 8.396 * [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))) 8.396 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 8.396 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.396 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.396 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.396 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.396 * [taylor]: Taking taylor expansion of 0.5 in k 8.396 * [backup-simplify]: Simplify 0.5 into 0.5 8.396 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.396 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.396 * [taylor]: Taking taylor expansion of k in k 8.396 * [backup-simplify]: Simplify 0 into 0 8.396 * [backup-simplify]: Simplify 1 into 1 8.396 * [backup-simplify]: Simplify (/ 1 1) into 1 8.396 * [taylor]: Taking taylor expansion of 1.0 in k 8.396 * [backup-simplify]: Simplify 1.0 into 1.0 8.396 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.397 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.397 * [taylor]: Taking taylor expansion of -2.0 in k 8.397 * [backup-simplify]: Simplify -2.0 into -2.0 8.397 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.397 * [taylor]: Taking taylor expansion of PI in k 8.397 * [backup-simplify]: Simplify PI into PI 8.397 * [taylor]: Taking taylor expansion of n in k 8.397 * [backup-simplify]: Simplify n into n 8.397 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.397 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.397 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.397 * [backup-simplify]: Simplify (+ 1 0) into 1 8.397 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.397 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 8.398 * [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)))))) 8.398 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.398 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.398 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.398 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.398 * [taylor]: Taking taylor expansion of 0.5 in n 8.398 * [backup-simplify]: Simplify 0.5 into 0.5 8.398 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.398 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.398 * [taylor]: Taking taylor expansion of k in n 8.398 * [backup-simplify]: Simplify k into k 8.398 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.398 * [taylor]: Taking taylor expansion of 1.0 in n 8.398 * [backup-simplify]: Simplify 1.0 into 1.0 8.398 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.398 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.398 * [taylor]: Taking taylor expansion of -2.0 in n 8.398 * [backup-simplify]: Simplify -2.0 into -2.0 8.398 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.398 * [taylor]: Taking taylor expansion of PI in n 8.398 * [backup-simplify]: Simplify PI into PI 8.398 * [taylor]: Taking taylor expansion of n in n 8.398 * [backup-simplify]: Simplify 0 into 0 8.398 * [backup-simplify]: Simplify 1 into 1 8.398 * [backup-simplify]: Simplify (/ PI 1) into PI 8.399 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.399 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.399 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.400 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.400 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.401 * [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)))) 8.402 * [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))))) 8.402 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.402 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.402 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.402 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.402 * [taylor]: Taking taylor expansion of 0.5 in n 8.402 * [backup-simplify]: Simplify 0.5 into 0.5 8.402 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.402 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.402 * [taylor]: Taking taylor expansion of k in n 8.402 * [backup-simplify]: Simplify k into k 8.402 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.402 * [taylor]: Taking taylor expansion of 1.0 in n 8.403 * [backup-simplify]: Simplify 1.0 into 1.0 8.403 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.403 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.403 * [taylor]: Taking taylor expansion of -2.0 in n 8.403 * [backup-simplify]: Simplify -2.0 into -2.0 8.403 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.403 * [taylor]: Taking taylor expansion of PI in n 8.403 * [backup-simplify]: Simplify PI into PI 8.403 * [taylor]: Taking taylor expansion of n in n 8.403 * [backup-simplify]: Simplify 0 into 0 8.403 * [backup-simplify]: Simplify 1 into 1 8.403 * [backup-simplify]: Simplify (/ PI 1) into PI 8.403 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.404 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.404 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.404 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.405 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.406 * [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)))) 8.406 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.407 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.407 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.407 * [taylor]: Taking taylor expansion of 0.5 in k 8.407 * [backup-simplify]: Simplify 0.5 into 0.5 8.407 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.407 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.407 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.407 * [taylor]: Taking taylor expansion of k in k 8.407 * [backup-simplify]: Simplify 0 into 0 8.407 * [backup-simplify]: Simplify 1 into 1 8.407 * [backup-simplify]: Simplify (/ 1 1) into 1 8.407 * [taylor]: Taking taylor expansion of 1.0 in k 8.407 * [backup-simplify]: Simplify 1.0 into 1.0 8.407 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.407 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.407 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.407 * [taylor]: Taking taylor expansion of -2.0 in k 8.407 * [backup-simplify]: Simplify -2.0 into -2.0 8.407 * [taylor]: Taking taylor expansion of PI in k 8.407 * [backup-simplify]: Simplify PI into PI 8.408 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.408 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.408 * [taylor]: Taking taylor expansion of (log n) in k 8.408 * [taylor]: Taking taylor expansion of n in k 8.408 * [backup-simplify]: Simplify n into n 8.408 * [backup-simplify]: Simplify (log n) into (log n) 8.409 * [backup-simplify]: Simplify (+ 1 0) into 1 8.409 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.409 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.410 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.411 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 8.411 * [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))))) 8.412 * [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))))) 8.413 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.413 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.414 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.414 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.415 * [backup-simplify]: Simplify (+ 0 0) into 0 8.415 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.416 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.417 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.418 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.418 * [taylor]: Taking taylor expansion of 0 in k 8.418 * [backup-simplify]: Simplify 0 into 0 8.418 * [backup-simplify]: Simplify 0 into 0 8.418 * [backup-simplify]: Simplify 0 into 0 8.419 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.419 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.421 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.421 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.422 * [backup-simplify]: Simplify (+ 0 0) into 0 8.422 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.423 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.424 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.426 * [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 8.426 * [taylor]: Taking taylor expansion of 0 in k 8.426 * [backup-simplify]: Simplify 0 into 0 8.426 * [backup-simplify]: Simplify 0 into 0 8.426 * [backup-simplify]: Simplify 0 into 0 8.426 * [backup-simplify]: Simplify 0 into 0 8.428 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.429 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.436 * [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 8.436 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.437 * [backup-simplify]: Simplify (+ 0 0) into 0 8.438 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.440 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.442 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.445 * [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 8.446 * [taylor]: Taking taylor expansion of 0 in k 8.446 * [backup-simplify]: Simplify 0 into 0 8.446 * [backup-simplify]: Simplify 0 into 0 8.447 * [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)))))) 8.447 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 8.448 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 8.448 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 8.448 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.448 * [taylor]: Taking taylor expansion of 1.0 in k 8.448 * [backup-simplify]: Simplify 1.0 into 1.0 8.448 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.448 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.448 * [taylor]: Taking taylor expansion of k in k 8.448 * [backup-simplify]: Simplify 0 into 0 8.448 * [backup-simplify]: Simplify 1 into 1 8.448 * [backup-simplify]: Simplify (/ 1 1) into 1 8.449 * [backup-simplify]: Simplify (sqrt 0) into 0 8.450 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.451 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.451 * [taylor]: Taking taylor expansion of 1.0 in k 8.451 * [backup-simplify]: Simplify 1.0 into 1.0 8.451 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.451 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.451 * [taylor]: Taking taylor expansion of k in k 8.451 * [backup-simplify]: Simplify 0 into 0 8.451 * [backup-simplify]: Simplify 1 into 1 8.451 * [backup-simplify]: Simplify (/ 1 1) into 1 8.452 * [backup-simplify]: Simplify (sqrt 0) into 0 8.453 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.453 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.454 * [backup-simplify]: Simplify 0 into 0 8.454 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.455 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.455 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.457 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.458 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.458 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.459 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.465 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.466 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.466 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.467 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 8.467 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 8.468 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 8.468 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.468 * [taylor]: Taking taylor expansion of 1.0 in k 8.468 * [backup-simplify]: Simplify 1.0 into 1.0 8.468 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.468 * [taylor]: Taking taylor expansion of k in k 8.468 * [backup-simplify]: Simplify 0 into 0 8.468 * [backup-simplify]: Simplify 1 into 1 8.468 * [backup-simplify]: Simplify (sqrt 0) into 0 8.469 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.469 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.469 * [taylor]: Taking taylor expansion of 1.0 in k 8.469 * [backup-simplify]: Simplify 1.0 into 1.0 8.469 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.469 * [taylor]: Taking taylor expansion of k in k 8.469 * [backup-simplify]: Simplify 0 into 0 8.469 * [backup-simplify]: Simplify 1 into 1 8.469 * [backup-simplify]: Simplify (sqrt 0) into 0 8.470 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.470 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.470 * [backup-simplify]: Simplify 0 into 0 8.471 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.471 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.473 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.474 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.475 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.477 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.478 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.479 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.480 * [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)))))))) 8.480 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 8.480 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 8.480 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.480 * [taylor]: Taking taylor expansion of 1.0 in k 8.480 * [backup-simplify]: Simplify 1.0 into 1.0 8.480 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.480 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.480 * [taylor]: Taking taylor expansion of -1 in k 8.480 * [backup-simplify]: Simplify -1 into -1 8.480 * [taylor]: Taking taylor expansion of k in k 8.480 * [backup-simplify]: Simplify 0 into 0 8.480 * [backup-simplify]: Simplify 1 into 1 8.480 * [backup-simplify]: Simplify (/ -1 1) into -1 8.481 * [backup-simplify]: Simplify (sqrt 0) into 0 8.481 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.482 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.482 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.482 * [taylor]: Taking taylor expansion of 1.0 in k 8.482 * [backup-simplify]: Simplify 1.0 into 1.0 8.482 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.482 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.482 * [taylor]: Taking taylor expansion of -1 in k 8.482 * [backup-simplify]: Simplify -1 into -1 8.482 * [taylor]: Taking taylor expansion of k in k 8.482 * [backup-simplify]: Simplify 0 into 0 8.482 * [backup-simplify]: Simplify 1 into 1 8.482 * [backup-simplify]: Simplify (/ -1 1) into -1 8.482 * [backup-simplify]: Simplify (sqrt 0) into 0 8.483 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.484 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.484 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.484 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.487 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.489 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 8.489 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.490 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.494 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.497 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 8.498 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.499 * [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))))) 8.499 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 8.500 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.500 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 8.500 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.500 * [taylor]: Taking taylor expansion of 2.0 in n 8.500 * [backup-simplify]: Simplify 2.0 into 2.0 8.500 * [taylor]: Taking taylor expansion of (* n PI) in n 8.500 * [taylor]: Taking taylor expansion of n in n 8.500 * [backup-simplify]: Simplify 0 into 0 8.500 * [backup-simplify]: Simplify 1 into 1 8.500 * [taylor]: Taking taylor expansion of PI in n 8.500 * [backup-simplify]: Simplify PI into PI 8.500 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.500 * [taylor]: Taking taylor expansion of 2.0 in n 8.500 * [backup-simplify]: Simplify 2.0 into 2.0 8.500 * [taylor]: Taking taylor expansion of (* n PI) in n 8.500 * [taylor]: Taking taylor expansion of n in n 8.500 * [backup-simplify]: Simplify 0 into 0 8.500 * [backup-simplify]: Simplify 1 into 1 8.500 * [taylor]: Taking taylor expansion of PI in n 8.500 * [backup-simplify]: Simplify PI into PI 8.501 * [backup-simplify]: Simplify (* 0 PI) into 0 8.501 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.501 * [backup-simplify]: Simplify 0 into 0 8.503 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.504 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.505 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.506 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.507 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.507 * [backup-simplify]: Simplify 0 into 0 8.508 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.510 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.510 * [backup-simplify]: Simplify 0 into 0 8.511 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.513 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 8.513 * [backup-simplify]: Simplify 0 into 0 8.514 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.514 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 8.514 * [backup-simplify]: Simplify 0 into 0 8.515 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.516 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 8.516 * [backup-simplify]: Simplify 0 into 0 8.517 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 8.519 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 8.519 * [backup-simplify]: Simplify 0 into 0 8.519 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.519 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 8.519 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 8.519 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.519 * [taylor]: Taking taylor expansion of 2.0 in n 8.519 * [backup-simplify]: Simplify 2.0 into 2.0 8.519 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.519 * [taylor]: Taking taylor expansion of PI in n 8.519 * [backup-simplify]: Simplify PI into PI 8.519 * [taylor]: Taking taylor expansion of n in n 8.519 * [backup-simplify]: Simplify 0 into 0 8.520 * [backup-simplify]: Simplify 1 into 1 8.520 * [backup-simplify]: Simplify (/ PI 1) into PI 8.520 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.520 * [taylor]: Taking taylor expansion of 2.0 in n 8.520 * [backup-simplify]: Simplify 2.0 into 2.0 8.520 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.520 * [taylor]: Taking taylor expansion of PI in n 8.520 * [backup-simplify]: Simplify PI into PI 8.520 * [taylor]: Taking taylor expansion of n in n 8.520 * [backup-simplify]: Simplify 0 into 0 8.520 * [backup-simplify]: Simplify 1 into 1 8.520 * [backup-simplify]: Simplify (/ PI 1) into PI 8.521 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.521 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.522 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.522 * [backup-simplify]: Simplify 0 into 0 8.523 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.523 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.523 * [backup-simplify]: Simplify 0 into 0 8.524 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.525 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.525 * [backup-simplify]: Simplify 0 into 0 8.525 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.526 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.526 * [backup-simplify]: Simplify 0 into 0 8.527 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.527 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.528 * [backup-simplify]: Simplify 0 into 0 8.528 * [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 8.529 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.529 * [backup-simplify]: Simplify 0 into 0 8.530 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 8.530 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 8.530 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 8.530 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.530 * [taylor]: Taking taylor expansion of -2.0 in n 8.530 * [backup-simplify]: Simplify -2.0 into -2.0 8.530 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.530 * [taylor]: Taking taylor expansion of PI in n 8.530 * [backup-simplify]: Simplify PI into PI 8.530 * [taylor]: Taking taylor expansion of n in n 8.530 * [backup-simplify]: Simplify 0 into 0 8.530 * [backup-simplify]: Simplify 1 into 1 8.531 * [backup-simplify]: Simplify (/ PI 1) into PI 8.531 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.531 * [taylor]: Taking taylor expansion of -2.0 in n 8.531 * [backup-simplify]: Simplify -2.0 into -2.0 8.531 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.531 * [taylor]: Taking taylor expansion of PI in n 8.531 * [backup-simplify]: Simplify PI into PI 8.531 * [taylor]: Taking taylor expansion of n in n 8.531 * [backup-simplify]: Simplify 0 into 0 8.531 * [backup-simplify]: Simplify 1 into 1 8.531 * [backup-simplify]: Simplify (/ PI 1) into PI 8.531 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.532 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.532 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.533 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.533 * [backup-simplify]: Simplify 0 into 0 8.533 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.534 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.534 * [backup-simplify]: Simplify 0 into 0 8.535 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.535 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.536 * [backup-simplify]: Simplify 0 into 0 8.536 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.537 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.537 * [backup-simplify]: Simplify 0 into 0 8.538 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.539 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.539 * [backup-simplify]: Simplify 0 into 0 8.539 * [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 8.540 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.540 * [backup-simplify]: Simplify 0 into 0 8.541 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 8.541 * * * * [progress]: [ 4 / 4 ] generating series at (2) 8.541 * [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))))) 8.541 * [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 8.541 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 8.541 * [taylor]: Taking taylor expansion of 1.0 in n 8.542 * [backup-simplify]: Simplify 1.0 into 1.0 8.542 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 8.542 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 8.542 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.542 * [taylor]: Taking taylor expansion of k in n 8.542 * [backup-simplify]: Simplify k into k 8.542 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.542 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 8.542 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.542 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 8.542 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.542 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.542 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.542 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.542 * [taylor]: Taking taylor expansion of 0.5 in n 8.542 * [backup-simplify]: Simplify 0.5 into 0.5 8.542 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.542 * [taylor]: Taking taylor expansion of 1.0 in n 8.542 * [backup-simplify]: Simplify 1.0 into 1.0 8.542 * [taylor]: Taking taylor expansion of k in n 8.542 * [backup-simplify]: Simplify k into k 8.542 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.542 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.542 * [taylor]: Taking taylor expansion of 2.0 in n 8.542 * [backup-simplify]: Simplify 2.0 into 2.0 8.542 * [taylor]: Taking taylor expansion of (* n PI) in n 8.542 * [taylor]: Taking taylor expansion of n in n 8.542 * [backup-simplify]: Simplify 0 into 0 8.542 * [backup-simplify]: Simplify 1 into 1 8.542 * [taylor]: Taking taylor expansion of PI in n 8.542 * [backup-simplify]: Simplify PI into PI 8.543 * [backup-simplify]: Simplify (* 0 PI) into 0 8.543 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.544 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.545 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.545 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.545 * [backup-simplify]: Simplify (- k) into (- k) 8.545 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.546 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.546 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.547 * [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)))) 8.548 * [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))))) 8.548 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 8.548 * [taylor]: Taking taylor expansion of 1.0 in k 8.548 * [backup-simplify]: Simplify 1.0 into 1.0 8.548 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 8.548 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.548 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.548 * [taylor]: Taking taylor expansion of k in k 8.548 * [backup-simplify]: Simplify 0 into 0 8.548 * [backup-simplify]: Simplify 1 into 1 8.548 * [backup-simplify]: Simplify (/ 1 1) into 1 8.549 * [backup-simplify]: Simplify (sqrt 0) into 0 8.550 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.550 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 8.550 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.550 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.550 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.550 * [taylor]: Taking taylor expansion of 0.5 in k 8.550 * [backup-simplify]: Simplify 0.5 into 0.5 8.550 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.550 * [taylor]: Taking taylor expansion of 1.0 in k 8.550 * [backup-simplify]: Simplify 1.0 into 1.0 8.550 * [taylor]: Taking taylor expansion of k in k 8.550 * [backup-simplify]: Simplify 0 into 0 8.550 * [backup-simplify]: Simplify 1 into 1 8.550 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.550 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.550 * [taylor]: Taking taylor expansion of 2.0 in k 8.550 * [backup-simplify]: Simplify 2.0 into 2.0 8.550 * [taylor]: Taking taylor expansion of (* n PI) in k 8.550 * [taylor]: Taking taylor expansion of n in k 8.550 * [backup-simplify]: Simplify n into n 8.550 * [taylor]: Taking taylor expansion of PI in k 8.550 * [backup-simplify]: Simplify PI into PI 8.550 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.550 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.550 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.550 * [backup-simplify]: Simplify (- 0) into 0 8.551 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.551 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.551 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 8.551 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 8.551 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 8.551 * [taylor]: Taking taylor expansion of 1.0 in k 8.551 * [backup-simplify]: Simplify 1.0 into 1.0 8.551 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 8.551 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.551 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.551 * [taylor]: Taking taylor expansion of k in k 8.551 * [backup-simplify]: Simplify 0 into 0 8.551 * [backup-simplify]: Simplify 1 into 1 8.552 * [backup-simplify]: Simplify (/ 1 1) into 1 8.552 * [backup-simplify]: Simplify (sqrt 0) into 0 8.553 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.553 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 8.554 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.554 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.554 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.554 * [taylor]: Taking taylor expansion of 0.5 in k 8.554 * [backup-simplify]: Simplify 0.5 into 0.5 8.554 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.554 * [taylor]: Taking taylor expansion of 1.0 in k 8.554 * [backup-simplify]: Simplify 1.0 into 1.0 8.554 * [taylor]: Taking taylor expansion of k in k 8.554 * [backup-simplify]: Simplify 0 into 0 8.554 * [backup-simplify]: Simplify 1 into 1 8.554 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.554 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.554 * [taylor]: Taking taylor expansion of 2.0 in k 8.554 * [backup-simplify]: Simplify 2.0 into 2.0 8.554 * [taylor]: Taking taylor expansion of (* n PI) in k 8.554 * [taylor]: Taking taylor expansion of n in k 8.554 * [backup-simplify]: Simplify n into n 8.554 * [taylor]: Taking taylor expansion of PI in k 8.554 * [backup-simplify]: Simplify PI into PI 8.554 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.554 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.554 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.555 * [backup-simplify]: Simplify (- 0) into 0 8.555 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.556 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.556 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 8.556 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 8.556 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 8.557 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.557 * [taylor]: Taking taylor expansion of 0 in n 8.557 * [backup-simplify]: Simplify 0 into 0 8.557 * [backup-simplify]: Simplify 0 into 0 8.557 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 8.558 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 8.559 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 8.559 * [backup-simplify]: Simplify (- 1) into -1 8.559 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.561 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 8.562 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 8.562 * [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))) 8.564 * [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))) 8.566 * [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))) 8.566 * [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 8.566 * [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 8.566 * [taylor]: Taking taylor expansion of +nan.0 in n 8.566 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.566 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 8.566 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 8.566 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 8.567 * [taylor]: Taking taylor expansion of 0.5 in n 8.567 * [backup-simplify]: Simplify 0.5 into 0.5 8.567 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 8.567 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 8.567 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.567 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.567 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.567 * [taylor]: Taking taylor expansion of 1.0 in n 8.567 * [backup-simplify]: Simplify 1.0 into 1.0 8.567 * [taylor]: Taking taylor expansion of (log PI) in n 8.567 * [taylor]: Taking taylor expansion of PI in n 8.567 * [backup-simplify]: Simplify PI into PI 8.567 * [backup-simplify]: Simplify (log PI) into (log PI) 8.568 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.570 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.570 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 8.570 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.570 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.570 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.570 * [taylor]: Taking taylor expansion of 1.0 in n 8.570 * [backup-simplify]: Simplify 1.0 into 1.0 8.570 * [taylor]: Taking taylor expansion of (log n) in n 8.570 * [taylor]: Taking taylor expansion of n in n 8.570 * [backup-simplify]: Simplify 0 into 0 8.570 * [backup-simplify]: Simplify 1 into 1 8.571 * [backup-simplify]: Simplify (log 1) into 0 8.571 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.571 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.571 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.572 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.572 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.572 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.572 * [taylor]: Taking taylor expansion of 1.0 in n 8.572 * [backup-simplify]: Simplify 1.0 into 1.0 8.572 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.572 * [taylor]: Taking taylor expansion of 2.0 in n 8.572 * [backup-simplify]: Simplify 2.0 into 2.0 8.572 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.578 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.580 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.580 * [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) 8.582 * [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) 8.583 * [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)) 8.584 * [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))) 8.586 * [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) 8.588 * [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)) 8.590 * [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))) 8.591 * [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))) 8.591 * [backup-simplify]: Simplify 0 into 0 8.592 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 8.593 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 8.595 * [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 8.595 * [backup-simplify]: Simplify (- 0) into 0 8.596 * [backup-simplify]: Simplify (+ 0 0) into 0 8.597 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 8.598 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 8.599 * [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))) 8.600 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.603 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.607 * [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)))))))) 8.612 * [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)))))))) 8.613 * [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 8.613 * [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 8.613 * [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 8.613 * [taylor]: Taking taylor expansion of +nan.0 in n 8.613 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.613 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 8.613 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 8.613 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 8.613 * [taylor]: Taking taylor expansion of 0.5 in n 8.613 * [backup-simplify]: Simplify 0.5 into 0.5 8.613 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 8.613 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 8.613 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.613 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.613 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.613 * [taylor]: Taking taylor expansion of 1.0 in n 8.613 * [backup-simplify]: Simplify 1.0 into 1.0 8.613 * [taylor]: Taking taylor expansion of (log PI) in n 8.613 * [taylor]: Taking taylor expansion of PI in n 8.613 * [backup-simplify]: Simplify PI into PI 8.614 * [backup-simplify]: Simplify (log PI) into (log PI) 8.615 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.616 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.617 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 8.617 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.617 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.617 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.617 * [taylor]: Taking taylor expansion of 1.0 in n 8.617 * [backup-simplify]: Simplify 1.0 into 1.0 8.617 * [taylor]: Taking taylor expansion of (log n) in n 8.617 * [taylor]: Taking taylor expansion of n in n 8.617 * [backup-simplify]: Simplify 0 into 0 8.617 * [backup-simplify]: Simplify 1 into 1 8.617 * [backup-simplify]: Simplify (log 1) into 0 8.618 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.618 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.618 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.618 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.618 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.618 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.618 * [taylor]: Taking taylor expansion of 1.0 in n 8.618 * [backup-simplify]: Simplify 1.0 into 1.0 8.618 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.618 * [taylor]: Taking taylor expansion of 2.0 in n 8.618 * [backup-simplify]: Simplify 2.0 into 2.0 8.619 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.619 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.621 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.622 * [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) 8.623 * [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) 8.624 * [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)) 8.625 * [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))) 8.626 * [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) 8.626 * [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 8.627 * [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 8.627 * [taylor]: Taking taylor expansion of +nan.0 in n 8.627 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.627 * [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 8.627 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 8.627 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 8.627 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 8.627 * [taylor]: Taking taylor expansion of 0.5 in n 8.627 * [backup-simplify]: Simplify 0.5 into 0.5 8.627 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 8.627 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 8.627 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.627 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.627 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.627 * [taylor]: Taking taylor expansion of 1.0 in n 8.627 * [backup-simplify]: Simplify 1.0 into 1.0 8.627 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.627 * [taylor]: Taking taylor expansion of 2.0 in n 8.627 * [backup-simplify]: Simplify 2.0 into 2.0 8.627 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.628 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.629 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.629 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 8.629 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.629 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.629 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.629 * [taylor]: Taking taylor expansion of 1.0 in n 8.629 * [backup-simplify]: Simplify 1.0 into 1.0 8.629 * [taylor]: Taking taylor expansion of (log PI) in n 8.629 * [taylor]: Taking taylor expansion of PI in n 8.629 * [backup-simplify]: Simplify PI into PI 8.629 * [backup-simplify]: Simplify (log PI) into (log PI) 8.630 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.631 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.631 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.631 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.631 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.631 * [taylor]: Taking taylor expansion of 1.0 in n 8.631 * [backup-simplify]: Simplify 1.0 into 1.0 8.631 * [taylor]: Taking taylor expansion of (log n) in n 8.631 * [taylor]: Taking taylor expansion of n in n 8.631 * [backup-simplify]: Simplify 0 into 0 8.631 * [backup-simplify]: Simplify 1 into 1 8.631 * [backup-simplify]: Simplify (log 1) into 0 8.632 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.632 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.632 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.632 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 8.633 * [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) 8.634 * [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)) 8.635 * [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))) 8.636 * [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) 8.636 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.636 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.636 * [taylor]: Taking taylor expansion of 2.0 in n 8.636 * [backup-simplify]: Simplify 2.0 into 2.0 8.636 * [taylor]: Taking taylor expansion of (* n PI) in n 8.636 * [taylor]: Taking taylor expansion of n in n 8.636 * [backup-simplify]: Simplify 0 into 0 8.636 * [backup-simplify]: Simplify 1 into 1 8.636 * [taylor]: Taking taylor expansion of PI in n 8.636 * [backup-simplify]: Simplify PI into PI 8.636 * [backup-simplify]: Simplify (* 0 PI) into 0 8.636 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.637 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.638 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.639 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.640 * [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)) 8.641 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.643 * [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)) 8.644 * [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))) 8.646 * [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)))))) 8.650 * [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)))))))) 8.654 * [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)))))))) 8.657 * [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)))))))) 8.659 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 8.660 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 8.662 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 8.664 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 8.664 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.665 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 8.666 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 8.667 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 8.668 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 8.669 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 8.671 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 8.673 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 8.675 * [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 8.677 * [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 8.679 * [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 8.681 * [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 8.682 * [backup-simplify]: Simplify (- 0) into 0 8.682 * [backup-simplify]: Simplify 0 into 0 8.682 * [backup-simplify]: Simplify 0 into 0 8.683 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.684 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 8.687 * [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 8.688 * [backup-simplify]: Simplify (- 0) into 0 8.688 * [backup-simplify]: Simplify (+ 0 0) into 0 8.689 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 8.690 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 8.691 * [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))) 8.692 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.694 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.698 * [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)))))))) 8.709 * [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)))))))) 8.709 * [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 8.709 * [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 8.709 * [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 8.709 * [taylor]: Taking taylor expansion of +nan.0 in n 8.709 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.709 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 8.709 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 8.709 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 8.709 * [taylor]: Taking taylor expansion of 0.5 in n 8.709 * [backup-simplify]: Simplify 0.5 into 0.5 8.709 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 8.709 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 8.709 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.709 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.709 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.709 * [taylor]: Taking taylor expansion of 1.0 in n 8.709 * [backup-simplify]: Simplify 1.0 into 1.0 8.709 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.709 * [taylor]: Taking taylor expansion of 2.0 in n 8.709 * [backup-simplify]: Simplify 2.0 into 2.0 8.710 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.710 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.711 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.711 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 8.711 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.711 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.711 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.711 * [taylor]: Taking taylor expansion of 1.0 in n 8.711 * [backup-simplify]: Simplify 1.0 into 1.0 8.711 * [taylor]: Taking taylor expansion of (log n) in n 8.711 * [taylor]: Taking taylor expansion of n in n 8.711 * [backup-simplify]: Simplify 0 into 0 8.711 * [backup-simplify]: Simplify 1 into 1 8.712 * [backup-simplify]: Simplify (log 1) into 0 8.712 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.712 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.712 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.712 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.712 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.712 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.712 * [taylor]: Taking taylor expansion of 1.0 in n 8.712 * [backup-simplify]: Simplify 1.0 into 1.0 8.712 * [taylor]: Taking taylor expansion of (log PI) in n 8.712 * [taylor]: Taking taylor expansion of PI in n 8.712 * [backup-simplify]: Simplify PI into PI 8.712 * [backup-simplify]: Simplify (log PI) into (log PI) 8.713 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.714 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.714 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 8.715 * [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) 8.716 * [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)) 8.717 * [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))) 8.718 * [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) 8.718 * [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 8.718 * [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 8.718 * [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 8.718 * [taylor]: Taking taylor expansion of +nan.0 in n 8.718 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.718 * [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 8.718 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 8.718 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 8.718 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 8.718 * [taylor]: Taking taylor expansion of 0.5 in n 8.718 * [backup-simplify]: Simplify 0.5 into 0.5 8.718 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 8.718 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 8.718 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.718 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.718 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.718 * [taylor]: Taking taylor expansion of 1.0 in n 8.718 * [backup-simplify]: Simplify 1.0 into 1.0 8.718 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.718 * [taylor]: Taking taylor expansion of 2.0 in n 8.718 * [backup-simplify]: Simplify 2.0 into 2.0 8.719 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.719 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.720 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.720 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 8.720 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.720 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.720 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.720 * [taylor]: Taking taylor expansion of 1.0 in n 8.720 * [backup-simplify]: Simplify 1.0 into 1.0 8.720 * [taylor]: Taking taylor expansion of (log PI) in n 8.720 * [taylor]: Taking taylor expansion of PI in n 8.720 * [backup-simplify]: Simplify PI into PI 8.720 * [backup-simplify]: Simplify (log PI) into (log PI) 8.721 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.722 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.722 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.722 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.722 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.722 * [taylor]: Taking taylor expansion of 1.0 in n 8.722 * [backup-simplify]: Simplify 1.0 into 1.0 8.722 * [taylor]: Taking taylor expansion of (log n) in n 8.722 * [taylor]: Taking taylor expansion of n in n 8.722 * [backup-simplify]: Simplify 0 into 0 8.722 * [backup-simplify]: Simplify 1 into 1 8.722 * [backup-simplify]: Simplify (log 1) into 0 8.723 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.723 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.723 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.724 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 8.724 * [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) 8.725 * [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)) 8.726 * [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))) 8.727 * [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) 8.727 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.727 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.727 * [taylor]: Taking taylor expansion of 2.0 in n 8.727 * [backup-simplify]: Simplify 2.0 into 2.0 8.727 * [taylor]: Taking taylor expansion of (* n PI) in n 8.727 * [taylor]: Taking taylor expansion of n in n 8.727 * [backup-simplify]: Simplify 0 into 0 8.727 * [backup-simplify]: Simplify 1 into 1 8.727 * [taylor]: Taking taylor expansion of PI in n 8.727 * [backup-simplify]: Simplify PI into PI 8.727 * [backup-simplify]: Simplify (* 0 PI) into 0 8.728 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.729 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.730 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.730 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.730 * [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 8.730 * [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 8.730 * [taylor]: Taking taylor expansion of +nan.0 in n 8.730 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.730 * [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 8.730 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 8.730 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 8.730 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 8.730 * [taylor]: Taking taylor expansion of 0.5 in n 8.730 * [backup-simplify]: Simplify 0.5 into 0.5 8.730 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 8.730 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 8.731 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.731 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.731 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.731 * [taylor]: Taking taylor expansion of 1.0 in n 8.731 * [backup-simplify]: Simplify 1.0 into 1.0 8.731 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.731 * [taylor]: Taking taylor expansion of 2.0 in n 8.731 * [backup-simplify]: Simplify 2.0 into 2.0 8.731 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.731 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.732 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.732 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 8.732 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.732 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.733 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.733 * [taylor]: Taking taylor expansion of 1.0 in n 8.733 * [backup-simplify]: Simplify 1.0 into 1.0 8.733 * [taylor]: Taking taylor expansion of (log PI) in n 8.733 * [taylor]: Taking taylor expansion of PI in n 8.733 * [backup-simplify]: Simplify PI into PI 8.733 * [backup-simplify]: Simplify (log PI) into (log PI) 8.733 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.734 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.734 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.735 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.735 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.735 * [taylor]: Taking taylor expansion of 1.0 in n 8.735 * [backup-simplify]: Simplify 1.0 into 1.0 8.735 * [taylor]: Taking taylor expansion of (log n) in n 8.735 * [taylor]: Taking taylor expansion of n in n 8.735 * [backup-simplify]: Simplify 0 into 0 8.735 * [backup-simplify]: Simplify 1 into 1 8.735 * [backup-simplify]: Simplify (log 1) into 0 8.735 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.735 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.735 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.736 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 8.737 * [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) 8.738 * [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)) 8.739 * [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))) 8.740 * [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) 8.740 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 8.740 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.740 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.740 * [taylor]: Taking taylor expansion of 2.0 in n 8.740 * [backup-simplify]: Simplify 2.0 into 2.0 8.740 * [taylor]: Taking taylor expansion of (* n PI) in n 8.740 * [taylor]: Taking taylor expansion of n in n 8.740 * [backup-simplify]: Simplify 0 into 0 8.740 * [backup-simplify]: Simplify 1 into 1 8.740 * [taylor]: Taking taylor expansion of PI in n 8.740 * [backup-simplify]: Simplify PI into PI 8.741 * [backup-simplify]: Simplify (* 0 PI) into 0 8.741 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.743 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.744 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.745 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.747 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.748 * [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)) 8.750 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.753 * [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)) 8.755 * [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))) 8.757 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.758 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.759 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 8.761 * [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)) 8.762 * [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))) 8.764 * [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)))))))) 8.771 * [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)))))))))))) 8.782 * [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)))))))))))) 8.796 * [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)))))))))))))) 8.807 * [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)))))))))))))) 8.821 * [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)))))))))))))) 8.841 * [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)))))))))))))))))))))) 8.842 * [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)))))) 8.843 * [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 8.843 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 8.843 * [taylor]: Taking taylor expansion of 1.0 in n 8.843 * [backup-simplify]: Simplify 1.0 into 1.0 8.843 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 8.843 * [taylor]: Taking taylor expansion of (sqrt k) in n 8.843 * [taylor]: Taking taylor expansion of k in n 8.843 * [backup-simplify]: Simplify k into k 8.843 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 8.843 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 8.843 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.843 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.843 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.843 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.843 * [taylor]: Taking taylor expansion of 0.5 in n 8.843 * [backup-simplify]: Simplify 0.5 into 0.5 8.843 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.843 * [taylor]: Taking taylor expansion of 1.0 in n 8.843 * [backup-simplify]: Simplify 1.0 into 1.0 8.843 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.843 * [taylor]: Taking taylor expansion of k in n 8.843 * [backup-simplify]: Simplify k into k 8.843 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.843 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.843 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.843 * [taylor]: Taking taylor expansion of 2.0 in n 8.844 * [backup-simplify]: Simplify 2.0 into 2.0 8.844 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.844 * [taylor]: Taking taylor expansion of PI in n 8.844 * [backup-simplify]: Simplify PI into PI 8.844 * [taylor]: Taking taylor expansion of n in n 8.844 * [backup-simplify]: Simplify 0 into 0 8.844 * [backup-simplify]: Simplify 1 into 1 8.845 * [backup-simplify]: Simplify (/ PI 1) into PI 8.845 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.846 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.846 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.846 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.846 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.848 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.849 * [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)))) 8.850 * [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))))) 8.850 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 8.850 * [taylor]: Taking taylor expansion of 1.0 in k 8.850 * [backup-simplify]: Simplify 1.0 into 1.0 8.850 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 8.850 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.850 * [taylor]: Taking taylor expansion of k in k 8.851 * [backup-simplify]: Simplify 0 into 0 8.851 * [backup-simplify]: Simplify 1 into 1 8.851 * [backup-simplify]: Simplify (sqrt 0) into 0 8.852 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.852 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.852 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.852 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.852 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.852 * [taylor]: Taking taylor expansion of 0.5 in k 8.853 * [backup-simplify]: Simplify 0.5 into 0.5 8.853 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.853 * [taylor]: Taking taylor expansion of 1.0 in k 8.853 * [backup-simplify]: Simplify 1.0 into 1.0 8.853 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.853 * [taylor]: Taking taylor expansion of k in k 8.853 * [backup-simplify]: Simplify 0 into 0 8.853 * [backup-simplify]: Simplify 1 into 1 8.853 * [backup-simplify]: Simplify (/ 1 1) into 1 8.853 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.853 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.853 * [taylor]: Taking taylor expansion of 2.0 in k 8.853 * [backup-simplify]: Simplify 2.0 into 2.0 8.853 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.853 * [taylor]: Taking taylor expansion of PI in k 8.853 * [backup-simplify]: Simplify PI into PI 8.853 * [taylor]: Taking taylor expansion of n in k 8.853 * [backup-simplify]: Simplify n into n 8.853 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.854 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.854 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.854 * [backup-simplify]: Simplify (- 1) into -1 8.854 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.855 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.855 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 8.855 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 8.855 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 8.855 * [taylor]: Taking taylor expansion of 1.0 in k 8.855 * [backup-simplify]: Simplify 1.0 into 1.0 8.855 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 8.856 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.856 * [taylor]: Taking taylor expansion of k in k 8.856 * [backup-simplify]: Simplify 0 into 0 8.856 * [backup-simplify]: Simplify 1 into 1 8.856 * [backup-simplify]: Simplify (sqrt 0) into 0 8.857 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.857 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.857 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.857 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.857 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.857 * [taylor]: Taking taylor expansion of 0.5 in k 8.857 * [backup-simplify]: Simplify 0.5 into 0.5 8.857 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.857 * [taylor]: Taking taylor expansion of 1.0 in k 8.857 * [backup-simplify]: Simplify 1.0 into 1.0 8.857 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.857 * [taylor]: Taking taylor expansion of k in k 8.857 * [backup-simplify]: Simplify 0 into 0 8.857 * [backup-simplify]: Simplify 1 into 1 8.858 * [backup-simplify]: Simplify (/ 1 1) into 1 8.858 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.858 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.858 * [taylor]: Taking taylor expansion of 2.0 in k 8.858 * [backup-simplify]: Simplify 2.0 into 2.0 8.858 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.858 * [taylor]: Taking taylor expansion of PI in k 8.858 * [backup-simplify]: Simplify PI into PI 8.858 * [taylor]: Taking taylor expansion of n in k 8.858 * [backup-simplify]: Simplify n into n 8.858 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.858 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.858 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.858 * [backup-simplify]: Simplify (- 1) into -1 8.859 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.859 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.859 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 8.859 * [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))))) 8.859 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 8.860 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.860 * [taylor]: Taking taylor expansion of 0 in n 8.860 * [backup-simplify]: Simplify 0 into 0 8.860 * [backup-simplify]: Simplify 0 into 0 8.860 * [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))))))) 8.860 * [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))))))) 8.860 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 8.861 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 8.861 * [taylor]: Taking taylor expansion of +nan.0 in n 8.861 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.861 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 8.861 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 8.861 * [taylor]: Taking taylor expansion of 0.5 in n 8.861 * [backup-simplify]: Simplify 0.5 into 0.5 8.861 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 8.861 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.861 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.861 * [taylor]: Taking taylor expansion of 2.0 in n 8.861 * [backup-simplify]: Simplify 2.0 into 2.0 8.861 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.861 * [taylor]: Taking taylor expansion of PI in n 8.861 * [backup-simplify]: Simplify PI into PI 8.861 * [taylor]: Taking taylor expansion of n in n 8.861 * [backup-simplify]: Simplify 0 into 0 8.861 * [backup-simplify]: Simplify 1 into 1 8.861 * [backup-simplify]: Simplify (/ PI 1) into PI 8.861 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.862 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.862 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.862 * [taylor]: Taking taylor expansion of 1.0 in n 8.862 * [backup-simplify]: Simplify 1.0 into 1.0 8.862 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.862 * [taylor]: Taking taylor expansion of k in n 8.862 * [backup-simplify]: Simplify k into k 8.862 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.863 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.863 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.863 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.864 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 8.865 * [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)))) 8.865 * [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))))) 8.866 * [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)))))) 8.867 * [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))))))) 8.868 * [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))))))) 8.868 * [backup-simplify]: Simplify 0 into 0 8.870 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.870 * [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))))))) 8.871 * [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))))))) 8.871 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 8.871 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 8.871 * [taylor]: Taking taylor expansion of +nan.0 in n 8.871 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.871 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 8.871 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 8.871 * [taylor]: Taking taylor expansion of 0.5 in n 8.871 * [backup-simplify]: Simplify 0.5 into 0.5 8.871 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 8.871 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.871 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.871 * [taylor]: Taking taylor expansion of 2.0 in n 8.871 * [backup-simplify]: Simplify 2.0 into 2.0 8.871 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.871 * [taylor]: Taking taylor expansion of PI in n 8.871 * [backup-simplify]: Simplify PI into PI 8.871 * [taylor]: Taking taylor expansion of n in n 8.871 * [backup-simplify]: Simplify 0 into 0 8.871 * [backup-simplify]: Simplify 1 into 1 8.872 * [backup-simplify]: Simplify (/ PI 1) into PI 8.872 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.873 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.873 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.873 * [taylor]: Taking taylor expansion of 1.0 in n 8.873 * [backup-simplify]: Simplify 1.0 into 1.0 8.873 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.873 * [taylor]: Taking taylor expansion of k in n 8.873 * [backup-simplify]: Simplify k into k 8.873 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.874 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.874 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.874 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.875 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 8.876 * [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)))) 8.876 * [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))))) 8.877 * [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)))))) 8.878 * [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))))))) 8.879 * [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))))))) 8.880 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.880 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.880 * [backup-simplify]: Simplify (- 0) into 0 8.880 * [backup-simplify]: Simplify (+ 0 0) into 0 8.881 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.881 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.883 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.883 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.884 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 8.886 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.887 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 8.887 * [backup-simplify]: Simplify (- 0) into 0 8.887 * [backup-simplify]: Simplify 0 into 0 8.887 * [backup-simplify]: Simplify 0 into 0 8.890 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.892 * [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))))))) 8.893 * [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))))))) 8.894 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 8.894 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 8.894 * [taylor]: Taking taylor expansion of +nan.0 in n 8.894 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.894 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 8.894 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 8.894 * [taylor]: Taking taylor expansion of 0.5 in n 8.894 * [backup-simplify]: Simplify 0.5 into 0.5 8.894 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 8.894 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.894 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.894 * [taylor]: Taking taylor expansion of 2.0 in n 8.894 * [backup-simplify]: Simplify 2.0 into 2.0 8.894 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.894 * [taylor]: Taking taylor expansion of PI in n 8.894 * [backup-simplify]: Simplify PI into PI 8.894 * [taylor]: Taking taylor expansion of n in n 8.894 * [backup-simplify]: Simplify 0 into 0 8.894 * [backup-simplify]: Simplify 1 into 1 8.895 * [backup-simplify]: Simplify (/ PI 1) into PI 8.895 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.897 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.897 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.897 * [taylor]: Taking taylor expansion of 1.0 in n 8.897 * [backup-simplify]: Simplify 1.0 into 1.0 8.897 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.897 * [taylor]: Taking taylor expansion of k in n 8.897 * [backup-simplify]: Simplify k into k 8.897 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.899 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.899 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.899 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.900 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 8.901 * [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)))) 8.903 * [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))))) 8.904 * [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)))))) 8.905 * [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))))))) 8.907 * [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))))))) 8.912 * [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)))))))) 8.913 * [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)))) 8.913 * [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 8.913 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 8.913 * [taylor]: Taking taylor expansion of 1.0 in n 8.913 * [backup-simplify]: Simplify 1.0 into 1.0 8.913 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 8.913 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.913 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.913 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.913 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.913 * [taylor]: Taking taylor expansion of 0.5 in n 8.913 * [backup-simplify]: Simplify 0.5 into 0.5 8.913 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.914 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.914 * [taylor]: Taking taylor expansion of k in n 8.914 * [backup-simplify]: Simplify k into k 8.914 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.914 * [taylor]: Taking taylor expansion of 1.0 in n 8.914 * [backup-simplify]: Simplify 1.0 into 1.0 8.914 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.914 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.914 * [taylor]: Taking taylor expansion of -2.0 in n 8.914 * [backup-simplify]: Simplify -2.0 into -2.0 8.914 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.914 * [taylor]: Taking taylor expansion of PI in n 8.914 * [backup-simplify]: Simplify PI into PI 8.914 * [taylor]: Taking taylor expansion of n in n 8.914 * [backup-simplify]: Simplify 0 into 0 8.914 * [backup-simplify]: Simplify 1 into 1 8.915 * [backup-simplify]: Simplify (/ PI 1) into PI 8.915 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.916 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.916 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.916 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.918 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.919 * [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)))) 8.921 * [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))))) 8.921 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 8.921 * [taylor]: Taking taylor expansion of (/ -1 k) in n 8.921 * [taylor]: Taking taylor expansion of -1 in n 8.921 * [backup-simplify]: Simplify -1 into -1 8.921 * [taylor]: Taking taylor expansion of k in n 8.921 * [backup-simplify]: Simplify k into k 8.921 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 8.921 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 8.921 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 8.921 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 8.923 * [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))) 8.923 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 8.923 * [taylor]: Taking taylor expansion of 1.0 in k 8.923 * [backup-simplify]: Simplify 1.0 into 1.0 8.923 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 8.923 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.923 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.923 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.923 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.923 * [taylor]: Taking taylor expansion of 0.5 in k 8.923 * [backup-simplify]: Simplify 0.5 into 0.5 8.923 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.923 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.923 * [taylor]: Taking taylor expansion of k in k 8.923 * [backup-simplify]: Simplify 0 into 0 8.923 * [backup-simplify]: Simplify 1 into 1 8.924 * [backup-simplify]: Simplify (/ 1 1) into 1 8.924 * [taylor]: Taking taylor expansion of 1.0 in k 8.924 * [backup-simplify]: Simplify 1.0 into 1.0 8.924 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.924 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.924 * [taylor]: Taking taylor expansion of -2.0 in k 8.924 * [backup-simplify]: Simplify -2.0 into -2.0 8.924 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.924 * [taylor]: Taking taylor expansion of PI in k 8.924 * [backup-simplify]: Simplify PI into PI 8.924 * [taylor]: Taking taylor expansion of n in k 8.924 * [backup-simplify]: Simplify n into n 8.924 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.925 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.925 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.925 * [backup-simplify]: Simplify (+ 1 0) into 1 8.926 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.926 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 8.926 * [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)))))) 8.926 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.926 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.926 * [taylor]: Taking taylor expansion of -1 in k 8.926 * [backup-simplify]: Simplify -1 into -1 8.926 * [taylor]: Taking taylor expansion of k in k 8.926 * [backup-simplify]: Simplify 0 into 0 8.926 * [backup-simplify]: Simplify 1 into 1 8.927 * [backup-simplify]: Simplify (/ -1 1) into -1 8.927 * [backup-simplify]: Simplify (sqrt 0) into 0 8.929 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.929 * [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))))))) 8.929 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 8.929 * [taylor]: Taking taylor expansion of 1.0 in k 8.929 * [backup-simplify]: Simplify 1.0 into 1.0 8.929 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 8.929 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.929 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.929 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.929 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.929 * [taylor]: Taking taylor expansion of 0.5 in k 8.930 * [backup-simplify]: Simplify 0.5 into 0.5 8.930 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.930 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.930 * [taylor]: Taking taylor expansion of k in k 8.930 * [backup-simplify]: Simplify 0 into 0 8.930 * [backup-simplify]: Simplify 1 into 1 8.930 * [backup-simplify]: Simplify (/ 1 1) into 1 8.930 * [taylor]: Taking taylor expansion of 1.0 in k 8.930 * [backup-simplify]: Simplify 1.0 into 1.0 8.930 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.930 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.930 * [taylor]: Taking taylor expansion of -2.0 in k 8.930 * [backup-simplify]: Simplify -2.0 into -2.0 8.930 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.930 * [taylor]: Taking taylor expansion of PI in k 8.930 * [backup-simplify]: Simplify PI into PI 8.931 * [taylor]: Taking taylor expansion of n in k 8.931 * [backup-simplify]: Simplify n into n 8.931 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.931 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.931 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.931 * [backup-simplify]: Simplify (+ 1 0) into 1 8.932 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.932 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 8.932 * [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)))))) 8.932 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.932 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.932 * [taylor]: Taking taylor expansion of -1 in k 8.932 * [backup-simplify]: Simplify -1 into -1 8.932 * [taylor]: Taking taylor expansion of k in k 8.932 * [backup-simplify]: Simplify 0 into 0 8.933 * [backup-simplify]: Simplify 1 into 1 8.933 * [backup-simplify]: Simplify (/ -1 1) into -1 8.933 * [backup-simplify]: Simplify (sqrt 0) into 0 8.935 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.935 * [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))))))) 8.936 * [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))))))) 8.936 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 8.936 * [taylor]: Taking taylor expansion of +nan.0 in n 8.936 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.936 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 8.936 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 8.936 * [taylor]: Taking taylor expansion of 0.5 in n 8.936 * [backup-simplify]: Simplify 0.5 into 0.5 8.936 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 8.936 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.936 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.936 * [taylor]: Taking taylor expansion of k in n 8.936 * [backup-simplify]: Simplify k into k 8.936 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.936 * [taylor]: Taking taylor expansion of 1.0 in n 8.936 * [backup-simplify]: Simplify 1.0 into 1.0 8.936 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.936 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.936 * [taylor]: Taking taylor expansion of -2.0 in n 8.936 * [backup-simplify]: Simplify -2.0 into -2.0 8.936 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.936 * [taylor]: Taking taylor expansion of PI in n 8.936 * [backup-simplify]: Simplify PI into PI 8.936 * [taylor]: Taking taylor expansion of n in n 8.936 * [backup-simplify]: Simplify 0 into 0 8.936 * [backup-simplify]: Simplify 1 into 1 8.937 * [backup-simplify]: Simplify (/ PI 1) into PI 8.938 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.939 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.939 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.945 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.946 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 8.947 * [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)))) 8.948 * [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))))) 8.949 * [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)))))) 8.949 * [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)))))) 8.950 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.952 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.953 * [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)))))))) 8.953 * [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)))))))) 8.953 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 8.953 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 8.953 * [taylor]: Taking taylor expansion of +nan.0 in n 8.953 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.953 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 8.953 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 8.953 * [taylor]: Taking taylor expansion of 0.5 in n 8.953 * [backup-simplify]: Simplify 0.5 into 0.5 8.953 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 8.953 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.953 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.953 * [taylor]: Taking taylor expansion of k in n 8.953 * [backup-simplify]: Simplify k into k 8.953 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.953 * [taylor]: Taking taylor expansion of 1.0 in n 8.953 * [backup-simplify]: Simplify 1.0 into 1.0 8.953 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.953 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.953 * [taylor]: Taking taylor expansion of -2.0 in n 8.953 * [backup-simplify]: Simplify -2.0 into -2.0 8.953 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.954 * [taylor]: Taking taylor expansion of PI in n 8.954 * [backup-simplify]: Simplify PI into PI 8.954 * [taylor]: Taking taylor expansion of n in n 8.954 * [backup-simplify]: Simplify 0 into 0 8.954 * [backup-simplify]: Simplify 1 into 1 8.954 * [backup-simplify]: Simplify (/ PI 1) into PI 8.954 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.955 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.955 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.956 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.957 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 8.957 * [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)))) 8.958 * [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))))) 8.959 * [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)))))) 8.960 * [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))))))) 8.961 * [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))))))) 8.961 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.962 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.963 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.963 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.963 * [backup-simplify]: Simplify (+ 0 0) into 0 8.964 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.965 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.966 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 8.967 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.968 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 8.968 * [backup-simplify]: Simplify 0 into 0 8.969 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.971 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.972 * [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)))))))) 8.973 * [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)))))))) 8.973 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 8.973 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 8.973 * [taylor]: Taking taylor expansion of +nan.0 in n 8.973 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.973 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 8.973 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 8.973 * [taylor]: Taking taylor expansion of 0.5 in n 8.973 * [backup-simplify]: Simplify 0.5 into 0.5 8.973 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 8.973 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.973 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.973 * [taylor]: Taking taylor expansion of k in n 8.973 * [backup-simplify]: Simplify k into k 8.974 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.974 * [taylor]: Taking taylor expansion of 1.0 in n 8.974 * [backup-simplify]: Simplify 1.0 into 1.0 8.974 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.974 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.974 * [taylor]: Taking taylor expansion of -2.0 in n 8.974 * [backup-simplify]: Simplify -2.0 into -2.0 8.974 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.974 * [taylor]: Taking taylor expansion of PI in n 8.974 * [backup-simplify]: Simplify PI into PI 8.974 * [taylor]: Taking taylor expansion of n in n 8.974 * [backup-simplify]: Simplify 0 into 0 8.974 * [backup-simplify]: Simplify 1 into 1 8.975 * [backup-simplify]: Simplify (/ PI 1) into PI 8.975 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.976 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.977 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.978 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.979 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 8.981 * [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)))) 8.982 * [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))))) 8.983 * [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)))))) 8.985 * [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))))))) 8.986 * [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))))))) 8.991 * [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)))))))))))) 8.991 * * * [progress]: simplifying candidates 8.996 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 9.006 * * [simplify]: Extracting # 0 : cost 0 9.007 * * [simplify]: Extracting # 1 : cost 0 9.007 * * [simplify]: Extracting # 2 : cost 0 9.008 * * [simplify]: Extracting # 3 : cost 0 9.009 * * [simplify]: Extracting # 4 : cost 0 9.010 * * [simplify]: Extracting # 5 : cost 0 9.011 * * [simplify]: Extracting # 6 : cost 0 9.012 * * [simplify]: Extracting # 7 : cost 0 9.013 * * [simplify]: Extracting # 8 : cost 0 9.013 * * [simplify]: Extracting # 9 : cost 0 9.014 * * [simplify]: Extracting # 10 : cost 0 9.014 * * [simplify]: Extracting # 11 : cost 0 9.015 * * [simplify]: Extracting # 12 : cost 0 9.016 * * [simplify]: Extracting # 13 : cost 0 9.016 * * [simplify]: Extracting # 14 : cost 0 9.017 * * [simplify]: Extracting # 15 : cost 0 9.018 * * [simplify]: Extracting # 16 : cost 0 9.019 * * [simplify]: Extracting # 17 : cost 0 9.020 * * [simplify]: Extracting # 18 : cost 0 9.021 * * [simplify]: Extracting # 19 : cost 0 9.022 * * [simplify]: Extracting # 20 : cost 0 9.023 * * [simplify]: Extracting # 21 : cost 0 9.025 * * [simplify]: Extracting # 22 : cost 0 9.026 * * [simplify]: Extracting # 23 : cost 0 9.027 * * [simplify]: Extracting # 24 : cost 0 9.028 * * [simplify]: Extracting # 25 : cost 0 9.029 * * [simplify]: Extracting # 26 : cost 0 9.030 * * [simplify]: Extracting # 27 : cost 0 9.031 * * [simplify]: Extracting # 28 : cost 0 9.032 * * [simplify]: Extracting # 29 : cost 0 9.033 * * [simplify]: Extracting # 30 : cost 0 9.035 * * [simplify]: Extracting # 31 : cost 0 9.036 * * [simplify]: Extracting # 32 : cost 0 9.037 * * [simplify]: iteration 0 : 369 enodes (cost 2880 ) 9.711 * * [simplify]: Extracting # 0 : cost 0 9.720 * * [simplify]: Extracting # 1 : cost 0 9.733 * * [simplify]: Extracting # 2 : cost 0 9.745 * * [simplify]: Extracting # 3 : cost 0 9.756 * * [simplify]: Extracting # 4 : cost 0 9.767 * * [simplify]: Extracting # 5 : cost 0 9.782 * * [simplify]: Extracting # 6 : cost 0 9.793 * * [simplify]: Extracting # 7 : cost 0 9.804 * * [simplify]: Extracting # 8 : cost 0 9.815 * * [simplify]: iteration 1 : 4100 enodes (cost 2706 ) 11.549 * * [simplify]: Extracting # 0 : cost 0 11.556 * * [simplify]: Extracting # 1 : cost 0 11.563 * * [simplify]: Extracting # 2 : cost 0 11.569 * * [simplify]: Extracting # 3 : cost 0 11.575 * * [simplify]: Extracting # 4 : cost 0 11.582 * * [simplify]: Extracting # 5 : cost 0 11.591 * * [simplify]: Extracting # 6 : cost 0 11.598 * * [simplify]: iteration done: 5001 enodes (cost 2568 ) 11.600 * [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 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 (* 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))) (* 2.0 (* n 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))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (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 (* (* 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 PI) n) (/ (- 1.0 k) 2.0)) 3) (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 (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 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (log (* 2.0 (* n PI))) (log (* 2.0 (* n PI))) (log (* 2.0 (* n 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 1.0 3) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 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))) (* (/ 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))) (- (fma (* (pow (* 2.0 (* n PI)) 0.5) (* (pow k 2) (pow (log (* 2.0 PI)) 2))) 0.125 (fma (* 0.125 (pow k 2)) (* (pow (* 2.0 (* n PI)) 0.5) (pow (log n) 2)) (fma (* 0.25 (pow k 2)) (* (log n) (* (pow (* 2.0 (* n PI)) 0.5) (log (* 2.0 PI)))) (pow (* 2.0 (* n PI)) 0.5)))) (* (fma (* k (log (* 2.0 PI))) (pow (* 2.0 (* n PI)) 0.5) (* (* k (pow (* 2.0 (* n PI)) 0.5)) (log n))) 0.5)) (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (fma +nan.0 k (- (- (* +nan.0 (pow k 2)) +nan.0)))) (- (fma +nan.0 (/ 1 (pow k 2)) (- (* (+ (/ 1 k) (- (/ 1 (pow k 3)))) +nan.0)))) (- (- (* +nan.0 (/ 1 (pow k 2))) (fma +nan.0 (/ 1 k) (- +nan.0)))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (- (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (* +nan.0 (fma (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2) (- (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) (- (- (* (/ +nan.0 (pow k 3)) (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k))) (* (+ (/ (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) k) (- (/ (/ (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) k) k))) +nan.0))) (- (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (* (+ (/ (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)))))))) +nan.0))) 11.601 * * * [progress]: adding candidates to table 12.311 * * [progress]: iteration 2 / 4 12.311 * * * [progress]: picking best candidate 12.339 * * * * [pick]: Picked # 12.339 * * * [progress]: localizing error 12.367 * * * [progress]: generating rewritten candidates 12.367 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 12.420 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 12.456 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 12.463 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 12.495 * * * [progress]: generating series expansions 12.496 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 12.497 * [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))) 12.497 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 12.497 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 12.497 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.497 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.497 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 12.497 * [taylor]: Taking taylor expansion of 0.25 in k 12.497 * [backup-simplify]: Simplify 0.25 into 0.25 12.497 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.497 * [taylor]: Taking taylor expansion of 1.0 in k 12.497 * [backup-simplify]: Simplify 1.0 into 1.0 12.497 * [taylor]: Taking taylor expansion of k in k 12.497 * [backup-simplify]: Simplify 0 into 0 12.497 * [backup-simplify]: Simplify 1 into 1 12.497 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.497 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.497 * [taylor]: Taking taylor expansion of 2.0 in k 12.497 * [backup-simplify]: Simplify 2.0 into 2.0 12.498 * [taylor]: Taking taylor expansion of (* n PI) in k 12.498 * [taylor]: Taking taylor expansion of n in k 12.498 * [backup-simplify]: Simplify n into n 12.498 * [taylor]: Taking taylor expansion of PI in k 12.498 * [backup-simplify]: Simplify PI into PI 12.498 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.498 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.498 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.499 * [backup-simplify]: Simplify (- 0) into 0 12.499 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.500 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 12.500 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 12.500 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 12.500 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.500 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.500 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.500 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.500 * [taylor]: Taking taylor expansion of 0.25 in n 12.500 * [backup-simplify]: Simplify 0.25 into 0.25 12.500 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.500 * [taylor]: Taking taylor expansion of 1.0 in n 12.500 * [backup-simplify]: Simplify 1.0 into 1.0 12.501 * [taylor]: Taking taylor expansion of k in n 12.501 * [backup-simplify]: Simplify k into k 12.501 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.501 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.501 * [taylor]: Taking taylor expansion of 2.0 in n 12.501 * [backup-simplify]: Simplify 2.0 into 2.0 12.501 * [taylor]: Taking taylor expansion of (* n PI) in n 12.501 * [taylor]: Taking taylor expansion of n in n 12.501 * [backup-simplify]: Simplify 0 into 0 12.501 * [backup-simplify]: Simplify 1 into 1 12.501 * [taylor]: Taking taylor expansion of PI in n 12.501 * [backup-simplify]: Simplify PI into PI 12.502 * [backup-simplify]: Simplify (* 0 PI) into 0 12.502 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.504 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.506 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.507 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.507 * [backup-simplify]: Simplify (- k) into (- k) 12.507 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.507 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.509 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.510 * [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)))) 12.512 * [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))))) 12.512 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.512 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.512 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.512 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.512 * [taylor]: Taking taylor expansion of 0.25 in n 12.512 * [backup-simplify]: Simplify 0.25 into 0.25 12.512 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.512 * [taylor]: Taking taylor expansion of 1.0 in n 12.512 * [backup-simplify]: Simplify 1.0 into 1.0 12.512 * [taylor]: Taking taylor expansion of k in n 12.512 * [backup-simplify]: Simplify k into k 12.512 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.512 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.512 * [taylor]: Taking taylor expansion of 2.0 in n 12.512 * [backup-simplify]: Simplify 2.0 into 2.0 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 12.513 * [backup-simplify]: Simplify (* 0 PI) into 0 12.513 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.515 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.517 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.518 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.518 * [backup-simplify]: Simplify (- k) into (- k) 12.519 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.519 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.520 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.521 * [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)))) 12.522 * [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))))) 12.523 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.523 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.523 * [taylor]: Taking taylor expansion of 0.25 in k 12.523 * [backup-simplify]: Simplify 0.25 into 0.25 12.523 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.523 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.523 * [taylor]: Taking taylor expansion of 1.0 in k 12.523 * [backup-simplify]: Simplify 1.0 into 1.0 12.523 * [taylor]: Taking taylor expansion of k in k 12.523 * [backup-simplify]: Simplify 0 into 0 12.523 * [backup-simplify]: Simplify 1 into 1 12.523 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.523 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.523 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.523 * [taylor]: Taking taylor expansion of 2.0 in k 12.523 * [backup-simplify]: Simplify 2.0 into 2.0 12.523 * [taylor]: Taking taylor expansion of PI in k 12.523 * [backup-simplify]: Simplify PI into PI 12.524 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.525 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.525 * [taylor]: Taking taylor expansion of (log n) in k 12.525 * [taylor]: Taking taylor expansion of n in k 12.525 * [backup-simplify]: Simplify n into n 12.525 * [backup-simplify]: Simplify (log n) into (log n) 12.525 * [backup-simplify]: Simplify (- 0) into 0 12.526 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.527 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.528 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.529 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 12.530 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.532 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.533 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.534 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.536 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.536 * [backup-simplify]: Simplify (- 0) into 0 12.536 * [backup-simplify]: Simplify (+ 0 0) into 0 12.537 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 12.539 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.540 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.542 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.542 * [taylor]: Taking taylor expansion of 0 in k 12.542 * [backup-simplify]: Simplify 0 into 0 12.542 * [backup-simplify]: Simplify 0 into 0 12.543 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.545 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.546 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.546 * [backup-simplify]: Simplify (+ 0 0) into 0 12.547 * [backup-simplify]: Simplify (- 1) into -1 12.547 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.549 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.551 * [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)))) 12.555 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 12.558 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 12.559 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.560 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.564 * [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 12.565 * [backup-simplify]: Simplify (- 0) into 0 12.565 * [backup-simplify]: Simplify (+ 0 0) into 0 12.566 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.568 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.569 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.571 * [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 12.571 * [taylor]: Taking taylor expansion of 0 in k 12.571 * [backup-simplify]: Simplify 0 into 0 12.571 * [backup-simplify]: Simplify 0 into 0 12.571 * [backup-simplify]: Simplify 0 into 0 12.571 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.573 * [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 12.574 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.575 * [backup-simplify]: Simplify (+ 0 0) into 0 12.575 * [backup-simplify]: Simplify (- 0) into 0 12.575 * [backup-simplify]: Simplify (+ 0 0) into 0 12.576 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.578 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.580 * [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))))) 12.584 * [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))))) 12.590 * [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)))))) 12.590 * [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)))) 12.590 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 12.590 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 12.590 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.590 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.590 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 12.590 * [taylor]: Taking taylor expansion of 0.25 in k 12.590 * [backup-simplify]: Simplify 0.25 into 0.25 12.590 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.590 * [taylor]: Taking taylor expansion of 1.0 in k 12.590 * [backup-simplify]: Simplify 1.0 into 1.0 12.590 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.590 * [taylor]: Taking taylor expansion of k in k 12.590 * [backup-simplify]: Simplify 0 into 0 12.591 * [backup-simplify]: Simplify 1 into 1 12.591 * [backup-simplify]: Simplify (/ 1 1) into 1 12.591 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.591 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.591 * [taylor]: Taking taylor expansion of 2.0 in k 12.591 * [backup-simplify]: Simplify 2.0 into 2.0 12.591 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.591 * [taylor]: Taking taylor expansion of PI in k 12.591 * [backup-simplify]: Simplify PI into PI 12.591 * [taylor]: Taking taylor expansion of n in k 12.591 * [backup-simplify]: Simplify n into n 12.591 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.591 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.591 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.591 * [backup-simplify]: Simplify (- 1) into -1 12.592 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.592 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 12.592 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 12.592 * [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))))) 12.592 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.592 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.592 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.592 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.592 * [taylor]: Taking taylor expansion of 0.25 in n 12.592 * [backup-simplify]: Simplify 0.25 into 0.25 12.592 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.592 * [taylor]: Taking taylor expansion of 1.0 in n 12.592 * [backup-simplify]: Simplify 1.0 into 1.0 12.592 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.592 * [taylor]: Taking taylor expansion of k in n 12.592 * [backup-simplify]: Simplify k into k 12.592 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.593 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.593 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.593 * [taylor]: Taking taylor expansion of 2.0 in n 12.593 * [backup-simplify]: Simplify 2.0 into 2.0 12.593 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.593 * [taylor]: Taking taylor expansion of PI in n 12.593 * [backup-simplify]: Simplify PI into PI 12.593 * [taylor]: Taking taylor expansion of n in n 12.593 * [backup-simplify]: Simplify 0 into 0 12.593 * [backup-simplify]: Simplify 1 into 1 12.593 * [backup-simplify]: Simplify (/ PI 1) into PI 12.593 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.601 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.601 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.601 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.601 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.602 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.603 * [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)))) 12.604 * [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))))) 12.604 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.604 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.604 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.604 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.604 * [taylor]: Taking taylor expansion of 0.25 in n 12.604 * [backup-simplify]: Simplify 0.25 into 0.25 12.604 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.604 * [taylor]: Taking taylor expansion of 1.0 in n 12.604 * [backup-simplify]: Simplify 1.0 into 1.0 12.604 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.604 * [taylor]: Taking taylor expansion of k in n 12.604 * [backup-simplify]: Simplify k into k 12.604 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.604 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.604 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.604 * [taylor]: Taking taylor expansion of 2.0 in n 12.604 * [backup-simplify]: Simplify 2.0 into 2.0 12.604 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.604 * [taylor]: Taking taylor expansion of PI in n 12.604 * [backup-simplify]: Simplify PI into PI 12.604 * [taylor]: Taking taylor expansion of n in n 12.605 * [backup-simplify]: Simplify 0 into 0 12.605 * [backup-simplify]: Simplify 1 into 1 12.605 * [backup-simplify]: Simplify (/ PI 1) into PI 12.605 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.606 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.606 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.606 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.607 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.608 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.609 * [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)))) 12.610 * [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))))) 12.610 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.610 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.610 * [taylor]: Taking taylor expansion of 0.25 in k 12.610 * [backup-simplify]: Simplify 0.25 into 0.25 12.610 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.610 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.611 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.611 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.611 * [taylor]: Taking taylor expansion of 2.0 in k 12.611 * [backup-simplify]: Simplify 2.0 into 2.0 12.611 * [taylor]: Taking taylor expansion of PI in k 12.611 * [backup-simplify]: Simplify PI into PI 12.611 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.612 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.612 * [taylor]: Taking taylor expansion of (log n) in k 12.612 * [taylor]: Taking taylor expansion of n in k 12.612 * [backup-simplify]: Simplify n into n 12.612 * [backup-simplify]: Simplify (log n) into (log n) 12.612 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.612 * [taylor]: Taking taylor expansion of 1.0 in k 12.612 * [backup-simplify]: Simplify 1.0 into 1.0 12.612 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.612 * [taylor]: Taking taylor expansion of k in k 12.612 * [backup-simplify]: Simplify 0 into 0 12.612 * [backup-simplify]: Simplify 1 into 1 12.613 * [backup-simplify]: Simplify (/ 1 1) into 1 12.613 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.614 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.614 * [backup-simplify]: Simplify (- 1) into -1 12.614 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.615 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.616 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 12.618 * [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))))) 12.619 * [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))))) 12.620 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.621 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.622 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.622 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.623 * [backup-simplify]: Simplify (- 0) into 0 12.623 * [backup-simplify]: Simplify (+ 0 0) into 0 12.624 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.625 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.626 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.627 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.627 * [taylor]: Taking taylor expansion of 0 in k 12.627 * [backup-simplify]: Simplify 0 into 0 12.627 * [backup-simplify]: Simplify 0 into 0 12.627 * [backup-simplify]: Simplify 0 into 0 12.628 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.628 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.630 * [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 12.630 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.630 * [backup-simplify]: Simplify (- 0) into 0 12.631 * [backup-simplify]: Simplify (+ 0 0) into 0 12.631 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.632 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.633 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.635 * [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 12.635 * [taylor]: Taking taylor expansion of 0 in k 12.635 * [backup-simplify]: Simplify 0 into 0 12.635 * [backup-simplify]: Simplify 0 into 0 12.635 * [backup-simplify]: Simplify 0 into 0 12.635 * [backup-simplify]: Simplify 0 into 0 12.635 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.636 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.639 * [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 12.639 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.640 * [backup-simplify]: Simplify (- 0) into 0 12.640 * [backup-simplify]: Simplify (+ 0 0) into 0 12.641 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.642 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.643 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.645 * [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 12.645 * [taylor]: Taking taylor expansion of 0 in k 12.645 * [backup-simplify]: Simplify 0 into 0 12.645 * [backup-simplify]: Simplify 0 into 0 12.646 * [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)))) 12.646 * [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))) 12.646 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 12.646 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 12.646 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.646 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.646 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 12.646 * [taylor]: Taking taylor expansion of 0.25 in k 12.646 * [backup-simplify]: Simplify 0.25 into 0.25 12.646 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.646 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.646 * [taylor]: Taking taylor expansion of k in k 12.646 * [backup-simplify]: Simplify 0 into 0 12.646 * [backup-simplify]: Simplify 1 into 1 12.647 * [backup-simplify]: Simplify (/ 1 1) into 1 12.647 * [taylor]: Taking taylor expansion of 1.0 in k 12.647 * [backup-simplify]: Simplify 1.0 into 1.0 12.647 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.647 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.647 * [taylor]: Taking taylor expansion of -2.0 in k 12.647 * [backup-simplify]: Simplify -2.0 into -2.0 12.647 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.647 * [taylor]: Taking taylor expansion of PI in k 12.647 * [backup-simplify]: Simplify PI into PI 12.647 * [taylor]: Taking taylor expansion of n in k 12.647 * [backup-simplify]: Simplify n into n 12.647 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.647 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.647 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.647 * [backup-simplify]: Simplify (+ 1 0) into 1 12.648 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 12.648 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 12.648 * [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)))))) 12.648 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.648 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.648 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.648 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.648 * [taylor]: Taking taylor expansion of 0.25 in n 12.648 * [backup-simplify]: Simplify 0.25 into 0.25 12.648 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.648 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.648 * [taylor]: Taking taylor expansion of k in n 12.648 * [backup-simplify]: Simplify k into k 12.648 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.648 * [taylor]: Taking taylor expansion of 1.0 in n 12.648 * [backup-simplify]: Simplify 1.0 into 1.0 12.648 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.648 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.648 * [taylor]: Taking taylor expansion of -2.0 in n 12.648 * [backup-simplify]: Simplify -2.0 into -2.0 12.648 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.648 * [taylor]: Taking taylor expansion of PI in n 12.648 * [backup-simplify]: Simplify PI into PI 12.648 * [taylor]: Taking taylor expansion of n in n 12.648 * [backup-simplify]: Simplify 0 into 0 12.648 * [backup-simplify]: Simplify 1 into 1 12.649 * [backup-simplify]: Simplify (/ PI 1) into PI 12.649 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.650 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.650 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.650 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.651 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.651 * [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)))) 12.652 * [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))))) 12.652 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.652 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.652 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.652 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.652 * [taylor]: Taking taylor expansion of 0.25 in n 12.653 * [backup-simplify]: Simplify 0.25 into 0.25 12.653 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.653 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.653 * [taylor]: Taking taylor expansion of k in n 12.653 * [backup-simplify]: Simplify k into k 12.653 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.653 * [taylor]: Taking taylor expansion of 1.0 in n 12.653 * [backup-simplify]: Simplify 1.0 into 1.0 12.653 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.653 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.653 * [taylor]: Taking taylor expansion of -2.0 in n 12.653 * [backup-simplify]: Simplify -2.0 into -2.0 12.653 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.653 * [taylor]: Taking taylor expansion of PI in n 12.653 * [backup-simplify]: Simplify PI into PI 12.653 * [taylor]: Taking taylor expansion of n in n 12.653 * [backup-simplify]: Simplify 0 into 0 12.653 * [backup-simplify]: Simplify 1 into 1 12.653 * [backup-simplify]: Simplify (/ PI 1) into PI 12.654 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.654 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.654 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.654 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.655 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.656 * [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)))) 12.657 * [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))))) 12.657 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.657 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.657 * [taylor]: Taking taylor expansion of 0.25 in k 12.657 * [backup-simplify]: Simplify 0.25 into 0.25 12.657 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.657 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.657 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.657 * [taylor]: Taking taylor expansion of k in k 12.657 * [backup-simplify]: Simplify 0 into 0 12.657 * [backup-simplify]: Simplify 1 into 1 12.657 * [backup-simplify]: Simplify (/ 1 1) into 1 12.657 * [taylor]: Taking taylor expansion of 1.0 in k 12.658 * [backup-simplify]: Simplify 1.0 into 1.0 12.658 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.658 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.658 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.658 * [taylor]: Taking taylor expansion of -2.0 in k 12.658 * [backup-simplify]: Simplify -2.0 into -2.0 12.658 * [taylor]: Taking taylor expansion of PI in k 12.658 * [backup-simplify]: Simplify PI into PI 12.658 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.659 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.659 * [taylor]: Taking taylor expansion of (log n) in k 12.659 * [taylor]: Taking taylor expansion of n in k 12.659 * [backup-simplify]: Simplify n into n 12.659 * [backup-simplify]: Simplify (log n) into (log n) 12.659 * [backup-simplify]: Simplify (+ 1 0) into 1 12.659 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.660 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.660 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.661 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 12.662 * [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))))) 12.664 * [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))))) 12.665 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.666 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.668 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.668 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.668 * [backup-simplify]: Simplify (+ 0 0) into 0 12.669 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.670 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.672 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.674 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.674 * [taylor]: Taking taylor expansion of 0 in k 12.674 * [backup-simplify]: Simplify 0 into 0 12.674 * [backup-simplify]: Simplify 0 into 0 12.674 * [backup-simplify]: Simplify 0 into 0 12.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.676 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.680 * [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 12.681 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.681 * [backup-simplify]: Simplify (+ 0 0) into 0 12.682 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.683 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.685 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.687 * [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 12.687 * [taylor]: Taking taylor expansion of 0 in k 12.687 * [backup-simplify]: Simplify 0 into 0 12.687 * [backup-simplify]: Simplify 0 into 0 12.687 * [backup-simplify]: Simplify 0 into 0 12.687 * [backup-simplify]: Simplify 0 into 0 12.689 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.690 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.697 * [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 12.697 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.698 * [backup-simplify]: Simplify (+ 0 0) into 0 12.699 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.701 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.703 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.706 * [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 12.706 * [taylor]: Taking taylor expansion of 0 in k 12.706 * [backup-simplify]: Simplify 0 into 0 12.706 * [backup-simplify]: Simplify 0 into 0 12.708 * [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)))))) 12.708 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 12.709 * [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))) 12.709 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 12.709 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 12.709 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.709 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.709 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 12.709 * [taylor]: Taking taylor expansion of 0.25 in k 12.709 * [backup-simplify]: Simplify 0.25 into 0.25 12.709 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.709 * [taylor]: Taking taylor expansion of 1.0 in k 12.709 * [backup-simplify]: Simplify 1.0 into 1.0 12.709 * [taylor]: Taking taylor expansion of k in k 12.709 * [backup-simplify]: Simplify 0 into 0 12.709 * [backup-simplify]: Simplify 1 into 1 12.709 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.709 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.709 * [taylor]: Taking taylor expansion of 2.0 in k 12.709 * [backup-simplify]: Simplify 2.0 into 2.0 12.709 * [taylor]: Taking taylor expansion of (* n PI) in k 12.710 * [taylor]: Taking taylor expansion of n in k 12.710 * [backup-simplify]: Simplify n into n 12.710 * [taylor]: Taking taylor expansion of PI in k 12.710 * [backup-simplify]: Simplify PI into PI 12.710 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.710 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.710 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.710 * [backup-simplify]: Simplify (- 0) into 0 12.711 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.712 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 12.712 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 12.712 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 12.712 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.712 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.712 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.712 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.712 * [taylor]: Taking taylor expansion of 0.25 in n 12.712 * [backup-simplify]: Simplify 0.25 into 0.25 12.712 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.712 * [taylor]: Taking taylor expansion of 1.0 in n 12.712 * [backup-simplify]: Simplify 1.0 into 1.0 12.712 * [taylor]: Taking taylor expansion of k in n 12.712 * [backup-simplify]: Simplify k into k 12.712 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.712 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.712 * [taylor]: Taking taylor expansion of 2.0 in n 12.712 * [backup-simplify]: Simplify 2.0 into 2.0 12.712 * [taylor]: Taking taylor expansion of (* n PI) in n 12.712 * [taylor]: Taking taylor expansion of n in n 12.712 * [backup-simplify]: Simplify 0 into 0 12.713 * [backup-simplify]: Simplify 1 into 1 12.713 * [taylor]: Taking taylor expansion of PI in n 12.713 * [backup-simplify]: Simplify PI into PI 12.713 * [backup-simplify]: Simplify (* 0 PI) into 0 12.714 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.715 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.717 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.718 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.718 * [backup-simplify]: Simplify (- k) into (- k) 12.718 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.718 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.720 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.721 * [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)))) 12.722 * [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))))) 12.722 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.722 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.722 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.722 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.722 * [taylor]: Taking taylor expansion of 0.25 in n 12.723 * [backup-simplify]: Simplify 0.25 into 0.25 12.723 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.723 * [taylor]: Taking taylor expansion of 1.0 in n 12.723 * [backup-simplify]: Simplify 1.0 into 1.0 12.723 * [taylor]: Taking taylor expansion of k in n 12.723 * [backup-simplify]: Simplify k into k 12.723 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.723 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.723 * [taylor]: Taking taylor expansion of 2.0 in n 12.723 * [backup-simplify]: Simplify 2.0 into 2.0 12.723 * [taylor]: Taking taylor expansion of (* n PI) in n 12.723 * [taylor]: Taking taylor expansion of n in n 12.723 * [backup-simplify]: Simplify 0 into 0 12.723 * [backup-simplify]: Simplify 1 into 1 12.723 * [taylor]: Taking taylor expansion of PI in n 12.723 * [backup-simplify]: Simplify PI into PI 12.723 * [backup-simplify]: Simplify (* 0 PI) into 0 12.724 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.725 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.734 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.735 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.736 * [backup-simplify]: Simplify (- k) into (- k) 12.736 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.736 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.737 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.738 * [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)))) 12.739 * [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))))) 12.740 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.740 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.740 * [taylor]: Taking taylor expansion of 0.25 in k 12.740 * [backup-simplify]: Simplify 0.25 into 0.25 12.740 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.740 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.740 * [taylor]: Taking taylor expansion of 1.0 in k 12.740 * [backup-simplify]: Simplify 1.0 into 1.0 12.740 * [taylor]: Taking taylor expansion of k in k 12.740 * [backup-simplify]: Simplify 0 into 0 12.740 * [backup-simplify]: Simplify 1 into 1 12.740 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.740 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.740 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.740 * [taylor]: Taking taylor expansion of 2.0 in k 12.740 * [backup-simplify]: Simplify 2.0 into 2.0 12.740 * [taylor]: Taking taylor expansion of PI in k 12.740 * [backup-simplify]: Simplify PI into PI 12.741 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.742 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.742 * [taylor]: Taking taylor expansion of (log n) in k 12.742 * [taylor]: Taking taylor expansion of n in k 12.742 * [backup-simplify]: Simplify n into n 12.742 * [backup-simplify]: Simplify (log n) into (log n) 12.742 * [backup-simplify]: Simplify (- 0) into 0 12.743 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.744 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.745 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.746 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 12.747 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.748 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.749 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.750 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.752 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.753 * [backup-simplify]: Simplify (- 0) into 0 12.753 * [backup-simplify]: Simplify (+ 0 0) into 0 12.754 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 12.755 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.756 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.758 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.758 * [taylor]: Taking taylor expansion of 0 in k 12.758 * [backup-simplify]: Simplify 0 into 0 12.758 * [backup-simplify]: Simplify 0 into 0 12.759 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.761 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.762 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.762 * [backup-simplify]: Simplify (+ 0 0) into 0 12.763 * [backup-simplify]: Simplify (- 1) into -1 12.763 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.765 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.767 * [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)))) 12.770 * [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)))))) 12.773 * [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)))))) 12.775 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.776 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.780 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.781 * [backup-simplify]: Simplify (- 0) into 0 12.781 * [backup-simplify]: Simplify (+ 0 0) into 0 12.782 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.784 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.785 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.788 * [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 12.788 * [taylor]: Taking taylor expansion of 0 in k 12.788 * [backup-simplify]: Simplify 0 into 0 12.788 * [backup-simplify]: Simplify 0 into 0 12.788 * [backup-simplify]: Simplify 0 into 0 12.789 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.791 * [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 12.792 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.793 * [backup-simplify]: Simplify (+ 0 0) into 0 12.793 * [backup-simplify]: Simplify (- 0) into 0 12.793 * [backup-simplify]: Simplify (+ 0 0) into 0 12.795 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.796 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.799 * [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))))) 12.802 * [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))))) 12.808 * [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)))))) 12.809 * [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)))) 12.809 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 12.809 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 12.809 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.809 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.809 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 12.809 * [taylor]: Taking taylor expansion of 0.25 in k 12.809 * [backup-simplify]: Simplify 0.25 into 0.25 12.809 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.809 * [taylor]: Taking taylor expansion of 1.0 in k 12.809 * [backup-simplify]: Simplify 1.0 into 1.0 12.809 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.809 * [taylor]: Taking taylor expansion of k in k 12.809 * [backup-simplify]: Simplify 0 into 0 12.809 * [backup-simplify]: Simplify 1 into 1 12.809 * [backup-simplify]: Simplify (/ 1 1) into 1 12.809 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.809 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.809 * [taylor]: Taking taylor expansion of 2.0 in k 12.810 * [backup-simplify]: Simplify 2.0 into 2.0 12.810 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.810 * [taylor]: Taking taylor expansion of PI in k 12.810 * [backup-simplify]: Simplify PI into PI 12.810 * [taylor]: Taking taylor expansion of n in k 12.810 * [backup-simplify]: Simplify n into n 12.810 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.810 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.810 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.810 * [backup-simplify]: Simplify (- 1) into -1 12.810 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.811 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 12.811 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 12.811 * [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))))) 12.811 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.811 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.811 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.811 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.811 * [taylor]: Taking taylor expansion of 0.25 in n 12.811 * [backup-simplify]: Simplify 0.25 into 0.25 12.811 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.811 * [taylor]: Taking taylor expansion of 1.0 in n 12.811 * [backup-simplify]: Simplify 1.0 into 1.0 12.811 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.811 * [taylor]: Taking taylor expansion of k in n 12.811 * [backup-simplify]: Simplify k into k 12.811 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.811 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.811 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.811 * [taylor]: Taking taylor expansion of 2.0 in n 12.811 * [backup-simplify]: Simplify 2.0 into 2.0 12.811 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.811 * [taylor]: Taking taylor expansion of PI in n 12.811 * [backup-simplify]: Simplify PI into PI 12.811 * [taylor]: Taking taylor expansion of n in n 12.811 * [backup-simplify]: Simplify 0 into 0 12.811 * [backup-simplify]: Simplify 1 into 1 12.812 * [backup-simplify]: Simplify (/ PI 1) into PI 12.812 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.812 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.813 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.813 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.813 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.814 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.814 * [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)))) 12.815 * [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))))) 12.815 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.815 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.815 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.815 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.815 * [taylor]: Taking taylor expansion of 0.25 in n 12.815 * [backup-simplify]: Simplify 0.25 into 0.25 12.815 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.815 * [taylor]: Taking taylor expansion of 1.0 in n 12.815 * [backup-simplify]: Simplify 1.0 into 1.0 12.815 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.815 * [taylor]: Taking taylor expansion of k in n 12.815 * [backup-simplify]: Simplify k into k 12.815 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.815 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.815 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.815 * [taylor]: Taking taylor expansion of 2.0 in n 12.815 * [backup-simplify]: Simplify 2.0 into 2.0 12.815 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.815 * [taylor]: Taking taylor expansion of PI in n 12.815 * [backup-simplify]: Simplify PI into PI 12.815 * [taylor]: Taking taylor expansion of n in n 12.815 * [backup-simplify]: Simplify 0 into 0 12.815 * [backup-simplify]: Simplify 1 into 1 12.816 * [backup-simplify]: Simplify (/ PI 1) into PI 12.816 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.817 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.817 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.817 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.817 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.818 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.819 * [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)))) 12.820 * [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))))) 12.820 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.820 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.820 * [taylor]: Taking taylor expansion of 0.25 in k 12.820 * [backup-simplify]: Simplify 0.25 into 0.25 12.820 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.820 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.820 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.820 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.820 * [taylor]: Taking taylor expansion of 2.0 in k 12.820 * [backup-simplify]: Simplify 2.0 into 2.0 12.820 * [taylor]: Taking taylor expansion of PI in k 12.820 * [backup-simplify]: Simplify PI into PI 12.820 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.821 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.821 * [taylor]: Taking taylor expansion of (log n) in k 12.821 * [taylor]: Taking taylor expansion of n in k 12.821 * [backup-simplify]: Simplify n into n 12.821 * [backup-simplify]: Simplify (log n) into (log n) 12.821 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.821 * [taylor]: Taking taylor expansion of 1.0 in k 12.821 * [backup-simplify]: Simplify 1.0 into 1.0 12.821 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.821 * [taylor]: Taking taylor expansion of k in k 12.821 * [backup-simplify]: Simplify 0 into 0 12.821 * [backup-simplify]: Simplify 1 into 1 12.821 * [backup-simplify]: Simplify (/ 1 1) into 1 12.821 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.822 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.822 * [backup-simplify]: Simplify (- 1) into -1 12.822 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.823 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.824 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 12.825 * [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))))) 12.826 * [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))))) 12.827 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.827 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.829 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.829 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.830 * [backup-simplify]: Simplify (- 0) into 0 12.830 * [backup-simplify]: Simplify (+ 0 0) into 0 12.831 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.832 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.833 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.835 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.835 * [taylor]: Taking taylor expansion of 0 in k 12.835 * [backup-simplify]: Simplify 0 into 0 12.835 * [backup-simplify]: Simplify 0 into 0 12.835 * [backup-simplify]: Simplify 0 into 0 12.837 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.838 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.841 * [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 12.841 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.842 * [backup-simplify]: Simplify (- 0) into 0 12.842 * [backup-simplify]: Simplify (+ 0 0) into 0 12.843 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.844 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.846 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.848 * [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 12.849 * [taylor]: Taking taylor expansion of 0 in k 12.849 * [backup-simplify]: Simplify 0 into 0 12.849 * [backup-simplify]: Simplify 0 into 0 12.849 * [backup-simplify]: Simplify 0 into 0 12.849 * [backup-simplify]: Simplify 0 into 0 12.850 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.851 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.857 * [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 12.858 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.858 * [backup-simplify]: Simplify (- 0) into 0 12.858 * [backup-simplify]: Simplify (+ 0 0) into 0 12.867 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.870 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.872 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.874 * [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 12.874 * [taylor]: Taking taylor expansion of 0 in k 12.874 * [backup-simplify]: Simplify 0 into 0 12.874 * [backup-simplify]: Simplify 0 into 0 12.875 * [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)))) 12.875 * [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))) 12.875 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 12.875 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 12.875 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.876 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.876 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 12.876 * [taylor]: Taking taylor expansion of 0.25 in k 12.876 * [backup-simplify]: Simplify 0.25 into 0.25 12.876 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.876 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.876 * [taylor]: Taking taylor expansion of k in k 12.876 * [backup-simplify]: Simplify 0 into 0 12.876 * [backup-simplify]: Simplify 1 into 1 12.876 * [backup-simplify]: Simplify (/ 1 1) into 1 12.876 * [taylor]: Taking taylor expansion of 1.0 in k 12.876 * [backup-simplify]: Simplify 1.0 into 1.0 12.876 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.876 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.876 * [taylor]: Taking taylor expansion of -2.0 in k 12.876 * [backup-simplify]: Simplify -2.0 into -2.0 12.876 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.876 * [taylor]: Taking taylor expansion of PI in k 12.876 * [backup-simplify]: Simplify PI into PI 12.876 * [taylor]: Taking taylor expansion of n in k 12.876 * [backup-simplify]: Simplify n into n 12.876 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.876 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.876 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.877 * [backup-simplify]: Simplify (+ 1 0) into 1 12.877 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 12.877 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 12.877 * [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)))))) 12.877 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.877 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.877 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.877 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.877 * [taylor]: Taking taylor expansion of 0.25 in n 12.877 * [backup-simplify]: Simplify 0.25 into 0.25 12.877 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.877 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.877 * [taylor]: Taking taylor expansion of k in n 12.877 * [backup-simplify]: Simplify k into k 12.877 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.877 * [taylor]: Taking taylor expansion of 1.0 in n 12.877 * [backup-simplify]: Simplify 1.0 into 1.0 12.877 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.877 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.877 * [taylor]: Taking taylor expansion of -2.0 in n 12.877 * [backup-simplify]: Simplify -2.0 into -2.0 12.877 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.877 * [taylor]: Taking taylor expansion of PI in n 12.877 * [backup-simplify]: Simplify PI into PI 12.878 * [taylor]: Taking taylor expansion of n in n 12.878 * [backup-simplify]: Simplify 0 into 0 12.878 * [backup-simplify]: Simplify 1 into 1 12.878 * [backup-simplify]: Simplify (/ PI 1) into PI 12.878 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.879 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.879 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.879 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.880 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.881 * [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)))) 12.881 * [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))))) 12.882 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.882 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.882 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.882 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.882 * [taylor]: Taking taylor expansion of 0.25 in n 12.882 * [backup-simplify]: Simplify 0.25 into 0.25 12.882 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.882 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.882 * [taylor]: Taking taylor expansion of k in n 12.882 * [backup-simplify]: Simplify k into k 12.882 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.882 * [taylor]: Taking taylor expansion of 1.0 in n 12.882 * [backup-simplify]: Simplify 1.0 into 1.0 12.882 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.882 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.882 * [taylor]: Taking taylor expansion of -2.0 in n 12.882 * [backup-simplify]: Simplify -2.0 into -2.0 12.882 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.882 * [taylor]: Taking taylor expansion of PI in n 12.882 * [backup-simplify]: Simplify PI into PI 12.882 * [taylor]: Taking taylor expansion of n in n 12.882 * [backup-simplify]: Simplify 0 into 0 12.882 * [backup-simplify]: Simplify 1 into 1 12.882 * [backup-simplify]: Simplify (/ PI 1) into PI 12.883 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.883 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.883 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.883 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.885 * [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)))) 12.886 * [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))))) 12.886 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.886 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.886 * [taylor]: Taking taylor expansion of 0.25 in k 12.886 * [backup-simplify]: Simplify 0.25 into 0.25 12.886 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.886 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.886 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.886 * [taylor]: Taking taylor expansion of k in k 12.886 * [backup-simplify]: Simplify 0 into 0 12.886 * [backup-simplify]: Simplify 1 into 1 12.886 * [backup-simplify]: Simplify (/ 1 1) into 1 12.886 * [taylor]: Taking taylor expansion of 1.0 in k 12.886 * [backup-simplify]: Simplify 1.0 into 1.0 12.886 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.886 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.886 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.886 * [taylor]: Taking taylor expansion of -2.0 in k 12.886 * [backup-simplify]: Simplify -2.0 into -2.0 12.886 * [taylor]: Taking taylor expansion of PI in k 12.886 * [backup-simplify]: Simplify PI into PI 12.887 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.887 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.887 * [taylor]: Taking taylor expansion of (log n) in k 12.887 * [taylor]: Taking taylor expansion of n in k 12.887 * [backup-simplify]: Simplify n into n 12.888 * [backup-simplify]: Simplify (log n) into (log n) 12.888 * [backup-simplify]: Simplify (+ 1 0) into 1 12.888 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.888 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.889 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.890 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 12.891 * [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))))) 12.891 * [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))))) 12.892 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.892 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.893 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.894 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.894 * [backup-simplify]: Simplify (+ 0 0) into 0 12.894 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.896 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.897 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.898 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.898 * [taylor]: Taking taylor expansion of 0 in k 12.898 * [backup-simplify]: Simplify 0 into 0 12.898 * [backup-simplify]: Simplify 0 into 0 12.898 * [backup-simplify]: Simplify 0 into 0 12.898 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.899 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.901 * [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 12.901 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.901 * [backup-simplify]: Simplify (+ 0 0) into 0 12.902 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.903 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.904 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.905 * [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 12.905 * [taylor]: Taking taylor expansion of 0 in k 12.905 * [backup-simplify]: Simplify 0 into 0 12.905 * [backup-simplify]: Simplify 0 into 0 12.905 * [backup-simplify]: Simplify 0 into 0 12.905 * [backup-simplify]: Simplify 0 into 0 12.906 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.907 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.910 * [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 12.910 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.911 * [backup-simplify]: Simplify (+ 0 0) into 0 12.911 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.912 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.914 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.915 * [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 12.915 * [taylor]: Taking taylor expansion of 0 in k 12.915 * [backup-simplify]: Simplify 0 into 0 12.915 * [backup-simplify]: Simplify 0 into 0 12.916 * [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)))))) 12.916 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 12.916 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 12.916 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 12.916 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.916 * [taylor]: Taking taylor expansion of 1.0 in k 12.916 * [backup-simplify]: Simplify 1.0 into 1.0 12.916 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.916 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.916 * [taylor]: Taking taylor expansion of k in k 12.916 * [backup-simplify]: Simplify 0 into 0 12.916 * [backup-simplify]: Simplify 1 into 1 12.917 * [backup-simplify]: Simplify (/ 1 1) into 1 12.917 * [backup-simplify]: Simplify (sqrt 0) into 0 12.918 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.918 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.918 * [taylor]: Taking taylor expansion of 1.0 in k 12.918 * [backup-simplify]: Simplify 1.0 into 1.0 12.918 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.918 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.918 * [taylor]: Taking taylor expansion of k in k 12.918 * [backup-simplify]: Simplify 0 into 0 12.918 * [backup-simplify]: Simplify 1 into 1 12.918 * [backup-simplify]: Simplify (/ 1 1) into 1 12.918 * [backup-simplify]: Simplify (sqrt 0) into 0 12.919 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.920 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.920 * [backup-simplify]: Simplify 0 into 0 12.920 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.921 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.921 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.923 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.924 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.924 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.925 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.927 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.929 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.929 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.930 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 12.930 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 12.930 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 12.930 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.930 * [taylor]: Taking taylor expansion of 1.0 in k 12.930 * [backup-simplify]: Simplify 1.0 into 1.0 12.930 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.930 * [taylor]: Taking taylor expansion of k in k 12.930 * [backup-simplify]: Simplify 0 into 0 12.930 * [backup-simplify]: Simplify 1 into 1 12.930 * [backup-simplify]: Simplify (sqrt 0) into 0 12.931 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.931 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.931 * [taylor]: Taking taylor expansion of 1.0 in k 12.931 * [backup-simplify]: Simplify 1.0 into 1.0 12.931 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.931 * [taylor]: Taking taylor expansion of k in k 12.931 * [backup-simplify]: Simplify 0 into 0 12.931 * [backup-simplify]: Simplify 1 into 1 12.931 * [backup-simplify]: Simplify (sqrt 0) into 0 12.932 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.932 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.933 * [backup-simplify]: Simplify 0 into 0 12.933 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.934 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.935 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.936 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.937 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.939 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.940 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.941 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.942 * [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)))))))) 12.942 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 12.942 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 12.942 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.942 * [taylor]: Taking taylor expansion of 1.0 in k 12.942 * [backup-simplify]: Simplify 1.0 into 1.0 12.942 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.942 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.942 * [taylor]: Taking taylor expansion of -1 in k 12.942 * [backup-simplify]: Simplify -1 into -1 12.942 * [taylor]: Taking taylor expansion of k in k 12.942 * [backup-simplify]: Simplify 0 into 0 12.942 * [backup-simplify]: Simplify 1 into 1 12.942 * [backup-simplify]: Simplify (/ -1 1) into -1 12.942 * [backup-simplify]: Simplify (sqrt 0) into 0 12.943 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.944 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.944 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.944 * [taylor]: Taking taylor expansion of 1.0 in k 12.944 * [backup-simplify]: Simplify 1.0 into 1.0 12.944 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.944 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.944 * [taylor]: Taking taylor expansion of -1 in k 12.944 * [backup-simplify]: Simplify -1 into -1 12.944 * [taylor]: Taking taylor expansion of k in k 12.944 * [backup-simplify]: Simplify 0 into 0 12.944 * [backup-simplify]: Simplify 1 into 1 12.944 * [backup-simplify]: Simplify (/ -1 1) into -1 12.944 * [backup-simplify]: Simplify (sqrt 0) into 0 12.945 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.945 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.946 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.947 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.950 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.952 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 12.953 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.954 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.958 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.962 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 12.963 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.964 * [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))))) 12.964 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 12.965 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 12.965 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 12.965 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.965 * [taylor]: Taking taylor expansion of 2.0 in n 12.965 * [backup-simplify]: Simplify 2.0 into 2.0 12.965 * [taylor]: Taking taylor expansion of (* n PI) in n 12.965 * [taylor]: Taking taylor expansion of n in n 12.965 * [backup-simplify]: Simplify 0 into 0 12.965 * [backup-simplify]: Simplify 1 into 1 12.965 * [taylor]: Taking taylor expansion of PI in n 12.965 * [backup-simplify]: Simplify PI into PI 12.965 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.965 * [taylor]: Taking taylor expansion of 2.0 in n 12.965 * [backup-simplify]: Simplify 2.0 into 2.0 12.965 * [taylor]: Taking taylor expansion of (* n PI) in n 12.965 * [taylor]: Taking taylor expansion of n in n 12.965 * [backup-simplify]: Simplify 0 into 0 12.965 * [backup-simplify]: Simplify 1 into 1 12.965 * [taylor]: Taking taylor expansion of PI in n 12.965 * [backup-simplify]: Simplify PI into PI 12.966 * [backup-simplify]: Simplify (* 0 PI) into 0 12.966 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.966 * [backup-simplify]: Simplify 0 into 0 12.968 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.977 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.977 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.978 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.979 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.979 * [backup-simplify]: Simplify 0 into 0 12.980 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.981 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.981 * [backup-simplify]: Simplify 0 into 0 12.981 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.982 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 12.982 * [backup-simplify]: Simplify 0 into 0 12.983 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.984 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 12.984 * [backup-simplify]: Simplify 0 into 0 12.985 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.986 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 12.986 * [backup-simplify]: Simplify 0 into 0 12.987 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 12.988 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 12.988 * [backup-simplify]: Simplify 0 into 0 12.989 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 12.989 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 12.989 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 12.989 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.989 * [taylor]: Taking taylor expansion of 2.0 in n 12.989 * [backup-simplify]: Simplify 2.0 into 2.0 12.989 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.989 * [taylor]: Taking taylor expansion of PI in n 12.989 * [backup-simplify]: Simplify PI into PI 12.989 * [taylor]: Taking taylor expansion of n in n 12.989 * [backup-simplify]: Simplify 0 into 0 12.989 * [backup-simplify]: Simplify 1 into 1 12.990 * [backup-simplify]: Simplify (/ PI 1) into PI 12.990 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.990 * [taylor]: Taking taylor expansion of 2.0 in n 12.990 * [backup-simplify]: Simplify 2.0 into 2.0 12.990 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.990 * [taylor]: Taking taylor expansion of PI in n 12.990 * [backup-simplify]: Simplify PI into PI 12.990 * [taylor]: Taking taylor expansion of n in n 12.990 * [backup-simplify]: Simplify 0 into 0 12.990 * [backup-simplify]: Simplify 1 into 1 12.990 * [backup-simplify]: Simplify (/ PI 1) into PI 12.990 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.991 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.991 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.992 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.992 * [backup-simplify]: Simplify 0 into 0 12.992 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.993 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.993 * [backup-simplify]: Simplify 0 into 0 12.994 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.994 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.994 * [backup-simplify]: Simplify 0 into 0 12.995 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.996 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.996 * [backup-simplify]: Simplify 0 into 0 12.997 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.997 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.998 * [backup-simplify]: Simplify 0 into 0 12.998 * [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 12.999 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.999 * [backup-simplify]: Simplify 0 into 0 13.000 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 13.000 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 13.000 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 13.000 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.000 * [taylor]: Taking taylor expansion of -2.0 in n 13.000 * [backup-simplify]: Simplify -2.0 into -2.0 13.000 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.000 * [taylor]: Taking taylor expansion of PI in n 13.000 * [backup-simplify]: Simplify PI into PI 13.000 * [taylor]: Taking taylor expansion of n in n 13.000 * [backup-simplify]: Simplify 0 into 0 13.000 * [backup-simplify]: Simplify 1 into 1 13.001 * [backup-simplify]: Simplify (/ PI 1) into PI 13.001 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.001 * [taylor]: Taking taylor expansion of -2.0 in n 13.001 * [backup-simplify]: Simplify -2.0 into -2.0 13.001 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.001 * [taylor]: Taking taylor expansion of PI in n 13.001 * [backup-simplify]: Simplify PI into PI 13.001 * [taylor]: Taking taylor expansion of n in n 13.001 * [backup-simplify]: Simplify 0 into 0 13.001 * [backup-simplify]: Simplify 1 into 1 13.001 * [backup-simplify]: Simplify (/ PI 1) into PI 13.001 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.002 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.002 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.003 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.003 * [backup-simplify]: Simplify 0 into 0 13.003 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.004 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.004 * [backup-simplify]: Simplify 0 into 0 13.005 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.005 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.005 * [backup-simplify]: Simplify 0 into 0 13.006 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.007 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.007 * [backup-simplify]: Simplify 0 into 0 13.007 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.008 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.008 * [backup-simplify]: Simplify 0 into 0 13.009 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.011 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.011 * [backup-simplify]: Simplify 0 into 0 13.011 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 13.012 * * * [progress]: simplifying candidates 13.018 * [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 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PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 13.029 * * [simplify]: Extracting # 0 : cost 0 13.029 * * [simplify]: Extracting # 1 : cost 0 13.030 * * [simplify]: Extracting # 2 : cost 0 13.031 * * [simplify]: Extracting # 3 : cost 0 13.032 * * [simplify]: Extracting # 4 : cost 0 13.033 * * [simplify]: Extracting # 5 : cost 0 13.034 * * [simplify]: Extracting # 6 : cost 0 13.035 * * [simplify]: Extracting # 7 : cost 0 13.036 * * [simplify]: Extracting # 8 : cost 0 13.037 * * [simplify]: Extracting # 9 : cost 0 13.038 * * [simplify]: Extracting # 10 : cost 0 13.039 * * [simplify]: Extracting # 11 : cost 0 13.040 * * [simplify]: Extracting # 12 : cost 0 13.042 * * [simplify]: Extracting # 13 : cost 0 13.043 * * [simplify]: Extracting # 14 : cost 0 13.044 * * [simplify]: iteration 0 : 332 enodes (cost 3588 ) 13.533 * * [simplify]: Extracting # 0 : cost 0 13.540 * * [simplify]: Extracting # 1 : cost 0 13.547 * * [simplify]: Extracting # 2 : cost 0 13.554 * * [simplify]: Extracting # 3 : cost 0 13.562 * * [simplify]: Extracting # 4 : cost 0 13.568 * * [simplify]: Extracting # 5 : cost 0 13.575 * * [simplify]: Extracting # 6 : cost 0 13.582 * * [simplify]: Extracting # 7 : cost 0 13.588 * * [simplify]: iteration 1 : 2514 enodes (cost 3313 ) 23.570 * * [simplify]: Extracting # 0 : cost 0 23.581 * * [simplify]: Extracting # 1 : cost 0 23.590 * * [simplify]: Extracting # 2 : cost 0 23.599 * * [simplify]: Extracting # 3 : cost 0 23.608 * * [simplify]: Extracting # 4 : cost 0 23.617 * * [simplify]: iteration done: 5001 enodes (cost 3212 ) 23.620 * [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) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 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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 (* n (* 2.0 PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 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 (* 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 (* n (* 2.0 PI)) (/ (/ (sqrt (- 1.0 k)) (cbrt 2)) 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(/ (- 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) 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 (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)) (* 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 (* n (* 2.0 PI)) 3) (pow (* n (* 2.0 PI)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* n (* 2.0 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) (fma (* (pow k 2) (* (pow (* n (* 2.0 PI)) 0.25) (pow (log (* 2.0 PI)) 2))) 0.03125 (- (fma (* 0.03125 (pow k 2)) (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.25)) (+ (pow (* n (* 2.0 PI)) 0.25) (* (* 0.0625 (pow k 2)) (* (* (log n) (pow (* n (* 2.0 PI)) 0.25)) (log (* 2.0 PI)))))) (* (fma (* k (log (* 2.0 PI))) (pow (* n (* 2.0 PI)) 0.25) (* (* k (pow (* n (* 2.0 PI)) 0.25)) (log n))) 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 (* (pow k 2) (* (pow (* n (* 2.0 PI)) 0.25) (pow (log (* 2.0 PI)) 2))) 0.03125 (- (fma (* 0.03125 (pow k 2)) (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.25)) (+ (pow (* n (* 2.0 PI)) 0.25) (* (* 0.0625 (pow k 2)) (* (* (log n) (pow (* n (* 2.0 PI)) 0.25)) (log (* 2.0 PI)))))) (* (fma (* k (log (* 2.0 PI))) (pow (* n (* 2.0 PI)) 0.25) (* (* k (pow (* n (* 2.0 PI)) 0.25)) (log n))) 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))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) 23.623 * * * [progress]: adding candidates to table 24.885 * * [progress]: iteration 3 / 4 24.885 * * * [progress]: picking best candidate 24.923 * * * * [pick]: Picked # 24.924 * * * [progress]: localizing error 24.981 * * * [progress]: generating rewritten candidates 24.981 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 25.002 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 25.047 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 25.058 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 2) 25.089 * * * [progress]: generating series expansions 25.089 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 25.089 * [backup-simplify]: Simplify (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 25.089 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 25.089 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 25.089 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 25.089 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 25.089 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 25.089 * [taylor]: Taking taylor expansion of 0.5 in k 25.089 * [backup-simplify]: Simplify 0.5 into 0.5 25.089 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 25.089 * [taylor]: Taking taylor expansion of 1.0 in k 25.089 * [backup-simplify]: Simplify 1.0 into 1.0 25.089 * [taylor]: Taking taylor expansion of k in k 25.089 * [backup-simplify]: Simplify 0 into 0 25.090 * [backup-simplify]: Simplify 1 into 1 25.090 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 25.090 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 25.090 * [taylor]: Taking taylor expansion of 2.0 in k 25.090 * [backup-simplify]: Simplify 2.0 into 2.0 25.090 * [taylor]: Taking taylor expansion of (* n PI) in k 25.090 * [taylor]: Taking taylor expansion of n in k 25.090 * [backup-simplify]: Simplify n into n 25.090 * [taylor]: Taking taylor expansion of PI in k 25.090 * [backup-simplify]: Simplify PI into PI 25.090 * [backup-simplify]: Simplify (* n PI) into (* n PI) 25.090 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 25.090 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 25.091 * [backup-simplify]: Simplify (- 0) into 0 25.091 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 25.092 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 25.092 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 25.092 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 25.092 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 25.092 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 25.092 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 25.092 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 25.092 * [taylor]: Taking taylor expansion of 0.5 in n 25.092 * [backup-simplify]: Simplify 0.5 into 0.5 25.093 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 25.093 * [taylor]: Taking taylor expansion of 1.0 in n 25.093 * [backup-simplify]: Simplify 1.0 into 1.0 25.093 * [taylor]: Taking taylor expansion of k in n 25.093 * [backup-simplify]: Simplify k into k 25.093 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 25.093 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 25.093 * [taylor]: Taking taylor expansion of 2.0 in n 25.093 * [backup-simplify]: Simplify 2.0 into 2.0 25.093 * [taylor]: Taking taylor expansion of (* n PI) in n 25.093 * [taylor]: Taking taylor expansion of n in n 25.093 * [backup-simplify]: Simplify 0 into 0 25.093 * [backup-simplify]: Simplify 1 into 1 25.093 * [taylor]: Taking taylor expansion of PI in n 25.093 * [backup-simplify]: Simplify PI into PI 25.093 * [backup-simplify]: Simplify (* 0 PI) into 0 25.094 * [backup-simplify]: Simplify (* 2.0 0) into 0 25.095 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 25.097 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 25.098 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.098 * [backup-simplify]: Simplify (- k) into (- k) 25.098 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 25.098 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 25.100 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 25.101 * [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)))) 25.102 * [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))))) 25.102 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 25.102 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 25.102 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 25.102 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 25.102 * [taylor]: Taking taylor expansion of 0.5 in n 25.102 * [backup-simplify]: Simplify 0.5 into 0.5 25.102 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 25.102 * [taylor]: Taking taylor expansion of 1.0 in n 25.102 * [backup-simplify]: Simplify 1.0 into 1.0 25.102 * [taylor]: Taking taylor expansion of k in n 25.102 * [backup-simplify]: Simplify k into k 25.102 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 25.102 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 25.102 * [taylor]: Taking taylor expansion of 2.0 in n 25.102 * [backup-simplify]: Simplify 2.0 into 2.0 25.102 * [taylor]: Taking taylor expansion of (* n PI) in n 25.102 * [taylor]: Taking taylor expansion of n in n 25.102 * [backup-simplify]: Simplify 0 into 0 25.102 * [backup-simplify]: Simplify 1 into 1 25.102 * [taylor]: Taking taylor expansion of PI in n 25.102 * [backup-simplify]: Simplify PI into PI 25.103 * [backup-simplify]: Simplify (* 0 PI) into 0 25.103 * [backup-simplify]: Simplify (* 2.0 0) into 0 25.104 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 25.106 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 25.107 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.107 * [backup-simplify]: Simplify (- k) into (- k) 25.107 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 25.107 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 25.108 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 25.109 * [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)))) 25.110 * [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))))) 25.111 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 25.111 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 25.111 * [taylor]: Taking taylor expansion of 0.5 in k 25.111 * [backup-simplify]: Simplify 0.5 into 0.5 25.111 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 25.111 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 25.111 * [taylor]: Taking taylor expansion of 1.0 in k 25.111 * [backup-simplify]: Simplify 1.0 into 1.0 25.111 * [taylor]: Taking taylor expansion of k in k 25.111 * [backup-simplify]: Simplify 0 into 0 25.111 * [backup-simplify]: Simplify 1 into 1 25.111 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 25.111 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 25.111 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 25.111 * [taylor]: Taking taylor expansion of 2.0 in k 25.111 * [backup-simplify]: Simplify 2.0 into 2.0 25.111 * [taylor]: Taking taylor expansion of PI in k 25.111 * [backup-simplify]: Simplify PI into PI 25.112 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 25.113 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.113 * [taylor]: Taking taylor expansion of (log n) in k 25.113 * [taylor]: Taking taylor expansion of n in k 25.113 * [backup-simplify]: Simplify n into n 25.113 * [backup-simplify]: Simplify (log n) into (log n) 25.113 * [backup-simplify]: Simplify (- 0) into 0 25.113 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 25.114 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 25.116 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 25.117 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 25.118 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 25.119 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 25.120 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 25.121 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 25.124 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 25.124 * [backup-simplify]: Simplify (- 0) into 0 25.125 * [backup-simplify]: Simplify (+ 0 0) into 0 25.125 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 25.126 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 25.127 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 25.128 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.128 * [taylor]: Taking taylor expansion of 0 in k 25.128 * [backup-simplify]: Simplify 0 into 0 25.128 * [backup-simplify]: Simplify 0 into 0 25.129 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 25.130 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 25.130 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 25.130 * [backup-simplify]: Simplify (+ 0 0) into 0 25.131 * [backup-simplify]: Simplify (- 1) into -1 25.131 * [backup-simplify]: Simplify (+ 0 -1) into -1 25.132 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 25.133 * [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)))) 25.135 * [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)))))) 25.137 * [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)))))) 25.138 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 25.139 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 25.141 * [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 25.141 * [backup-simplify]: Simplify (- 0) into 0 25.141 * [backup-simplify]: Simplify (+ 0 0) into 0 25.142 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 25.143 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 25.144 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 25.146 * [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 25.146 * [taylor]: Taking taylor expansion of 0 in k 25.146 * [backup-simplify]: Simplify 0 into 0 25.146 * [backup-simplify]: Simplify 0 into 0 25.146 * [backup-simplify]: Simplify 0 into 0 25.147 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 25.148 * [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 25.150 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 25.150 * [backup-simplify]: Simplify (+ 0 0) into 0 25.150 * [backup-simplify]: Simplify (- 0) into 0 25.150 * [backup-simplify]: Simplify (+ 0 0) into 0 25.151 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 25.153 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 25.158 * [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)))))) 25.163 * [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)))))) 25.174 * [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)))))) 25.175 * [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)))) 25.175 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 25.175 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 25.175 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 25.175 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 25.175 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 25.175 * [taylor]: Taking taylor expansion of 0.5 in k 25.175 * [backup-simplify]: Simplify 0.5 into 0.5 25.175 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 25.175 * [taylor]: Taking taylor expansion of 1.0 in k 25.175 * [backup-simplify]: Simplify 1.0 into 1.0 25.175 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.175 * [taylor]: Taking taylor expansion of k in k 25.175 * [backup-simplify]: Simplify 0 into 0 25.175 * [backup-simplify]: Simplify 1 into 1 25.175 * [backup-simplify]: Simplify (/ 1 1) into 1 25.175 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 25.176 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 25.176 * [taylor]: Taking taylor expansion of 2.0 in k 25.176 * [backup-simplify]: Simplify 2.0 into 2.0 25.176 * [taylor]: Taking taylor expansion of (/ PI n) in k 25.176 * [taylor]: Taking taylor expansion of PI in k 25.176 * [backup-simplify]: Simplify PI into PI 25.176 * [taylor]: Taking taylor expansion of n in k 25.176 * [backup-simplify]: Simplify n into n 25.176 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 25.176 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 25.176 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 25.176 * [backup-simplify]: Simplify (- 1) into -1 25.177 * [backup-simplify]: Simplify (+ 0 -1) into -1 25.177 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 25.177 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 25.178 * [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))))) 25.178 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 25.178 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 25.178 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 25.178 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 25.178 * [taylor]: Taking taylor expansion of 0.5 in n 25.178 * [backup-simplify]: Simplify 0.5 into 0.5 25.178 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 25.178 * [taylor]: Taking taylor expansion of 1.0 in n 25.178 * [backup-simplify]: Simplify 1.0 into 1.0 25.178 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.178 * [taylor]: Taking taylor expansion of k in n 25.178 * [backup-simplify]: Simplify k into k 25.178 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.178 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 25.178 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 25.178 * [taylor]: Taking taylor expansion of 2.0 in n 25.178 * [backup-simplify]: Simplify 2.0 into 2.0 25.178 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.178 * [taylor]: Taking taylor expansion of PI in n 25.178 * [backup-simplify]: Simplify PI into PI 25.178 * [taylor]: Taking taylor expansion of n in n 25.178 * [backup-simplify]: Simplify 0 into 0 25.179 * [backup-simplify]: Simplify 1 into 1 25.179 * [backup-simplify]: Simplify (/ PI 1) into PI 25.180 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 25.181 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.181 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 25.181 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 25.181 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 25.183 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 25.184 * [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)))) 25.185 * [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))))) 25.185 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 25.185 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 25.185 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 25.185 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 25.185 * [taylor]: Taking taylor expansion of 0.5 in n 25.186 * [backup-simplify]: Simplify 0.5 into 0.5 25.186 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 25.186 * [taylor]: Taking taylor expansion of 1.0 in n 25.186 * [backup-simplify]: Simplify 1.0 into 1.0 25.186 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.186 * [taylor]: Taking taylor expansion of k in n 25.186 * [backup-simplify]: Simplify k into k 25.186 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.186 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 25.186 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 25.186 * [taylor]: Taking taylor expansion of 2.0 in n 25.186 * [backup-simplify]: Simplify 2.0 into 2.0 25.186 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.186 * [taylor]: Taking taylor expansion of PI in n 25.186 * [backup-simplify]: Simplify PI into PI 25.186 * [taylor]: Taking taylor expansion of n in n 25.186 * [backup-simplify]: Simplify 0 into 0 25.186 * [backup-simplify]: Simplify 1 into 1 25.187 * [backup-simplify]: Simplify (/ PI 1) into PI 25.187 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 25.188 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.188 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 25.188 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 25.189 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 25.190 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 25.191 * [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)))) 25.193 * [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))))) 25.193 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 25.193 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 25.193 * [taylor]: Taking taylor expansion of 0.5 in k 25.193 * [backup-simplify]: Simplify 0.5 into 0.5 25.193 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 25.193 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 25.193 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 25.193 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 25.193 * [taylor]: Taking taylor expansion of 2.0 in k 25.194 * [backup-simplify]: Simplify 2.0 into 2.0 25.194 * [taylor]: Taking taylor expansion of PI in k 25.194 * [backup-simplify]: Simplify PI into PI 25.194 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 25.195 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.195 * [taylor]: Taking taylor expansion of (log n) in k 25.195 * [taylor]: Taking taylor expansion of n in k 25.196 * [backup-simplify]: Simplify n into n 25.196 * [backup-simplify]: Simplify (log n) into (log n) 25.196 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 25.196 * [taylor]: Taking taylor expansion of 1.0 in k 25.196 * [backup-simplify]: Simplify 1.0 into 1.0 25.196 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.196 * [taylor]: Taking taylor expansion of k in k 25.196 * [backup-simplify]: Simplify 0 into 0 25.196 * [backup-simplify]: Simplify 1 into 1 25.196 * [backup-simplify]: Simplify (/ 1 1) into 1 25.196 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 25.198 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 25.198 * [backup-simplify]: Simplify (- 1) into -1 25.198 * [backup-simplify]: Simplify (+ 0 -1) into -1 25.200 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 25.201 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 25.202 * [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))))) 25.214 * [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))))) 25.216 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.217 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 25.218 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 25.218 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 25.218 * [backup-simplify]: Simplify (- 0) into 0 25.218 * [backup-simplify]: Simplify (+ 0 0) into 0 25.219 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 25.220 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 25.221 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 25.222 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.222 * [taylor]: Taking taylor expansion of 0 in k 25.222 * [backup-simplify]: Simplify 0 into 0 25.222 * [backup-simplify]: Simplify 0 into 0 25.222 * [backup-simplify]: Simplify 0 into 0 25.223 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.223 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 25.225 * [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 25.225 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.226 * [backup-simplify]: Simplify (- 0) into 0 25.227 * [backup-simplify]: Simplify (+ 0 0) into 0 25.228 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 25.229 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 25.230 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 25.232 * [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 25.232 * [taylor]: Taking taylor expansion of 0 in k 25.232 * [backup-simplify]: Simplify 0 into 0 25.232 * [backup-simplify]: Simplify 0 into 0 25.232 * [backup-simplify]: Simplify 0 into 0 25.232 * [backup-simplify]: Simplify 0 into 0 25.233 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.233 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.237 * [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 25.237 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.237 * [backup-simplify]: Simplify (- 0) into 0 25.238 * [backup-simplify]: Simplify (+ 0 0) into 0 25.238 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 25.239 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 25.240 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 25.242 * [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 25.242 * [taylor]: Taking taylor expansion of 0 in k 25.242 * [backup-simplify]: Simplify 0 into 0 25.242 * [backup-simplify]: Simplify 0 into 0 25.243 * [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)))) 25.243 * [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))) 25.244 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 25.244 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 25.244 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 25.244 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 25.244 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 25.244 * [taylor]: Taking taylor expansion of 0.5 in k 25.244 * [backup-simplify]: Simplify 0.5 into 0.5 25.244 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 25.244 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.244 * [taylor]: Taking taylor expansion of k in k 25.244 * [backup-simplify]: Simplify 0 into 0 25.244 * [backup-simplify]: Simplify 1 into 1 25.244 * [backup-simplify]: Simplify (/ 1 1) into 1 25.244 * [taylor]: Taking taylor expansion of 1.0 in k 25.244 * [backup-simplify]: Simplify 1.0 into 1.0 25.244 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 25.244 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 25.244 * [taylor]: Taking taylor expansion of -2.0 in k 25.244 * [backup-simplify]: Simplify -2.0 into -2.0 25.244 * [taylor]: Taking taylor expansion of (/ PI n) in k 25.244 * [taylor]: Taking taylor expansion of PI in k 25.244 * [backup-simplify]: Simplify PI into PI 25.244 * [taylor]: Taking taylor expansion of n in k 25.244 * [backup-simplify]: Simplify n into n 25.244 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 25.244 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 25.244 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 25.245 * [backup-simplify]: Simplify (+ 1 0) into 1 25.245 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 25.245 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 25.245 * [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)))))) 25.245 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 25.245 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 25.245 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 25.245 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 25.245 * [taylor]: Taking taylor expansion of 0.5 in n 25.245 * [backup-simplify]: Simplify 0.5 into 0.5 25.245 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 25.245 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.245 * [taylor]: Taking taylor expansion of k in n 25.245 * [backup-simplify]: Simplify k into k 25.245 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.245 * [taylor]: Taking taylor expansion of 1.0 in n 25.245 * [backup-simplify]: Simplify 1.0 into 1.0 25.245 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 25.245 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 25.245 * [taylor]: Taking taylor expansion of -2.0 in n 25.245 * [backup-simplify]: Simplify -2.0 into -2.0 25.246 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.246 * [taylor]: Taking taylor expansion of PI in n 25.246 * [backup-simplify]: Simplify PI into PI 25.246 * [taylor]: Taking taylor expansion of n in n 25.246 * [backup-simplify]: Simplify 0 into 0 25.246 * [backup-simplify]: Simplify 1 into 1 25.246 * [backup-simplify]: Simplify (/ PI 1) into PI 25.246 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 25.247 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 25.247 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 25.247 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 25.248 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 25.249 * [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)))) 25.249 * [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))))) 25.249 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 25.249 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 25.250 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 25.250 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 25.250 * [taylor]: Taking taylor expansion of 0.5 in n 25.250 * [backup-simplify]: Simplify 0.5 into 0.5 25.250 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 25.250 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.250 * [taylor]: Taking taylor expansion of k in n 25.250 * [backup-simplify]: Simplify k into k 25.250 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.250 * [taylor]: Taking taylor expansion of 1.0 in n 25.250 * [backup-simplify]: Simplify 1.0 into 1.0 25.250 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 25.250 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 25.250 * [taylor]: Taking taylor expansion of -2.0 in n 25.250 * [backup-simplify]: Simplify -2.0 into -2.0 25.250 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.250 * [taylor]: Taking taylor expansion of PI in n 25.250 * [backup-simplify]: Simplify PI into PI 25.250 * [taylor]: Taking taylor expansion of n in n 25.250 * [backup-simplify]: Simplify 0 into 0 25.250 * [backup-simplify]: Simplify 1 into 1 25.250 * [backup-simplify]: Simplify (/ PI 1) into PI 25.250 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 25.251 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 25.251 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 25.251 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 25.252 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 25.253 * [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)))) 25.254 * [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))))) 25.254 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 25.254 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 25.254 * [taylor]: Taking taylor expansion of 0.5 in k 25.254 * [backup-simplify]: Simplify 0.5 into 0.5 25.255 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 25.255 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 25.255 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.255 * [taylor]: Taking taylor expansion of k in k 25.255 * [backup-simplify]: Simplify 0 into 0 25.255 * [backup-simplify]: Simplify 1 into 1 25.255 * [backup-simplify]: Simplify (/ 1 1) into 1 25.255 * [taylor]: Taking taylor expansion of 1.0 in k 25.255 * [backup-simplify]: Simplify 1.0 into 1.0 25.255 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 25.255 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 25.255 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 25.255 * [taylor]: Taking taylor expansion of -2.0 in k 25.255 * [backup-simplify]: Simplify -2.0 into -2.0 25.255 * [taylor]: Taking taylor expansion of PI in k 25.255 * [backup-simplify]: Simplify PI into PI 25.256 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 25.257 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 25.257 * [taylor]: Taking taylor expansion of (log n) in k 25.257 * [taylor]: Taking taylor expansion of n in k 25.257 * [backup-simplify]: Simplify n into n 25.257 * [backup-simplify]: Simplify (log n) into (log n) 25.258 * [backup-simplify]: Simplify (+ 1 0) into 1 25.258 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 25.259 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 25.260 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 25.262 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 25.263 * [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))))) 25.264 * [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))))) 25.265 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.266 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 25.268 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 25.268 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 25.269 * [backup-simplify]: Simplify (+ 0 0) into 0 25.269 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 25.270 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 25.271 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 25.272 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.272 * [taylor]: Taking taylor expansion of 0 in k 25.272 * [backup-simplify]: Simplify 0 into 0 25.272 * [backup-simplify]: Simplify 0 into 0 25.272 * [backup-simplify]: Simplify 0 into 0 25.273 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.273 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 25.275 * [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 25.275 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.276 * [backup-simplify]: Simplify (+ 0 0) into 0 25.276 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 25.277 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 25.278 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 25.280 * [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 25.280 * [taylor]: Taking taylor expansion of 0 in k 25.280 * [backup-simplify]: Simplify 0 into 0 25.280 * [backup-simplify]: Simplify 0 into 0 25.280 * [backup-simplify]: Simplify 0 into 0 25.280 * [backup-simplify]: Simplify 0 into 0 25.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.281 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.284 * [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 25.285 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.285 * [backup-simplify]: Simplify (+ 0 0) into 0 25.286 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 25.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 25.288 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 25.289 * [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 25.290 * [taylor]: Taking taylor expansion of 0 in k 25.290 * [backup-simplify]: Simplify 0 into 0 25.290 * [backup-simplify]: Simplify 0 into 0 25.290 * [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)))))) 25.290 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 25.291 * [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))) 25.291 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 25.291 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 25.291 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 25.291 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 25.291 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 25.291 * [taylor]: Taking taylor expansion of 0.25 in k 25.291 * [backup-simplify]: Simplify 0.25 into 0.25 25.291 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 25.291 * [taylor]: Taking taylor expansion of 1.0 in k 25.291 * [backup-simplify]: Simplify 1.0 into 1.0 25.291 * [taylor]: Taking taylor expansion of k in k 25.291 * [backup-simplify]: Simplify 0 into 0 25.291 * [backup-simplify]: Simplify 1 into 1 25.291 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 25.291 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 25.291 * [taylor]: Taking taylor expansion of 2.0 in k 25.291 * [backup-simplify]: Simplify 2.0 into 2.0 25.291 * [taylor]: Taking taylor expansion of (* n PI) in k 25.291 * [taylor]: Taking taylor expansion of n in k 25.291 * [backup-simplify]: Simplify n into n 25.291 * [taylor]: Taking taylor expansion of PI in k 25.291 * [backup-simplify]: Simplify PI into PI 25.291 * [backup-simplify]: Simplify (* n PI) into (* n PI) 25.291 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 25.292 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 25.292 * [backup-simplify]: Simplify (- 0) into 0 25.292 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 25.292 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 25.292 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 25.292 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 25.293 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 25.293 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 25.293 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 25.293 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 25.293 * [taylor]: Taking taylor expansion of 0.25 in n 25.293 * [backup-simplify]: Simplify 0.25 into 0.25 25.293 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 25.293 * [taylor]: Taking taylor expansion of 1.0 in n 25.293 * [backup-simplify]: Simplify 1.0 into 1.0 25.293 * [taylor]: Taking taylor expansion of k in n 25.293 * [backup-simplify]: Simplify k into k 25.293 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 25.293 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 25.293 * [taylor]: Taking taylor expansion of 2.0 in n 25.293 * [backup-simplify]: Simplify 2.0 into 2.0 25.293 * [taylor]: Taking taylor expansion of (* n PI) in n 25.293 * [taylor]: Taking taylor expansion of n in n 25.293 * [backup-simplify]: Simplify 0 into 0 25.293 * [backup-simplify]: Simplify 1 into 1 25.293 * [taylor]: Taking taylor expansion of PI in n 25.293 * [backup-simplify]: Simplify PI into PI 25.293 * [backup-simplify]: Simplify (* 0 PI) into 0 25.294 * [backup-simplify]: Simplify (* 2.0 0) into 0 25.295 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 25.296 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 25.296 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.296 * [backup-simplify]: Simplify (- k) into (- k) 25.296 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 25.296 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 25.297 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 25.299 * [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)))) 25.300 * [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))))) 25.300 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 25.300 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 25.300 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 25.300 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 25.300 * [taylor]: Taking taylor expansion of 0.25 in n 25.300 * [backup-simplify]: Simplify 0.25 into 0.25 25.300 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 25.300 * [taylor]: Taking taylor expansion of 1.0 in n 25.300 * [backup-simplify]: Simplify 1.0 into 1.0 25.300 * [taylor]: Taking taylor expansion of k in n 25.300 * [backup-simplify]: Simplify k into k 25.300 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 25.300 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 25.300 * [taylor]: Taking taylor expansion of 2.0 in n 25.300 * [backup-simplify]: Simplify 2.0 into 2.0 25.300 * [taylor]: Taking taylor expansion of (* n PI) in n 25.300 * [taylor]: Taking taylor expansion of n in n 25.301 * [backup-simplify]: Simplify 0 into 0 25.301 * [backup-simplify]: Simplify 1 into 1 25.301 * [taylor]: Taking taylor expansion of PI in n 25.301 * [backup-simplify]: Simplify PI into PI 25.301 * [backup-simplify]: Simplify (* 0 PI) into 0 25.302 * [backup-simplify]: Simplify (* 2.0 0) into 0 25.303 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 25.304 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 25.306 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.306 * [backup-simplify]: Simplify (- k) into (- k) 25.306 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 25.306 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 25.307 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 25.308 * [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)))) 25.310 * [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))))) 25.310 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 25.310 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 25.310 * [taylor]: Taking taylor expansion of 0.25 in k 25.310 * [backup-simplify]: Simplify 0.25 into 0.25 25.310 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 25.310 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 25.310 * [taylor]: Taking taylor expansion of 1.0 in k 25.310 * [backup-simplify]: Simplify 1.0 into 1.0 25.310 * [taylor]: Taking taylor expansion of k in k 25.310 * [backup-simplify]: Simplify 0 into 0 25.310 * [backup-simplify]: Simplify 1 into 1 25.310 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 25.310 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 25.310 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 25.310 * [taylor]: Taking taylor expansion of 2.0 in k 25.310 * [backup-simplify]: Simplify 2.0 into 2.0 25.310 * [taylor]: Taking taylor expansion of PI in k 25.310 * [backup-simplify]: Simplify PI into PI 25.311 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 25.312 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.312 * [taylor]: Taking taylor expansion of (log n) in k 25.312 * [taylor]: Taking taylor expansion of n in k 25.312 * [backup-simplify]: Simplify n into n 25.312 * [backup-simplify]: Simplify (log n) into (log n) 25.312 * [backup-simplify]: Simplify (- 0) into 0 25.313 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 25.314 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 25.314 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 25.315 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 25.316 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 25.316 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 25.317 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 25.318 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 25.319 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 25.319 * [backup-simplify]: Simplify (- 0) into 0 25.319 * [backup-simplify]: Simplify (+ 0 0) into 0 25.319 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 25.326 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 25.327 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 25.328 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.328 * [taylor]: Taking taylor expansion of 0 in k 25.329 * [backup-simplify]: Simplify 0 into 0 25.329 * [backup-simplify]: Simplify 0 into 0 25.329 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 25.330 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 25.331 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 25.331 * [backup-simplify]: Simplify (+ 0 0) into 0 25.331 * [backup-simplify]: Simplify (- 1) into -1 25.332 * [backup-simplify]: Simplify (+ 0 -1) into -1 25.332 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 25.334 * [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)))) 25.336 * [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)))))) 25.338 * [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)))))) 25.338 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 25.339 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 25.341 * [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 25.341 * [backup-simplify]: Simplify (- 0) into 0 25.342 * [backup-simplify]: Simplify (+ 0 0) into 0 25.342 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 25.343 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 25.344 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 25.346 * [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 25.346 * [taylor]: Taking taylor expansion of 0 in k 25.346 * [backup-simplify]: Simplify 0 into 0 25.346 * [backup-simplify]: Simplify 0 into 0 25.346 * [backup-simplify]: Simplify 0 into 0 25.346 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 25.348 * [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 25.350 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 25.350 * [backup-simplify]: Simplify (+ 0 0) into 0 25.350 * [backup-simplify]: Simplify (- 0) into 0 25.351 * [backup-simplify]: Simplify (+ 0 0) into 0 25.352 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 25.353 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 25.356 * [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))))) 25.359 * [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))))) 25.370 * [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)))))) 25.371 * [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)))) 25.371 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 25.371 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 25.371 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 25.371 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 25.371 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 25.371 * [taylor]: Taking taylor expansion of 0.25 in k 25.371 * [backup-simplify]: Simplify 0.25 into 0.25 25.371 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 25.371 * [taylor]: Taking taylor expansion of 1.0 in k 25.371 * [backup-simplify]: Simplify 1.0 into 1.0 25.371 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.371 * [taylor]: Taking taylor expansion of k in k 25.371 * [backup-simplify]: Simplify 0 into 0 25.372 * [backup-simplify]: Simplify 1 into 1 25.372 * [backup-simplify]: Simplify (/ 1 1) into 1 25.372 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 25.372 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 25.372 * [taylor]: Taking taylor expansion of 2.0 in k 25.372 * [backup-simplify]: Simplify 2.0 into 2.0 25.372 * [taylor]: Taking taylor expansion of (/ PI n) in k 25.372 * [taylor]: Taking taylor expansion of PI in k 25.372 * [backup-simplify]: Simplify PI into PI 25.372 * [taylor]: Taking taylor expansion of n in k 25.372 * [backup-simplify]: Simplify n into n 25.372 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 25.372 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 25.372 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 25.373 * [backup-simplify]: Simplify (- 1) into -1 25.373 * [backup-simplify]: Simplify (+ 0 -1) into -1 25.374 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 25.374 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 25.374 * [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))))) 25.374 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 25.374 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 25.374 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 25.374 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 25.374 * [taylor]: Taking taylor expansion of 0.25 in n 25.374 * [backup-simplify]: Simplify 0.25 into 0.25 25.374 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 25.374 * [taylor]: Taking taylor expansion of 1.0 in n 25.374 * [backup-simplify]: Simplify 1.0 into 1.0 25.374 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.374 * [taylor]: Taking taylor expansion of k in n 25.374 * [backup-simplify]: Simplify k into k 25.374 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.374 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 25.375 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 25.375 * [taylor]: Taking taylor expansion of 2.0 in n 25.375 * [backup-simplify]: Simplify 2.0 into 2.0 25.375 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.375 * [taylor]: Taking taylor expansion of PI in n 25.375 * [backup-simplify]: Simplify PI into PI 25.375 * [taylor]: Taking taylor expansion of n in n 25.375 * [backup-simplify]: Simplify 0 into 0 25.375 * [backup-simplify]: Simplify 1 into 1 25.375 * [backup-simplify]: Simplify (/ PI 1) into PI 25.376 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 25.377 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.377 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 25.377 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 25.377 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 25.378 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 25.379 * [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)))) 25.380 * [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))))) 25.380 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 25.380 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 25.380 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 25.380 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 25.380 * [taylor]: Taking taylor expansion of 0.25 in n 25.380 * [backup-simplify]: Simplify 0.25 into 0.25 25.380 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 25.380 * [taylor]: Taking taylor expansion of 1.0 in n 25.380 * [backup-simplify]: Simplify 1.0 into 1.0 25.380 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.380 * [taylor]: Taking taylor expansion of k in n 25.380 * [backup-simplify]: Simplify k into k 25.380 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.381 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 25.381 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 25.381 * [taylor]: Taking taylor expansion of 2.0 in n 25.381 * [backup-simplify]: Simplify 2.0 into 2.0 25.381 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.381 * [taylor]: Taking taylor expansion of PI in n 25.381 * [backup-simplify]: Simplify PI into PI 25.381 * [taylor]: Taking taylor expansion of n in n 25.381 * [backup-simplify]: Simplify 0 into 0 25.381 * [backup-simplify]: Simplify 1 into 1 25.381 * [backup-simplify]: Simplify (/ PI 1) into PI 25.382 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 25.383 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.383 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 25.383 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 25.383 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 25.385 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 25.386 * [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)))) 25.387 * [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))))) 25.387 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 25.387 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 25.387 * [taylor]: Taking taylor expansion of 0.25 in k 25.387 * [backup-simplify]: Simplify 0.25 into 0.25 25.387 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 25.387 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 25.387 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 25.387 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 25.387 * [taylor]: Taking taylor expansion of 2.0 in k 25.388 * [backup-simplify]: Simplify 2.0 into 2.0 25.388 * [taylor]: Taking taylor expansion of PI in k 25.388 * [backup-simplify]: Simplify PI into PI 25.388 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 25.389 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 25.389 * [taylor]: Taking taylor expansion of (log n) in k 25.389 * [taylor]: Taking taylor expansion of n in k 25.389 * [backup-simplify]: Simplify n into n 25.389 * [backup-simplify]: Simplify (log n) into (log n) 25.389 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 25.389 * [taylor]: Taking taylor expansion of 1.0 in k 25.390 * [backup-simplify]: Simplify 1.0 into 1.0 25.390 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.390 * [taylor]: Taking taylor expansion of k in k 25.390 * [backup-simplify]: Simplify 0 into 0 25.390 * [backup-simplify]: Simplify 1 into 1 25.390 * [backup-simplify]: Simplify (/ 1 1) into 1 25.390 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 25.391 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 25.392 * [backup-simplify]: Simplify (- 1) into -1 25.392 * [backup-simplify]: Simplify (+ 0 -1) into -1 25.393 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 25.395 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 25.396 * [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))))) 25.397 * [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))))) 25.398 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.399 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 25.401 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 25.401 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 25.401 * [backup-simplify]: Simplify (- 0) into 0 25.402 * [backup-simplify]: Simplify (+ 0 0) into 0 25.402 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 25.404 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 25.405 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 25.406 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.406 * [taylor]: Taking taylor expansion of 0 in k 25.406 * [backup-simplify]: Simplify 0 into 0 25.406 * [backup-simplify]: Simplify 0 into 0 25.406 * [backup-simplify]: Simplify 0 into 0 25.407 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.408 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 25.409 * [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 25.410 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.410 * [backup-simplify]: Simplify (- 0) into 0 25.410 * [backup-simplify]: Simplify (+ 0 0) into 0 25.411 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 25.412 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 25.412 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 25.414 * [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 25.414 * [taylor]: Taking taylor expansion of 0 in k 25.414 * [backup-simplify]: Simplify 0 into 0 25.414 * [backup-simplify]: Simplify 0 into 0 25.414 * [backup-simplify]: Simplify 0 into 0 25.414 * [backup-simplify]: Simplify 0 into 0 25.415 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.415 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.419 * [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 25.419 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.419 * [backup-simplify]: Simplify (- 0) into 0 25.419 * [backup-simplify]: Simplify (+ 0 0) into 0 25.420 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 25.421 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 25.422 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 25.424 * [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 25.424 * [taylor]: Taking taylor expansion of 0 in k 25.424 * [backup-simplify]: Simplify 0 into 0 25.424 * [backup-simplify]: Simplify 0 into 0 25.425 * [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)))) 25.425 * [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))) 25.425 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 25.425 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 25.425 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 25.425 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 25.425 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 25.425 * [taylor]: Taking taylor expansion of 0.25 in k 25.425 * [backup-simplify]: Simplify 0.25 into 0.25 25.426 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 25.426 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.426 * [taylor]: Taking taylor expansion of k in k 25.426 * [backup-simplify]: Simplify 0 into 0 25.426 * [backup-simplify]: Simplify 1 into 1 25.426 * [backup-simplify]: Simplify (/ 1 1) into 1 25.426 * [taylor]: Taking taylor expansion of 1.0 in k 25.426 * [backup-simplify]: Simplify 1.0 into 1.0 25.426 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 25.426 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 25.426 * [taylor]: Taking taylor expansion of -2.0 in k 25.426 * [backup-simplify]: Simplify -2.0 into -2.0 25.426 * [taylor]: Taking taylor expansion of (/ PI n) in k 25.426 * [taylor]: Taking taylor expansion of PI in k 25.426 * [backup-simplify]: Simplify PI into PI 25.426 * [taylor]: Taking taylor expansion of n in k 25.426 * [backup-simplify]: Simplify n into n 25.426 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 25.426 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 25.426 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 25.426 * [backup-simplify]: Simplify (+ 1 0) into 1 25.427 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 25.427 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 25.427 * [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)))))) 25.427 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 25.427 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 25.427 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 25.427 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 25.427 * [taylor]: Taking taylor expansion of 0.25 in n 25.427 * [backup-simplify]: Simplify 0.25 into 0.25 25.427 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 25.427 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.427 * [taylor]: Taking taylor expansion of k in n 25.427 * [backup-simplify]: Simplify k into k 25.427 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.427 * [taylor]: Taking taylor expansion of 1.0 in n 25.427 * [backup-simplify]: Simplify 1.0 into 1.0 25.427 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 25.427 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 25.427 * [taylor]: Taking taylor expansion of -2.0 in n 25.427 * [backup-simplify]: Simplify -2.0 into -2.0 25.427 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.427 * [taylor]: Taking taylor expansion of PI in n 25.427 * [backup-simplify]: Simplify PI into PI 25.427 * [taylor]: Taking taylor expansion of n in n 25.427 * [backup-simplify]: Simplify 0 into 0 25.427 * [backup-simplify]: Simplify 1 into 1 25.428 * [backup-simplify]: Simplify (/ PI 1) into PI 25.428 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 25.429 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 25.429 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 25.429 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 25.430 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 25.431 * [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)))) 25.431 * [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))))) 25.431 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 25.431 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 25.431 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 25.431 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 25.431 * [taylor]: Taking taylor expansion of 0.25 in n 25.431 * [backup-simplify]: Simplify 0.25 into 0.25 25.431 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 25.431 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.431 * [taylor]: Taking taylor expansion of k in n 25.432 * [backup-simplify]: Simplify k into k 25.432 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.432 * [taylor]: Taking taylor expansion of 1.0 in n 25.432 * [backup-simplify]: Simplify 1.0 into 1.0 25.432 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 25.432 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 25.432 * [taylor]: Taking taylor expansion of -2.0 in n 25.432 * [backup-simplify]: Simplify -2.0 into -2.0 25.432 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.432 * [taylor]: Taking taylor expansion of PI in n 25.432 * [backup-simplify]: Simplify PI into PI 25.432 * [taylor]: Taking taylor expansion of n in n 25.432 * [backup-simplify]: Simplify 0 into 0 25.432 * [backup-simplify]: Simplify 1 into 1 25.432 * [backup-simplify]: Simplify (/ PI 1) into PI 25.432 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 25.433 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 25.433 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 25.433 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 25.442 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 25.444 * [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)))) 25.446 * [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))))) 25.446 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 25.446 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 25.446 * [taylor]: Taking taylor expansion of 0.25 in k 25.446 * [backup-simplify]: Simplify 0.25 into 0.25 25.446 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 25.446 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 25.446 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.446 * [taylor]: Taking taylor expansion of k in k 25.446 * [backup-simplify]: Simplify 0 into 0 25.446 * [backup-simplify]: Simplify 1 into 1 25.447 * [backup-simplify]: Simplify (/ 1 1) into 1 25.447 * [taylor]: Taking taylor expansion of 1.0 in k 25.447 * [backup-simplify]: Simplify 1.0 into 1.0 25.447 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 25.447 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 25.447 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 25.447 * [taylor]: Taking taylor expansion of -2.0 in k 25.447 * [backup-simplify]: Simplify -2.0 into -2.0 25.447 * [taylor]: Taking taylor expansion of PI in k 25.447 * [backup-simplify]: Simplify PI into PI 25.447 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 25.449 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 25.449 * [taylor]: Taking taylor expansion of (log n) in k 25.449 * [taylor]: Taking taylor expansion of n in k 25.449 * [backup-simplify]: Simplify n into n 25.449 * [backup-simplify]: Simplify (log n) into (log n) 25.449 * [backup-simplify]: Simplify (+ 1 0) into 1 25.449 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 25.451 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 25.452 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 25.453 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 25.454 * [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))))) 25.456 * [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))))) 25.457 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.458 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 25.459 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 25.460 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 25.460 * [backup-simplify]: Simplify (+ 0 0) into 0 25.461 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 25.462 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 25.464 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 25.466 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.466 * [taylor]: Taking taylor expansion of 0 in k 25.466 * [backup-simplify]: Simplify 0 into 0 25.466 * [backup-simplify]: Simplify 0 into 0 25.466 * [backup-simplify]: Simplify 0 into 0 25.467 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.468 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 25.472 * [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 25.473 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.473 * [backup-simplify]: Simplify (+ 0 0) into 0 25.474 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 25.476 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 25.477 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 25.480 * [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 25.480 * [taylor]: Taking taylor expansion of 0 in k 25.480 * [backup-simplify]: Simplify 0 into 0 25.480 * [backup-simplify]: Simplify 0 into 0 25.480 * [backup-simplify]: Simplify 0 into 0 25.480 * [backup-simplify]: Simplify 0 into 0 25.482 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.483 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.490 * [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 25.491 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.491 * [backup-simplify]: Simplify (+ 0 0) into 0 25.492 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 25.494 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 25.496 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 25.499 * [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 25.499 * [taylor]: Taking taylor expansion of 0 in k 25.499 * [backup-simplify]: Simplify 0 into 0 25.499 * [backup-simplify]: Simplify 0 into 0 25.501 * [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)))))) 25.501 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 25.501 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 25.501 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 25.501 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 25.501 * [taylor]: Taking taylor expansion of 1.0 in k 25.501 * [backup-simplify]: Simplify 1.0 into 1.0 25.501 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 25.501 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.501 * [taylor]: Taking taylor expansion of k in k 25.501 * [backup-simplify]: Simplify 0 into 0 25.501 * [backup-simplify]: Simplify 1 into 1 25.502 * [backup-simplify]: Simplify (/ 1 1) into 1 25.502 * [backup-simplify]: Simplify (sqrt 0) into 0 25.504 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 25.504 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 25.504 * [taylor]: Taking taylor expansion of 1.0 in k 25.504 * [backup-simplify]: Simplify 1.0 into 1.0 25.504 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 25.504 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.504 * [taylor]: Taking taylor expansion of k in k 25.504 * [backup-simplify]: Simplify 0 into 0 25.504 * [backup-simplify]: Simplify 1 into 1 25.504 * [backup-simplify]: Simplify (/ 1 1) into 1 25.505 * [backup-simplify]: Simplify (sqrt 0) into 0 25.506 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 25.507 * [backup-simplify]: Simplify (* 1.0 0) into 0 25.507 * [backup-simplify]: Simplify 0 into 0 25.508 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 25.509 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 25.510 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 25.513 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 25.515 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 25.515 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 25.516 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.520 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 25.522 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 25.523 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 25.524 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 25.524 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 25.524 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 25.524 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 25.524 * [taylor]: Taking taylor expansion of 1.0 in k 25.525 * [backup-simplify]: Simplify 1.0 into 1.0 25.525 * [taylor]: Taking taylor expansion of (sqrt k) in k 25.525 * [taylor]: Taking taylor expansion of k in k 25.525 * [backup-simplify]: Simplify 0 into 0 25.525 * [backup-simplify]: Simplify 1 into 1 25.525 * [backup-simplify]: Simplify (sqrt 0) into 0 25.526 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 25.526 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 25.526 * [taylor]: Taking taylor expansion of 1.0 in k 25.526 * [backup-simplify]: Simplify 1.0 into 1.0 25.526 * [taylor]: Taking taylor expansion of (sqrt k) in k 25.527 * [taylor]: Taking taylor expansion of k in k 25.527 * [backup-simplify]: Simplify 0 into 0 25.527 * [backup-simplify]: Simplify 1 into 1 25.527 * [backup-simplify]: Simplify (sqrt 0) into 0 25.528 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 25.529 * [backup-simplify]: Simplify (* 1.0 0) into 0 25.529 * [backup-simplify]: Simplify 0 into 0 25.530 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 25.531 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 25.534 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 25.536 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 25.536 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 25.540 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 25.543 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 25.543 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 25.545 * [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)))))))) 25.545 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 25.545 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 25.545 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 25.545 * [taylor]: Taking taylor expansion of 1.0 in k 25.545 * [backup-simplify]: Simplify 1.0 into 1.0 25.545 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 25.545 * [taylor]: Taking taylor expansion of (/ -1 k) in k 25.545 * [taylor]: Taking taylor expansion of -1 in k 25.545 * [backup-simplify]: Simplify -1 into -1 25.545 * [taylor]: Taking taylor expansion of k in k 25.545 * [backup-simplify]: Simplify 0 into 0 25.545 * [backup-simplify]: Simplify 1 into 1 25.546 * [backup-simplify]: Simplify (/ -1 1) into -1 25.546 * [backup-simplify]: Simplify (sqrt 0) into 0 25.547 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 25.548 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 25.548 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 25.548 * [taylor]: Taking taylor expansion of 1.0 in k 25.548 * [backup-simplify]: Simplify 1.0 into 1.0 25.548 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 25.548 * [taylor]: Taking taylor expansion of (/ -1 k) in k 25.548 * [taylor]: Taking taylor expansion of -1 in k 25.548 * [backup-simplify]: Simplify -1 into -1 25.548 * [taylor]: Taking taylor expansion of k in k 25.548 * [backup-simplify]: Simplify 0 into 0 25.548 * [backup-simplify]: Simplify 1 into 1 25.549 * [backup-simplify]: Simplify (/ -1 1) into -1 25.549 * [backup-simplify]: Simplify (sqrt 0) into 0 25.550 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 25.551 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 25.551 * [backup-simplify]: Simplify +nan.0 into +nan.0 25.552 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 25.556 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 25.559 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 25.559 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 25.560 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.564 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 25.568 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 25.569 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 25.570 * [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))))) 25.570 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 2) 25.570 * [backup-simplify]: Simplify (* n PI) into (* n PI) 25.570 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 25.570 * [taylor]: Taking taylor expansion of (* n PI) in n 25.570 * [taylor]: Taking taylor expansion of n in n 25.570 * [backup-simplify]: Simplify 0 into 0 25.570 * [backup-simplify]: Simplify 1 into 1 25.570 * [taylor]: Taking taylor expansion of PI in n 25.570 * [backup-simplify]: Simplify PI into PI 25.570 * [taylor]: Taking taylor expansion of (* n PI) in n 25.570 * [taylor]: Taking taylor expansion of n in n 25.570 * [backup-simplify]: Simplify 0 into 0 25.570 * [backup-simplify]: Simplify 1 into 1 25.570 * [taylor]: Taking taylor expansion of PI in n 25.570 * [backup-simplify]: Simplify PI into PI 25.571 * [backup-simplify]: Simplify (* 0 PI) into 0 25.571 * [backup-simplify]: Simplify 0 into 0 25.573 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 25.573 * [backup-simplify]: Simplify PI into PI 25.573 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 25.573 * [backup-simplify]: Simplify 0 into 0 25.574 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 25.574 * [backup-simplify]: Simplify 0 into 0 25.575 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 25.575 * [backup-simplify]: Simplify 0 into 0 25.576 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 25.576 * [backup-simplify]: Simplify 0 into 0 25.577 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 25.577 * [backup-simplify]: Simplify 0 into 0 25.578 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 25.578 * [backup-simplify]: Simplify 0 into 0 25.578 * [backup-simplify]: Simplify (* PI n) into (* n PI) 25.578 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 25.578 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 25.578 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.578 * [taylor]: Taking taylor expansion of PI in n 25.578 * [backup-simplify]: Simplify PI into PI 25.578 * [taylor]: Taking taylor expansion of n in n 25.578 * [backup-simplify]: Simplify 0 into 0 25.578 * [backup-simplify]: Simplify 1 into 1 25.579 * [backup-simplify]: Simplify (/ PI 1) into PI 25.579 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.579 * [taylor]: Taking taylor expansion of PI in n 25.579 * [backup-simplify]: Simplify PI into PI 25.579 * [taylor]: Taking taylor expansion of n in n 25.579 * [backup-simplify]: Simplify 0 into 0 25.579 * [backup-simplify]: Simplify 1 into 1 25.579 * [backup-simplify]: Simplify (/ PI 1) into PI 25.579 * [backup-simplify]: Simplify PI into PI 25.580 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.580 * [backup-simplify]: Simplify 0 into 0 25.581 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.581 * [backup-simplify]: Simplify 0 into 0 25.581 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.581 * [backup-simplify]: Simplify 0 into 0 25.582 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.582 * [backup-simplify]: Simplify 0 into 0 25.583 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.583 * [backup-simplify]: Simplify 0 into 0 25.583 * [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 25.583 * [backup-simplify]: Simplify 0 into 0 25.583 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 25.583 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 25.583 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 25.583 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 25.584 * [taylor]: Taking taylor expansion of -1 in n 25.584 * [backup-simplify]: Simplify -1 into -1 25.584 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.584 * [taylor]: Taking taylor expansion of PI in n 25.584 * [backup-simplify]: Simplify PI into PI 25.584 * [taylor]: Taking taylor expansion of n in n 25.584 * [backup-simplify]: Simplify 0 into 0 25.584 * [backup-simplify]: Simplify 1 into 1 25.584 * [backup-simplify]: Simplify (/ PI 1) into PI 25.584 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 25.584 * [taylor]: Taking taylor expansion of -1 in n 25.584 * [backup-simplify]: Simplify -1 into -1 25.584 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.584 * [taylor]: Taking taylor expansion of PI in n 25.584 * [backup-simplify]: Simplify PI into PI 25.584 * [taylor]: Taking taylor expansion of n in n 25.584 * [backup-simplify]: Simplify 0 into 0 25.584 * [backup-simplify]: Simplify 1 into 1 25.584 * [backup-simplify]: Simplify (/ PI 1) into PI 25.585 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 25.585 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 25.586 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.586 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 25.586 * [backup-simplify]: Simplify 0 into 0 25.592 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.593 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 25.593 * [backup-simplify]: Simplify 0 into 0 25.594 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.595 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.595 * [backup-simplify]: Simplify 0 into 0 25.595 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.596 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 25.596 * [backup-simplify]: Simplify 0 into 0 25.597 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.598 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 25.598 * [backup-simplify]: Simplify 0 into 0 25.598 * [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 25.599 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 25.599 * [backup-simplify]: Simplify 0 into 0 25.600 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 25.600 * * * [progress]: simplifying candidates 25.603 * [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 (/ (- 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) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +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) 25.608 * * [simplify]: Extracting # 0 : cost 0 25.608 * * [simplify]: Extracting # 1 : cost 0 25.609 * * [simplify]: Extracting # 2 : cost 0 25.609 * * [simplify]: Extracting # 3 : cost 0 25.610 * * [simplify]: Extracting # 4 : cost 0 25.610 * * [simplify]: Extracting # 5 : cost 0 25.611 * * [simplify]: Extracting # 6 : cost 0 25.612 * * [simplify]: Extracting # 7 : cost 0 25.612 * * [simplify]: Extracting # 8 : cost 0 25.613 * * [simplify]: Extracting # 9 : cost 0 25.613 * * [simplify]: Extracting # 10 : cost 0 25.614 * * [simplify]: Extracting # 11 : cost 0 25.615 * * [simplify]: Extracting # 12 : cost 0 25.615 * * [simplify]: Extracting # 13 : cost 0 25.616 * * [simplify]: iteration 0 : 398 enodes (cost 2712 ) 26.077 * * [simplify]: Extracting # 0 : cost 0 26.084 * * [simplify]: Extracting # 1 : cost 0 26.091 * * [simplify]: Extracting # 2 : cost 0 26.098 * * [simplify]: Extracting # 3 : cost 0 26.111 * * [simplify]: Extracting # 4 : cost 0 26.118 * * [simplify]: Extracting # 5 : cost 0 26.124 * * [simplify]: Extracting # 6 : cost 0 26.131 * * [simplify]: iteration 1 : 2564 enodes (cost 2506 ) 28.257 * * [simplify]: Extracting # 0 : cost 0 28.264 * * [simplify]: Extracting # 1 : cost 0 28.271 * * [simplify]: Extracting # 2 : cost 0 28.277 * * [simplify]: Extracting # 3 : cost 0 28.283 * * [simplify]: Extracting # 4 : cost 0 28.289 * * [simplify]: Extracting # 5 : cost 0 28.301 * * [simplify]: iteration done: 5001 enodes (cost 2419 ) 28.303 * [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))) (/ (- 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)) (/ (- 1.0 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 (* n PI)) (/ k 2.0)) (pow (* n (* 2.0 PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (sqrt (- 1.0 k))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (+ (sqrt 1.0) (sqrt k))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (pow (* 2.0 (* n PI)) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)) (* (log (* 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 (pow (* (* 2.0 PI) n) (/ (- 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 (* 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 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) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 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 (* n (* 2.0 PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 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 (* 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)) (/ (sqrt 2) (cbrt (- 1.0 k))))) (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))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* 2.0 (* n PI)) (- 1.0 k)) (* n (* 2.0 PI)) (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 (* (* 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 (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)) (* 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 (* (pow (log (* 2.0 PI)) 2) (pow (* n (* 2.0 PI)) 0.5)) (* 0.125 (pow k 2)) (- (fma 0.125 (* (pow k 2) (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.5))) (fma (* (* (pow (* n (* 2.0 PI)) 0.5) (log n)) (* (pow k 2) (log (* 2.0 PI)))) 0.25 (pow (* n (* 2.0 PI)) 0.5))) (* (fma (* k (log (* 2.0 PI))) (pow (* n (* 2.0 PI)) 0.5) (* (* k (pow (* n (* 2.0 PI)) 0.5)) (log n))) 0.5))) (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 (log (* 2.0 PI)) 2)) (pow (* n (* 2.0 PI)) 0.25)) (- (fma (* (pow k 2) (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.25))) 0.03125 (+ (pow (* n (* 2.0 PI)) 0.25) (* (* 0.0625 (pow k 2)) (* (* (log (* 2.0 PI)) (pow (* n (* 2.0 PI)) 0.25)) (log n))))) (* 0.25 (fma (* (log (* 2.0 PI)) (pow (* n (* 2.0 PI)) 0.25)) k (* k (* (pow (* n (* 2.0 PI)) 0.25) (log n))))))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (- (* +nan.0 k) (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))) (* n PI) (* n PI) (* n PI) 28.306 * * * [progress]: adding candidates to table 29.480 * * [progress]: iteration 4 / 4 29.480 * * * [progress]: picking best candidate 29.513 * * * * [pick]: Picked # 29.513 * * * [progress]: localizing error 29.549 * * * [progress]: generating rewritten candidates 29.549 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 29.680 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 29.719 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 2 2 1) 29.720 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 2 1 2) 29.729 * * * [progress]: generating series expansions 29.729 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 29.730 * [backup-simplify]: Simplify (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 29.730 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 29.730 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 29.730 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 29.730 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 29.730 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 29.730 * [taylor]: Taking taylor expansion of 0.5 in k 29.730 * [backup-simplify]: Simplify 0.5 into 0.5 29.730 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 29.730 * [taylor]: Taking taylor expansion of 1.0 in k 29.730 * [backup-simplify]: Simplify 1.0 into 1.0 29.730 * [taylor]: Taking taylor expansion of k in k 29.730 * [backup-simplify]: Simplify 0 into 0 29.730 * [backup-simplify]: Simplify 1 into 1 29.730 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 29.730 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 29.730 * [taylor]: Taking taylor expansion of 2.0 in k 29.730 * [backup-simplify]: Simplify 2.0 into 2.0 29.730 * [taylor]: Taking taylor expansion of (* n PI) in k 29.730 * [taylor]: Taking taylor expansion of n in k 29.730 * [backup-simplify]: Simplify n into n 29.730 * [taylor]: Taking taylor expansion of PI in k 29.730 * [backup-simplify]: Simplify PI into PI 29.731 * [backup-simplify]: Simplify (* n PI) into (* n PI) 29.731 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 29.731 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 29.731 * [backup-simplify]: Simplify (- 0) into 0 29.732 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 29.732 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 29.732 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 29.732 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 29.733 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 29.733 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 29.733 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 29.733 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 29.733 * [taylor]: Taking taylor expansion of 0.5 in n 29.733 * [backup-simplify]: Simplify 0.5 into 0.5 29.733 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 29.733 * [taylor]: Taking taylor expansion of 1.0 in n 29.733 * [backup-simplify]: Simplify 1.0 into 1.0 29.733 * [taylor]: Taking taylor expansion of k in n 29.733 * [backup-simplify]: Simplify k into k 29.733 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 29.733 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 29.733 * [taylor]: Taking taylor expansion of 2.0 in n 29.733 * [backup-simplify]: Simplify 2.0 into 2.0 29.733 * [taylor]: Taking taylor expansion of (* n PI) in n 29.733 * [taylor]: Taking taylor expansion of n in n 29.733 * [backup-simplify]: Simplify 0 into 0 29.733 * [backup-simplify]: Simplify 1 into 1 29.733 * [taylor]: Taking taylor expansion of PI in n 29.733 * [backup-simplify]: Simplify PI into PI 29.733 * [backup-simplify]: Simplify (* 0 PI) into 0 29.734 * [backup-simplify]: Simplify (* 2.0 0) into 0 29.735 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 29.736 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 29.737 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 29.737 * [backup-simplify]: Simplify (- k) into (- k) 29.737 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 29.737 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 29.738 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 29.739 * [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)))) 29.739 * [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))))) 29.739 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 29.739 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 29.739 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 29.740 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 29.740 * [taylor]: Taking taylor expansion of 0.5 in n 29.740 * [backup-simplify]: Simplify 0.5 into 0.5 29.740 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 29.740 * [taylor]: Taking taylor expansion of 1.0 in n 29.740 * [backup-simplify]: Simplify 1.0 into 1.0 29.740 * [taylor]: Taking taylor expansion of k in n 29.740 * [backup-simplify]: Simplify k into k 29.740 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 29.740 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 29.740 * [taylor]: Taking taylor expansion of 2.0 in n 29.740 * [backup-simplify]: Simplify 2.0 into 2.0 29.740 * [taylor]: Taking taylor expansion of (* n PI) in n 29.740 * [taylor]: Taking taylor expansion of n in n 29.740 * [backup-simplify]: Simplify 0 into 0 29.740 * [backup-simplify]: Simplify 1 into 1 29.740 * [taylor]: Taking taylor expansion of PI in n 29.740 * [backup-simplify]: Simplify PI into PI 29.740 * [backup-simplify]: Simplify (* 0 PI) into 0 29.740 * [backup-simplify]: Simplify (* 2.0 0) into 0 29.741 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 29.742 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 29.743 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 29.743 * [backup-simplify]: Simplify (- k) into (- k) 29.743 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 29.743 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 29.744 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 29.745 * [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)))) 29.745 * [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))))) 29.746 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 29.746 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 29.746 * [taylor]: Taking taylor expansion of 0.5 in k 29.746 * [backup-simplify]: Simplify 0.5 into 0.5 29.746 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 29.746 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 29.746 * [taylor]: Taking taylor expansion of 1.0 in k 29.746 * [backup-simplify]: Simplify 1.0 into 1.0 29.746 * [taylor]: Taking taylor expansion of k in k 29.746 * [backup-simplify]: Simplify 0 into 0 29.746 * [backup-simplify]: Simplify 1 into 1 29.746 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 29.746 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 29.746 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 29.746 * [taylor]: Taking taylor expansion of 2.0 in k 29.746 * [backup-simplify]: Simplify 2.0 into 2.0 29.746 * [taylor]: Taking taylor expansion of PI in k 29.746 * [backup-simplify]: Simplify PI into PI 29.746 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 29.747 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 29.747 * [taylor]: Taking taylor expansion of (log n) in k 29.747 * [taylor]: Taking taylor expansion of n in k 29.747 * [backup-simplify]: Simplify n into n 29.747 * [backup-simplify]: Simplify (log n) into (log n) 29.747 * [backup-simplify]: Simplify (- 0) into 0 29.748 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 29.748 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 29.749 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 29.750 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 29.750 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 29.751 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 29.757 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 29.758 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 29.759 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 29.759 * [backup-simplify]: Simplify (- 0) into 0 29.759 * [backup-simplify]: Simplify (+ 0 0) into 0 29.760 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 29.761 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 29.761 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 29.763 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 29.763 * [taylor]: Taking taylor expansion of 0 in k 29.763 * [backup-simplify]: Simplify 0 into 0 29.763 * [backup-simplify]: Simplify 0 into 0 29.763 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 29.764 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 29.765 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 29.765 * [backup-simplify]: Simplify (+ 0 0) into 0 29.766 * [backup-simplify]: Simplify (- 1) into -1 29.766 * [backup-simplify]: Simplify (+ 0 -1) into -1 29.767 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 29.768 * [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)))) 29.770 * [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)))))) 29.772 * [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)))))) 29.773 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 29.774 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 29.776 * [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 29.776 * [backup-simplify]: Simplify (- 0) into 0 29.776 * [backup-simplify]: Simplify (+ 0 0) into 0 29.777 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 29.778 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 29.779 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 29.781 * [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 29.781 * [taylor]: Taking taylor expansion of 0 in k 29.781 * [backup-simplify]: Simplify 0 into 0 29.781 * [backup-simplify]: Simplify 0 into 0 29.781 * [backup-simplify]: Simplify 0 into 0 29.781 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 29.783 * [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 29.785 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 29.785 * [backup-simplify]: Simplify (+ 0 0) into 0 29.785 * [backup-simplify]: Simplify (- 0) into 0 29.785 * [backup-simplify]: Simplify (+ 0 0) into 0 29.787 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 29.788 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 29.791 * [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)))))) 29.794 * [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)))))) 29.800 * [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)))))) 29.801 * [backup-simplify]: Simplify (pow (* 2.0 (* (* (cbrt (/ 1 n)) (cbrt (/ 1 n))) (* (cbrt (/ 1 n)) PI))) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 29.801 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 29.801 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 29.801 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 29.801 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 29.801 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 29.801 * [taylor]: Taking taylor expansion of 0.5 in k 29.801 * [backup-simplify]: Simplify 0.5 into 0.5 29.801 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 29.801 * [taylor]: Taking taylor expansion of 1.0 in k 29.801 * [backup-simplify]: Simplify 1.0 into 1.0 29.801 * [taylor]: Taking taylor expansion of (/ 1 k) in k 29.801 * [taylor]: Taking taylor expansion of k in k 29.801 * [backup-simplify]: Simplify 0 into 0 29.801 * [backup-simplify]: Simplify 1 into 1 29.801 * [backup-simplify]: Simplify (/ 1 1) into 1 29.801 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 29.801 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 29.801 * [taylor]: Taking taylor expansion of 2.0 in k 29.801 * [backup-simplify]: Simplify 2.0 into 2.0 29.801 * [taylor]: Taking taylor expansion of (/ PI n) in k 29.801 * [taylor]: Taking taylor expansion of PI in k 29.802 * [backup-simplify]: Simplify PI into PI 29.802 * [taylor]: Taking taylor expansion of n in k 29.802 * [backup-simplify]: Simplify n into n 29.802 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 29.802 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 29.802 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 29.802 * [backup-simplify]: Simplify (- 1) into -1 29.802 * [backup-simplify]: Simplify (+ 0 -1) into -1 29.803 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 29.803 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 29.803 * [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))))) 29.803 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 29.803 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 29.803 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 29.803 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 29.803 * [taylor]: Taking taylor expansion of 0.5 in n 29.803 * [backup-simplify]: Simplify 0.5 into 0.5 29.803 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 29.803 * [taylor]: Taking taylor expansion of 1.0 in n 29.803 * [backup-simplify]: Simplify 1.0 into 1.0 29.803 * [taylor]: Taking taylor expansion of (/ 1 k) in n 29.803 * [taylor]: Taking taylor expansion of k in n 29.803 * [backup-simplify]: Simplify k into k 29.803 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 29.803 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 29.803 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 29.803 * [taylor]: Taking taylor expansion of 2.0 in n 29.803 * [backup-simplify]: Simplify 2.0 into 2.0 29.803 * [taylor]: Taking taylor expansion of (/ PI n) in n 29.803 * [taylor]: Taking taylor expansion of PI in n 29.803 * [backup-simplify]: Simplify PI into PI 29.803 * [taylor]: Taking taylor expansion of n in n 29.803 * [backup-simplify]: Simplify 0 into 0 29.803 * [backup-simplify]: Simplify 1 into 1 29.804 * [backup-simplify]: Simplify (/ PI 1) into PI 29.804 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 29.804 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 29.805 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 29.805 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 29.805 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 29.806 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 29.806 * [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)))) 29.807 * [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))))) 29.807 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 29.807 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 29.807 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 29.807 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 29.807 * [taylor]: Taking taylor expansion of 0.5 in n 29.807 * [backup-simplify]: Simplify 0.5 into 0.5 29.807 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 29.807 * [taylor]: Taking taylor expansion of 1.0 in n 29.807 * [backup-simplify]: Simplify 1.0 into 1.0 29.807 * [taylor]: Taking taylor expansion of (/ 1 k) in n 29.807 * [taylor]: Taking taylor expansion of k in n 29.807 * [backup-simplify]: Simplify k into k 29.807 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 29.807 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 29.807 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 29.807 * [taylor]: Taking taylor expansion of 2.0 in n 29.807 * [backup-simplify]: Simplify 2.0 into 2.0 29.807 * [taylor]: Taking taylor expansion of (/ PI n) in n 29.808 * [taylor]: Taking taylor expansion of PI in n 29.808 * [backup-simplify]: Simplify PI into PI 29.808 * [taylor]: Taking taylor expansion of n in n 29.808 * [backup-simplify]: Simplify 0 into 0 29.808 * [backup-simplify]: Simplify 1 into 1 29.808 * [backup-simplify]: Simplify (/ PI 1) into PI 29.808 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 29.809 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 29.809 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 29.809 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 29.809 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 29.810 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 29.811 * [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)))) 29.811 * [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))))) 29.812 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 29.812 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 29.812 * [taylor]: Taking taylor expansion of 0.5 in k 29.812 * [backup-simplify]: Simplify 0.5 into 0.5 29.812 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 29.812 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 29.812 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 29.812 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 29.812 * [taylor]: Taking taylor expansion of 2.0 in k 29.812 * [backup-simplify]: Simplify 2.0 into 2.0 29.812 * [taylor]: Taking taylor expansion of PI in k 29.812 * [backup-simplify]: Simplify PI into PI 29.812 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 29.813 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 29.813 * [taylor]: Taking taylor expansion of (log n) in k 29.813 * [taylor]: Taking taylor expansion of n in k 29.813 * [backup-simplify]: Simplify n into n 29.813 * [backup-simplify]: Simplify (log n) into (log n) 29.813 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 29.813 * [taylor]: Taking taylor expansion of 1.0 in k 29.813 * [backup-simplify]: Simplify 1.0 into 1.0 29.813 * [taylor]: Taking taylor expansion of (/ 1 k) in k 29.813 * [taylor]: Taking taylor expansion of k in k 29.813 * [backup-simplify]: Simplify 0 into 0 29.813 * [backup-simplify]: Simplify 1 into 1 29.814 * [backup-simplify]: Simplify (/ 1 1) into 1 29.814 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 29.815 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 29.815 * [backup-simplify]: Simplify (- 1) into -1 29.816 * [backup-simplify]: Simplify (+ 0 -1) into -1 29.817 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 29.818 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 29.819 * [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))))) 29.821 * [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))))) 29.822 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 29.823 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 29.825 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 29.825 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 29.826 * [backup-simplify]: Simplify (- 0) into 0 29.826 * [backup-simplify]: Simplify (+ 0 0) into 0 29.827 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 29.828 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 29.830 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 29.832 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 29.832 * [taylor]: Taking taylor expansion of 0 in k 29.832 * [backup-simplify]: Simplify 0 into 0 29.832 * [backup-simplify]: Simplify 0 into 0 29.832 * [backup-simplify]: Simplify 0 into 0 29.833 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 29.834 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 29.838 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 29.838 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 29.838 * [backup-simplify]: Simplify (- 0) into 0 29.839 * [backup-simplify]: Simplify (+ 0 0) into 0 29.840 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 29.841 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 29.843 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 29.846 * [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 29.846 * [taylor]: Taking taylor expansion of 0 in k 29.846 * [backup-simplify]: Simplify 0 into 0 29.846 * [backup-simplify]: Simplify 0 into 0 29.846 * [backup-simplify]: Simplify 0 into 0 29.846 * [backup-simplify]: Simplify 0 into 0 29.847 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 29.849 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 29.855 * [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 29.856 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 29.856 * [backup-simplify]: Simplify (- 0) into 0 29.856 * [backup-simplify]: Simplify (+ 0 0) into 0 29.858 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 29.859 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 29.861 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 29.864 * [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 29.864 * [taylor]: Taking taylor expansion of 0 in k 29.864 * [backup-simplify]: Simplify 0 into 0 29.864 * [backup-simplify]: Simplify 0 into 0 29.866 * [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)))) 29.867 * [backup-simplify]: Simplify (pow (* 2.0 (* (* (cbrt (/ 1 (- n))) (cbrt (/ 1 (- n)))) (* (cbrt (/ 1 (- n))) PI))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) 29.867 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 29.867 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 29.867 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in k 29.867 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in k 29.867 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 29.867 * [taylor]: Taking taylor expansion of 0.5 in k 29.867 * [backup-simplify]: Simplify 0.5 into 0.5 29.867 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 29.867 * [taylor]: Taking taylor expansion of (/ 1 k) in k 29.867 * [taylor]: Taking taylor expansion of k in k 29.867 * [backup-simplify]: Simplify 0 into 0 29.867 * [backup-simplify]: Simplify 1 into 1 29.867 * [backup-simplify]: Simplify (/ 1 1) into 1 29.867 * [taylor]: Taking taylor expansion of 1.0 in k 29.868 * [backup-simplify]: Simplify 1.0 into 1.0 29.868 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in k 29.868 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in k 29.868 * [taylor]: Taking taylor expansion of 2.0 in k 29.868 * [backup-simplify]: Simplify 2.0 into 2.0 29.868 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in k 29.868 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in k 29.868 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in k 29.868 * [taylor]: Taking taylor expansion of (cbrt -1) in k 29.868 * [taylor]: Taking taylor expansion of -1 in k 29.868 * [backup-simplify]: Simplify -1 into -1 29.868 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 29.869 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 29.869 * [taylor]: Taking taylor expansion of PI in k 29.869 * [backup-simplify]: Simplify PI into PI 29.869 * [taylor]: Taking taylor expansion of n in k 29.869 * [backup-simplify]: Simplify n into n 29.871 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 29.879 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 29.880 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 29.881 * [backup-simplify]: Simplify (/ (* -1 PI) n) into (* -1 (/ PI n)) 29.881 * [backup-simplify]: Simplify (* 2.0 (* -1 (/ PI n))) into (* -2.0 (/ PI n)) 29.881 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 29.881 * [backup-simplify]: Simplify (+ 1 0) into 1 29.881 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 29.881 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 29.883 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 29.883 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 29.883 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 29.883 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 29.883 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 29.883 * [taylor]: Taking taylor expansion of 0.5 in n 29.883 * [backup-simplify]: Simplify 0.5 into 0.5 29.883 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 29.883 * [taylor]: Taking taylor expansion of (/ 1 k) in n 29.883 * [taylor]: Taking taylor expansion of k in n 29.883 * [backup-simplify]: Simplify k into k 29.883 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 29.883 * [taylor]: Taking taylor expansion of 1.0 in n 29.883 * [backup-simplify]: Simplify 1.0 into 1.0 29.883 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 29.883 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 29.883 * [taylor]: Taking taylor expansion of 2.0 in n 29.883 * [backup-simplify]: Simplify 2.0 into 2.0 29.883 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 29.883 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 29.883 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 29.883 * [taylor]: Taking taylor expansion of (cbrt -1) in n 29.883 * [taylor]: Taking taylor expansion of -1 in n 29.883 * [backup-simplify]: Simplify -1 into -1 29.883 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 29.884 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 29.884 * [taylor]: Taking taylor expansion of PI in n 29.884 * [backup-simplify]: Simplify PI into PI 29.884 * [taylor]: Taking taylor expansion of n in n 29.884 * [backup-simplify]: Simplify 0 into 0 29.884 * [backup-simplify]: Simplify 1 into 1 29.885 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 29.886 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 29.887 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 29.888 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 29.889 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 29.889 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 29.889 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 29.889 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 29.890 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 29.891 * [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)))) 29.892 * [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))))) 29.892 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 29.892 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 29.892 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 29.892 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 29.892 * [taylor]: Taking taylor expansion of 0.5 in n 29.892 * [backup-simplify]: Simplify 0.5 into 0.5 29.892 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 29.892 * [taylor]: Taking taylor expansion of (/ 1 k) in n 29.892 * [taylor]: Taking taylor expansion of k in n 29.892 * [backup-simplify]: Simplify k into k 29.892 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 29.892 * [taylor]: Taking taylor expansion of 1.0 in n 29.892 * [backup-simplify]: Simplify 1.0 into 1.0 29.892 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 29.892 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 29.892 * [taylor]: Taking taylor expansion of 2.0 in n 29.892 * [backup-simplify]: Simplify 2.0 into 2.0 29.892 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 29.892 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 29.892 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 29.892 * [taylor]: Taking taylor expansion of (cbrt -1) in n 29.892 * [taylor]: Taking taylor expansion of -1 in n 29.892 * [backup-simplify]: Simplify -1 into -1 29.893 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 29.893 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 29.893 * [taylor]: Taking taylor expansion of PI in n 29.893 * [backup-simplify]: Simplify PI into PI 29.893 * [taylor]: Taking taylor expansion of n in n 29.893 * [backup-simplify]: Simplify 0 into 0 29.893 * [backup-simplify]: Simplify 1 into 1 29.894 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 29.895 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 29.896 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 29.897 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 29.898 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 29.898 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 29.898 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 29.898 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 29.899 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 29.900 * [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)))) 29.901 * [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))))) 29.901 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 29.901 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 29.901 * [taylor]: Taking taylor expansion of 0.5 in k 29.901 * [backup-simplify]: Simplify 0.5 into 0.5 29.901 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 29.901 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 29.901 * [taylor]: Taking taylor expansion of (/ 1 k) in k 29.901 * [taylor]: Taking taylor expansion of k in k 29.901 * [backup-simplify]: Simplify 0 into 0 29.901 * [backup-simplify]: Simplify 1 into 1 29.901 * [backup-simplify]: Simplify (/ 1 1) into 1 29.901 * [taylor]: Taking taylor expansion of 1.0 in k 29.902 * [backup-simplify]: Simplify 1.0 into 1.0 29.902 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 29.902 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 29.902 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 29.902 * [taylor]: Taking taylor expansion of -2.0 in k 29.902 * [backup-simplify]: Simplify -2.0 into -2.0 29.902 * [taylor]: Taking taylor expansion of PI in k 29.902 * [backup-simplify]: Simplify PI into PI 29.902 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 29.903 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 29.903 * [taylor]: Taking taylor expansion of (log n) in k 29.903 * [taylor]: Taking taylor expansion of n in k 29.903 * [backup-simplify]: Simplify n into n 29.903 * [backup-simplify]: Simplify (log n) into (log n) 29.903 * [backup-simplify]: Simplify (+ 1 0) into 1 29.903 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 29.904 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 29.904 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 29.905 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 29.906 * [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))))) 29.908 * [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))))) 29.909 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (cbrt -1))) into 0 29.910 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow (cbrt -1) 2))) into 0 29.911 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (* 0 PI)) into 0 29.912 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)))) into 0 29.913 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* -1 PI))) into 0 29.915 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 29.915 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 29.915 * [backup-simplify]: Simplify (+ 0 0) into 0 29.916 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 29.917 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 29.918 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 29.920 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 29.920 * [taylor]: Taking taylor expansion of 0 in k 29.920 * [backup-simplify]: Simplify 0 into 0 29.920 * [backup-simplify]: Simplify 0 into 0 29.920 * [backup-simplify]: Simplify 0 into 0 29.922 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 29.923 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (cbrt -1)))) into 0 29.924 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2)))) into 0 29.926 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (* 0 PI))) into 0 29.927 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)))) into 0 29.928 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* -1 PI)))) into 0 29.931 * [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 29.931 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 29.932 * [backup-simplify]: Simplify (+ 0 0) into 0 29.932 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 29.934 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 29.935 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 29.938 * [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 29.938 * [taylor]: Taking taylor expansion of 0 in k 29.938 * [backup-simplify]: Simplify 0 into 0 29.938 * [backup-simplify]: Simplify 0 into 0 29.938 * [backup-simplify]: Simplify 0 into 0 29.938 * [backup-simplify]: Simplify 0 into 0 29.940 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 29.941 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1))))) into 0 29.942 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2))))) into 0 29.944 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 29.945 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 29.947 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* -1 PI))))) into 0 29.954 * [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 29.954 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 29.955 * [backup-simplify]: Simplify (+ 0 0) into 0 29.957 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 29.958 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 29.960 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 29.962 * [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 29.962 * [taylor]: Taking taylor expansion of 0 in k 29.962 * [backup-simplify]: Simplify 0 into 0 29.962 * [backup-simplify]: Simplify 0 into 0 29.964 * [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)))))) 29.964 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 29.964 * [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))) 29.964 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 29.964 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 29.964 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 29.964 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 29.964 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 29.964 * [taylor]: Taking taylor expansion of 0.25 in k 29.964 * [backup-simplify]: Simplify 0.25 into 0.25 29.964 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 29.964 * [taylor]: Taking taylor expansion of 1.0 in k 29.964 * [backup-simplify]: Simplify 1.0 into 1.0 29.964 * [taylor]: Taking taylor expansion of k in k 29.965 * [backup-simplify]: Simplify 0 into 0 29.965 * [backup-simplify]: Simplify 1 into 1 29.965 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 29.965 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 29.965 * [taylor]: Taking taylor expansion of 2.0 in k 29.965 * [backup-simplify]: Simplify 2.0 into 2.0 29.965 * [taylor]: Taking taylor expansion of (* n PI) in k 29.965 * [taylor]: Taking taylor expansion of n in k 29.965 * [backup-simplify]: Simplify n into n 29.965 * [taylor]: Taking taylor expansion of PI in k 29.965 * [backup-simplify]: Simplify PI into PI 29.965 * [backup-simplify]: Simplify (* n PI) into (* n PI) 29.965 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 29.965 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 29.965 * [backup-simplify]: Simplify (- 0) into 0 29.965 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 29.966 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 29.966 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 29.966 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 29.966 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 29.966 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 29.966 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 29.966 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 29.966 * [taylor]: Taking taylor expansion of 0.25 in n 29.966 * [backup-simplify]: Simplify 0.25 into 0.25 29.966 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 29.966 * [taylor]: Taking taylor expansion of 1.0 in n 29.966 * [backup-simplify]: Simplify 1.0 into 1.0 29.966 * [taylor]: Taking taylor expansion of k in n 29.966 * [backup-simplify]: Simplify k into k 29.966 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 29.966 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 29.966 * [taylor]: Taking taylor expansion of 2.0 in n 29.966 * [backup-simplify]: Simplify 2.0 into 2.0 29.966 * [taylor]: Taking taylor expansion of (* n PI) in n 29.966 * [taylor]: Taking taylor expansion of n in n 29.966 * [backup-simplify]: Simplify 0 into 0 29.966 * [backup-simplify]: Simplify 1 into 1 29.966 * [taylor]: Taking taylor expansion of PI in n 29.966 * [backup-simplify]: Simplify PI into PI 29.966 * [backup-simplify]: Simplify (* 0 PI) into 0 29.967 * [backup-simplify]: Simplify (* 2.0 0) into 0 29.968 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 29.969 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 29.969 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 29.969 * [backup-simplify]: Simplify (- k) into (- k) 29.969 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 29.969 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 29.970 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 29.971 * [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)))) 29.972 * [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))))) 29.972 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 29.972 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 29.972 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 29.972 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 29.972 * [taylor]: Taking taylor expansion of 0.25 in n 29.972 * [backup-simplify]: Simplify 0.25 into 0.25 29.972 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 29.972 * [taylor]: Taking taylor expansion of 1.0 in n 29.972 * [backup-simplify]: Simplify 1.0 into 1.0 29.972 * [taylor]: Taking taylor expansion of k in n 29.972 * [backup-simplify]: Simplify k into k 29.972 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 29.972 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 29.972 * [taylor]: Taking taylor expansion of 2.0 in n 29.972 * [backup-simplify]: Simplify 2.0 into 2.0 29.972 * [taylor]: Taking taylor expansion of (* n PI) in n 29.972 * [taylor]: Taking taylor expansion of n in n 29.972 * [backup-simplify]: Simplify 0 into 0 29.972 * [backup-simplify]: Simplify 1 into 1 29.972 * [taylor]: Taking taylor expansion of PI in n 29.972 * [backup-simplify]: Simplify PI into PI 29.972 * [backup-simplify]: Simplify (* 0 PI) into 0 29.973 * [backup-simplify]: Simplify (* 2.0 0) into 0 29.974 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 29.975 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 29.975 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 29.976 * [backup-simplify]: Simplify (- k) into (- k) 29.976 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 29.976 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 29.976 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 29.977 * [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)))) 29.978 * [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))))) 29.978 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 29.978 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 29.978 * [taylor]: Taking taylor expansion of 0.25 in k 29.978 * [backup-simplify]: Simplify 0.25 into 0.25 29.978 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 29.978 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 29.978 * [taylor]: Taking taylor expansion of 1.0 in k 29.978 * [backup-simplify]: Simplify 1.0 into 1.0 29.978 * [taylor]: Taking taylor expansion of k in k 29.978 * [backup-simplify]: Simplify 0 into 0 29.978 * [backup-simplify]: Simplify 1 into 1 29.978 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 29.978 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 29.978 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 29.978 * [taylor]: Taking taylor expansion of 2.0 in k 29.978 * [backup-simplify]: Simplify 2.0 into 2.0 29.978 * [taylor]: Taking taylor expansion of PI in k 29.978 * [backup-simplify]: Simplify PI into PI 29.979 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 29.979 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 29.979 * [taylor]: Taking taylor expansion of (log n) in k 29.979 * [taylor]: Taking taylor expansion of n in k 29.979 * [backup-simplify]: Simplify n into n 29.979 * [backup-simplify]: Simplify (log n) into (log n) 29.980 * [backup-simplify]: Simplify (- 0) into 0 29.980 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 29.981 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 29.981 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 29.982 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 29.983 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 29.983 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 29.984 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 29.985 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 29.986 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 29.986 * [backup-simplify]: Simplify (- 0) into 0 29.986 * [backup-simplify]: Simplify (+ 0 0) into 0 29.986 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 29.987 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 29.988 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 29.989 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 29.989 * [taylor]: Taking taylor expansion of 0 in k 29.990 * [backup-simplify]: Simplify 0 into 0 29.990 * [backup-simplify]: Simplify 0 into 0 29.990 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 29.992 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 29.993 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 29.994 * [backup-simplify]: Simplify (+ 0 0) into 0 30.003 * [backup-simplify]: Simplify (- 1) into -1 30.004 * [backup-simplify]: Simplify (+ 0 -1) into -1 30.006 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 30.009 * [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)))) 30.012 * [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)))))) 30.016 * [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)))))) 30.017 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 30.018 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 30.022 * [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 30.022 * [backup-simplify]: Simplify (- 0) into 0 30.023 * [backup-simplify]: Simplify (+ 0 0) into 0 30.023 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 30.025 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 30.027 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 30.029 * [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 30.029 * [taylor]: Taking taylor expansion of 0 in k 30.029 * [backup-simplify]: Simplify 0 into 0 30.029 * [backup-simplify]: Simplify 0 into 0 30.029 * [backup-simplify]: Simplify 0 into 0 30.031 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 30.034 * [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 30.036 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 30.036 * [backup-simplify]: Simplify (+ 0 0) into 0 30.037 * [backup-simplify]: Simplify (- 0) into 0 30.037 * [backup-simplify]: Simplify (+ 0 0) into 0 30.039 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 30.042 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 30.046 * [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))))) 30.050 * [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))))) 30.056 * [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)))))) 30.057 * [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)))) 30.057 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 30.057 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 30.057 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 30.057 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 30.057 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 30.057 * [taylor]: Taking taylor expansion of 0.25 in k 30.057 * [backup-simplify]: Simplify 0.25 into 0.25 30.057 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 30.057 * [taylor]: Taking taylor expansion of 1.0 in k 30.057 * [backup-simplify]: Simplify 1.0 into 1.0 30.057 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.057 * [taylor]: Taking taylor expansion of k in k 30.057 * [backup-simplify]: Simplify 0 into 0 30.057 * [backup-simplify]: Simplify 1 into 1 30.057 * [backup-simplify]: Simplify (/ 1 1) into 1 30.057 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 30.057 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 30.058 * [taylor]: Taking taylor expansion of 2.0 in k 30.058 * [backup-simplify]: Simplify 2.0 into 2.0 30.058 * [taylor]: Taking taylor expansion of (/ PI n) in k 30.058 * [taylor]: Taking taylor expansion of PI in k 30.058 * [backup-simplify]: Simplify PI into PI 30.058 * [taylor]: Taking taylor expansion of n in k 30.058 * [backup-simplify]: Simplify n into n 30.058 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 30.058 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 30.058 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 30.058 * [backup-simplify]: Simplify (- 1) into -1 30.058 * [backup-simplify]: Simplify (+ 0 -1) into -1 30.059 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 30.059 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 30.059 * [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))))) 30.059 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 30.059 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 30.059 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 30.059 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 30.059 * [taylor]: Taking taylor expansion of 0.25 in n 30.059 * [backup-simplify]: Simplify 0.25 into 0.25 30.059 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 30.059 * [taylor]: Taking taylor expansion of 1.0 in n 30.059 * [backup-simplify]: Simplify 1.0 into 1.0 30.059 * [taylor]: Taking taylor expansion of (/ 1 k) in n 30.059 * [taylor]: Taking taylor expansion of k in n 30.059 * [backup-simplify]: Simplify k into k 30.059 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 30.059 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 30.059 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 30.059 * [taylor]: Taking taylor expansion of 2.0 in n 30.059 * [backup-simplify]: Simplify 2.0 into 2.0 30.059 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.059 * [taylor]: Taking taylor expansion of PI in n 30.059 * [backup-simplify]: Simplify PI into PI 30.059 * [taylor]: Taking taylor expansion of n in n 30.059 * [backup-simplify]: Simplify 0 into 0 30.059 * [backup-simplify]: Simplify 1 into 1 30.060 * [backup-simplify]: Simplify (/ PI 1) into PI 30.060 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 30.060 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 30.061 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 30.061 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 30.061 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 30.062 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 30.062 * [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)))) 30.063 * [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))))) 30.063 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 30.063 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 30.063 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 30.063 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 30.063 * [taylor]: Taking taylor expansion of 0.25 in n 30.063 * [backup-simplify]: Simplify 0.25 into 0.25 30.063 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 30.063 * [taylor]: Taking taylor expansion of 1.0 in n 30.063 * [backup-simplify]: Simplify 1.0 into 1.0 30.063 * [taylor]: Taking taylor expansion of (/ 1 k) in n 30.063 * [taylor]: Taking taylor expansion of k in n 30.063 * [backup-simplify]: Simplify k into k 30.063 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 30.063 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 30.063 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 30.063 * [taylor]: Taking taylor expansion of 2.0 in n 30.063 * [backup-simplify]: Simplify 2.0 into 2.0 30.063 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.063 * [taylor]: Taking taylor expansion of PI in n 30.063 * [backup-simplify]: Simplify PI into PI 30.063 * [taylor]: Taking taylor expansion of n in n 30.063 * [backup-simplify]: Simplify 0 into 0 30.063 * [backup-simplify]: Simplify 1 into 1 30.064 * [backup-simplify]: Simplify (/ PI 1) into PI 30.064 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 30.065 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 30.065 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 30.065 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 30.065 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 30.066 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 30.067 * [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)))) 30.067 * [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))))) 30.067 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 30.067 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 30.067 * [taylor]: Taking taylor expansion of 0.25 in k 30.068 * [backup-simplify]: Simplify 0.25 into 0.25 30.068 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 30.068 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 30.068 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 30.068 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 30.068 * [taylor]: Taking taylor expansion of 2.0 in k 30.068 * [backup-simplify]: Simplify 2.0 into 2.0 30.068 * [taylor]: Taking taylor expansion of PI in k 30.068 * [backup-simplify]: Simplify PI into PI 30.068 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 30.069 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 30.069 * [taylor]: Taking taylor expansion of (log n) in k 30.069 * [taylor]: Taking taylor expansion of n in k 30.069 * [backup-simplify]: Simplify n into n 30.069 * [backup-simplify]: Simplify (log n) into (log n) 30.069 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 30.069 * [taylor]: Taking taylor expansion of 1.0 in k 30.069 * [backup-simplify]: Simplify 1.0 into 1.0 30.069 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.069 * [taylor]: Taking taylor expansion of k in k 30.069 * [backup-simplify]: Simplify 0 into 0 30.069 * [backup-simplify]: Simplify 1 into 1 30.069 * [backup-simplify]: Simplify (/ 1 1) into 1 30.069 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 30.070 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 30.070 * [backup-simplify]: Simplify (- 1) into -1 30.070 * [backup-simplify]: Simplify (+ 0 -1) into -1 30.071 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 30.072 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 30.072 * [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))))) 30.073 * [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))))) 30.074 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 30.074 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 30.075 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 30.075 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 30.075 * [backup-simplify]: Simplify (- 0) into 0 30.076 * [backup-simplify]: Simplify (+ 0 0) into 0 30.076 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 30.077 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 30.078 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 30.080 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 30.080 * [taylor]: Taking taylor expansion of 0 in k 30.080 * [backup-simplify]: Simplify 0 into 0 30.080 * [backup-simplify]: Simplify 0 into 0 30.081 * [backup-simplify]: Simplify 0 into 0 30.082 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.083 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 30.087 * [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 30.087 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 30.088 * [backup-simplify]: Simplify (- 0) into 0 30.088 * [backup-simplify]: Simplify (+ 0 0) into 0 30.089 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 30.091 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 30.092 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 30.095 * [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 30.095 * [taylor]: Taking taylor expansion of 0 in k 30.095 * [backup-simplify]: Simplify 0 into 0 30.095 * [backup-simplify]: Simplify 0 into 0 30.095 * [backup-simplify]: Simplify 0 into 0 30.095 * [backup-simplify]: Simplify 0 into 0 30.096 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.098 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 30.104 * [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 30.104 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 30.105 * [backup-simplify]: Simplify (- 0) into 0 30.105 * [backup-simplify]: Simplify (+ 0 0) into 0 30.107 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 30.109 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 30.111 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 30.113 * [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 30.113 * [taylor]: Taking taylor expansion of 0 in k 30.114 * [backup-simplify]: Simplify 0 into 0 30.114 * [backup-simplify]: Simplify 0 into 0 30.115 * [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)))) 30.116 * [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))) 30.116 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 30.116 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 30.116 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 30.116 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 30.116 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 30.116 * [taylor]: Taking taylor expansion of 0.25 in k 30.116 * [backup-simplify]: Simplify 0.25 into 0.25 30.116 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 30.116 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.116 * [taylor]: Taking taylor expansion of k in k 30.116 * [backup-simplify]: Simplify 0 into 0 30.116 * [backup-simplify]: Simplify 1 into 1 30.117 * [backup-simplify]: Simplify (/ 1 1) into 1 30.117 * [taylor]: Taking taylor expansion of 1.0 in k 30.117 * [backup-simplify]: Simplify 1.0 into 1.0 30.117 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 30.117 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 30.117 * [taylor]: Taking taylor expansion of -2.0 in k 30.117 * [backup-simplify]: Simplify -2.0 into -2.0 30.117 * [taylor]: Taking taylor expansion of (/ PI n) in k 30.117 * [taylor]: Taking taylor expansion of PI in k 30.117 * [backup-simplify]: Simplify PI into PI 30.117 * [taylor]: Taking taylor expansion of n in k 30.117 * [backup-simplify]: Simplify n into n 30.117 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 30.117 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 30.117 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 30.118 * [backup-simplify]: Simplify (+ 1 0) into 1 30.118 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 30.118 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 30.118 * [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)))))) 30.118 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 30.119 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 30.119 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 30.119 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 30.119 * [taylor]: Taking taylor expansion of 0.25 in n 30.119 * [backup-simplify]: Simplify 0.25 into 0.25 30.119 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 30.119 * [taylor]: Taking taylor expansion of (/ 1 k) in n 30.119 * [taylor]: Taking taylor expansion of k in n 30.119 * [backup-simplify]: Simplify k into k 30.119 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 30.119 * [taylor]: Taking taylor expansion of 1.0 in n 30.119 * [backup-simplify]: Simplify 1.0 into 1.0 30.119 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 30.119 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 30.119 * [taylor]: Taking taylor expansion of -2.0 in n 30.119 * [backup-simplify]: Simplify -2.0 into -2.0 30.119 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.119 * [taylor]: Taking taylor expansion of PI in n 30.119 * [backup-simplify]: Simplify PI into PI 30.119 * [taylor]: Taking taylor expansion of n in n 30.119 * [backup-simplify]: Simplify 0 into 0 30.119 * [backup-simplify]: Simplify 1 into 1 30.120 * [backup-simplify]: Simplify (/ PI 1) into PI 30.120 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 30.121 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 30.121 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 30.122 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 30.123 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 30.124 * [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)))) 30.126 * [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))))) 30.126 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 30.126 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 30.126 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 30.126 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 30.126 * [taylor]: Taking taylor expansion of 0.25 in n 30.126 * [backup-simplify]: Simplify 0.25 into 0.25 30.126 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 30.126 * [taylor]: Taking taylor expansion of (/ 1 k) in n 30.126 * [taylor]: Taking taylor expansion of k in n 30.126 * [backup-simplify]: Simplify k into k 30.126 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 30.126 * [taylor]: Taking taylor expansion of 1.0 in n 30.126 * [backup-simplify]: Simplify 1.0 into 1.0 30.126 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 30.126 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 30.126 * [taylor]: Taking taylor expansion of -2.0 in n 30.126 * [backup-simplify]: Simplify -2.0 into -2.0 30.126 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.126 * [taylor]: Taking taylor expansion of PI in n 30.126 * [backup-simplify]: Simplify PI into PI 30.127 * [taylor]: Taking taylor expansion of n in n 30.127 * [backup-simplify]: Simplify 0 into 0 30.127 * [backup-simplify]: Simplify 1 into 1 30.127 * [backup-simplify]: Simplify (/ PI 1) into PI 30.128 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 30.129 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 30.129 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 30.129 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 30.131 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 30.132 * [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)))) 30.134 * [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))))) 30.134 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 30.134 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 30.134 * [taylor]: Taking taylor expansion of 0.25 in k 30.134 * [backup-simplify]: Simplify 0.25 into 0.25 30.134 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 30.134 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 30.134 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.134 * [taylor]: Taking taylor expansion of k in k 30.134 * [backup-simplify]: Simplify 0 into 0 30.134 * [backup-simplify]: Simplify 1 into 1 30.134 * [backup-simplify]: Simplify (/ 1 1) into 1 30.134 * [taylor]: Taking taylor expansion of 1.0 in k 30.135 * [backup-simplify]: Simplify 1.0 into 1.0 30.135 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 30.135 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 30.135 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 30.135 * [taylor]: Taking taylor expansion of -2.0 in k 30.135 * [backup-simplify]: Simplify -2.0 into -2.0 30.135 * [taylor]: Taking taylor expansion of PI in k 30.135 * [backup-simplify]: Simplify PI into PI 30.135 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 30.136 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 30.136 * [taylor]: Taking taylor expansion of (log n) in k 30.136 * [taylor]: Taking taylor expansion of n in k 30.136 * [backup-simplify]: Simplify n into n 30.137 * [backup-simplify]: Simplify (log n) into (log n) 30.137 * [backup-simplify]: Simplify (+ 1 0) into 1 30.137 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 30.147 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 30.148 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 30.150 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 30.151 * [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))))) 30.152 * [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))))) 30.153 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 30.154 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 30.156 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 30.156 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 30.156 * [backup-simplify]: Simplify (+ 0 0) into 0 30.157 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 30.159 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 30.160 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 30.162 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 30.162 * [taylor]: Taking taylor expansion of 0 in k 30.162 * [backup-simplify]: Simplify 0 into 0 30.162 * [backup-simplify]: Simplify 0 into 0 30.162 * [backup-simplify]: Simplify 0 into 0 30.163 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.164 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 30.168 * [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 30.168 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 30.168 * [backup-simplify]: Simplify (+ 0 0) into 0 30.169 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 30.171 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 30.173 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 30.175 * [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 30.175 * [taylor]: Taking taylor expansion of 0 in k 30.175 * [backup-simplify]: Simplify 0 into 0 30.175 * [backup-simplify]: Simplify 0 into 0 30.175 * [backup-simplify]: Simplify 0 into 0 30.175 * [backup-simplify]: Simplify 0 into 0 30.177 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.178 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 30.184 * [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 30.185 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 30.185 * [backup-simplify]: Simplify (+ 0 0) into 0 30.186 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 30.188 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 30.190 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 30.193 * [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 30.193 * [taylor]: Taking taylor expansion of 0 in k 30.193 * [backup-simplify]: Simplify 0 into 0 30.193 * [backup-simplify]: Simplify 0 into 0 30.195 * [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)))))) 30.195 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 2 2 1) 30.195 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 30.195 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 30.195 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 30.195 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 30.195 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 30.195 * [taylor]: Taking taylor expansion of 1/3 in n 30.195 * [backup-simplify]: Simplify 1/3 into 1/3 30.195 * [taylor]: Taking taylor expansion of (log n) in n 30.195 * [taylor]: Taking taylor expansion of n in n 30.195 * [backup-simplify]: Simplify 0 into 0 30.195 * [backup-simplify]: Simplify 1 into 1 30.196 * [backup-simplify]: Simplify (log 1) into 0 30.196 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.196 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 30.196 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 30.196 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 30.196 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 30.196 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 30.197 * [taylor]: Taking taylor expansion of 1/3 in n 30.197 * [backup-simplify]: Simplify 1/3 into 1/3 30.197 * [taylor]: Taking taylor expansion of (log n) in n 30.197 * [taylor]: Taking taylor expansion of n in n 30.197 * [backup-simplify]: Simplify 0 into 0 30.197 * [backup-simplify]: Simplify 1 into 1 30.198 * [backup-simplify]: Simplify (log 1) into 0 30.198 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.198 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 30.198 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 30.199 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 30.200 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 30.201 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.201 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 30.202 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 30.202 * [backup-simplify]: Simplify 0 into 0 30.206 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 30.206 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.207 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 30.209 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.209 * [backup-simplify]: Simplify 0 into 0 30.214 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 30.215 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.216 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 30.218 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.218 * [backup-simplify]: Simplify 0 into 0 30.230 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 30.230 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.232 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 30.235 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.235 * [backup-simplify]: Simplify 0 into 0 30.249 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 30.249 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.251 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 30.253 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.253 * [backup-simplify]: Simplify 0 into 0 30.275 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 30.276 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.279 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 30.294 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.294 * [backup-simplify]: Simplify 0 into 0 30.295 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 30.295 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 30.295 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 30.295 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 30.295 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 30.295 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 30.295 * [taylor]: Taking taylor expansion of 1/3 in n 30.295 * [backup-simplify]: Simplify 1/3 into 1/3 30.295 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 30.295 * [taylor]: Taking taylor expansion of (/ 1 n) in n 30.295 * [taylor]: Taking taylor expansion of n in n 30.295 * [backup-simplify]: Simplify 0 into 0 30.295 * [backup-simplify]: Simplify 1 into 1 30.296 * [backup-simplify]: Simplify (/ 1 1) into 1 30.296 * [backup-simplify]: Simplify (log 1) into 0 30.297 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.297 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 30.297 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 30.297 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 30.297 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 30.297 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 30.297 * [taylor]: Taking taylor expansion of 1/3 in n 30.297 * [backup-simplify]: Simplify 1/3 into 1/3 30.297 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 30.297 * [taylor]: Taking taylor expansion of (/ 1 n) in n 30.297 * [taylor]: Taking taylor expansion of n in n 30.297 * [backup-simplify]: Simplify 0 into 0 30.297 * [backup-simplify]: Simplify 1 into 1 30.298 * [backup-simplify]: Simplify (/ 1 1) into 1 30.298 * [backup-simplify]: Simplify (log 1) into 0 30.299 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.299 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 30.299 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 30.299 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 30.300 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 30.302 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 30.302 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.303 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 30.304 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 30.304 * [backup-simplify]: Simplify 0 into 0 30.305 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.309 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 30.309 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.310 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 30.312 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.312 * [backup-simplify]: Simplify 0 into 0 30.313 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.318 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 30.319 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.320 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 30.322 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.322 * [backup-simplify]: Simplify 0 into 0 30.323 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.334 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 30.335 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.336 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 30.339 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.339 * [backup-simplify]: Simplify 0 into 0 30.340 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.354 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 30.354 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.356 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 30.358 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.358 * [backup-simplify]: Simplify 0 into 0 30.359 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.378 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 30.379 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.380 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 30.383 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.383 * [backup-simplify]: Simplify 0 into 0 30.383 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 30.384 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 30.384 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 30.384 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 30.384 * [taylor]: Taking taylor expansion of (cbrt -1) in n 30.384 * [taylor]: Taking taylor expansion of -1 in n 30.384 * [backup-simplify]: Simplify -1 into -1 30.384 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 30.384 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 30.385 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 30.385 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 30.385 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 30.385 * [taylor]: Taking taylor expansion of 1/3 in n 30.385 * [backup-simplify]: Simplify 1/3 into 1/3 30.385 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 30.385 * [taylor]: Taking taylor expansion of (/ 1 n) in n 30.385 * [taylor]: Taking taylor expansion of n in n 30.385 * [backup-simplify]: Simplify 0 into 0 30.385 * [backup-simplify]: Simplify 1 into 1 30.385 * [backup-simplify]: Simplify (/ 1 1) into 1 30.385 * [backup-simplify]: Simplify (log 1) into 0 30.385 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.386 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 30.386 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 30.386 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 30.386 * [taylor]: Taking taylor expansion of (cbrt -1) in n 30.386 * [taylor]: Taking taylor expansion of -1 in n 30.386 * [backup-simplify]: Simplify -1 into -1 30.386 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 30.386 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 30.386 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 30.386 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 30.386 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 30.387 * [taylor]: Taking taylor expansion of 1/3 in n 30.387 * [backup-simplify]: Simplify 1/3 into 1/3 30.387 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 30.387 * [taylor]: Taking taylor expansion of (/ 1 n) in n 30.387 * [taylor]: Taking taylor expansion of n in n 30.387 * [backup-simplify]: Simplify 0 into 0 30.387 * [backup-simplify]: Simplify 1 into 1 30.387 * [backup-simplify]: Simplify (/ 1 1) into 1 30.387 * [backup-simplify]: Simplify (log 1) into 0 30.387 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.387 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 30.388 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 30.388 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 30.388 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 30.389 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 30.390 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 30.391 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.391 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 30.392 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 30.393 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 30.393 * [backup-simplify]: Simplify 0 into 0 30.394 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.396 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 30.397 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.398 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 30.399 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.401 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 30.402 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 30.402 * [backup-simplify]: Simplify 0 into 0 30.403 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.408 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 30.408 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.409 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 30.411 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.413 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 30.414 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 30.414 * [backup-simplify]: Simplify 0 into 0 30.415 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.436 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 30.437 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.439 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 30.442 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.444 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 30.446 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 30.447 * [backup-simplify]: Simplify 0 into 0 30.448 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.466 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 30.467 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.469 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 30.473 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.475 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 30.477 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 30.477 * [backup-simplify]: Simplify 0 into 0 30.478 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.506 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 30.507 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.508 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 30.512 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.513 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 30.514 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 30.514 * [backup-simplify]: Simplify 0 into 0 30.515 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 30.515 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 2 1 2) 30.515 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 30.515 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 30.515 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 30.515 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 30.515 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 30.515 * [taylor]: Taking taylor expansion of 1/3 in n 30.515 * [backup-simplify]: Simplify 1/3 into 1/3 30.515 * [taylor]: Taking taylor expansion of (log n) in n 30.515 * [taylor]: Taking taylor expansion of n in n 30.515 * [backup-simplify]: Simplify 0 into 0 30.515 * [backup-simplify]: Simplify 1 into 1 30.515 * [backup-simplify]: Simplify (log 1) into 0 30.516 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.516 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 30.516 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 30.516 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 30.516 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 30.516 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 30.516 * [taylor]: Taking taylor expansion of 1/3 in n 30.516 * [backup-simplify]: Simplify 1/3 into 1/3 30.516 * [taylor]: Taking taylor expansion of (log n) in n 30.516 * [taylor]: Taking taylor expansion of n in n 30.516 * [backup-simplify]: Simplify 0 into 0 30.516 * [backup-simplify]: Simplify 1 into 1 30.516 * [backup-simplify]: Simplify (log 1) into 0 30.517 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.517 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 30.517 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 30.517 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 30.518 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 30.518 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.518 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 30.519 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 30.519 * [backup-simplify]: Simplify 0 into 0 30.520 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 30.521 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.521 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 30.522 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.522 * [backup-simplify]: Simplify 0 into 0 30.525 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 30.525 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.526 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 30.527 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.527 * [backup-simplify]: Simplify 0 into 0 30.537 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 30.537 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.539 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 30.542 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.542 * [backup-simplify]: Simplify 0 into 0 30.559 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 30.560 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.562 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 30.566 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.566 * [backup-simplify]: Simplify 0 into 0 30.608 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 30.609 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 30.612 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 30.618 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.618 * [backup-simplify]: Simplify 0 into 0 30.618 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 30.618 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 30.618 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 30.618 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 30.618 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 30.618 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 30.618 * [taylor]: Taking taylor expansion of 1/3 in n 30.618 * [backup-simplify]: Simplify 1/3 into 1/3 30.618 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 30.618 * [taylor]: Taking taylor expansion of (/ 1 n) in n 30.618 * [taylor]: Taking taylor expansion of n in n 30.618 * [backup-simplify]: Simplify 0 into 0 30.618 * [backup-simplify]: Simplify 1 into 1 30.619 * [backup-simplify]: Simplify (/ 1 1) into 1 30.619 * [backup-simplify]: Simplify (log 1) into 0 30.619 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.619 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 30.619 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 30.619 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 30.619 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 30.619 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 30.619 * [taylor]: Taking taylor expansion of 1/3 in n 30.619 * [backup-simplify]: Simplify 1/3 into 1/3 30.620 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 30.620 * [taylor]: Taking taylor expansion of (/ 1 n) in n 30.620 * [taylor]: Taking taylor expansion of n in n 30.620 * [backup-simplify]: Simplify 0 into 0 30.620 * [backup-simplify]: Simplify 1 into 1 30.620 * [backup-simplify]: Simplify (/ 1 1) into 1 30.620 * [backup-simplify]: Simplify (log 1) into 0 30.620 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.620 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 30.620 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 30.621 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 30.621 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 30.622 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 30.622 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.623 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 30.623 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 30.623 * [backup-simplify]: Simplify 0 into 0 30.624 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.625 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 30.626 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.626 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 30.627 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.627 * [backup-simplify]: Simplify 0 into 0 30.627 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.630 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 30.631 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.631 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 30.632 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.632 * [backup-simplify]: Simplify 0 into 0 30.633 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.639 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 30.639 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.640 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 30.641 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.642 * [backup-simplify]: Simplify 0 into 0 30.642 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.653 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 30.654 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.656 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 30.660 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.660 * [backup-simplify]: Simplify 0 into 0 30.661 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.694 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 30.694 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.697 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 30.704 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.704 * [backup-simplify]: Simplify 0 into 0 30.704 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 30.704 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 30.705 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 30.705 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 30.705 * [taylor]: Taking taylor expansion of (cbrt -1) in n 30.705 * [taylor]: Taking taylor expansion of -1 in n 30.705 * [backup-simplify]: Simplify -1 into -1 30.705 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 30.706 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 30.706 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 30.706 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 30.706 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 30.706 * [taylor]: Taking taylor expansion of 1/3 in n 30.706 * [backup-simplify]: Simplify 1/3 into 1/3 30.706 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 30.706 * [taylor]: Taking taylor expansion of (/ 1 n) in n 30.706 * [taylor]: Taking taylor expansion of n in n 30.706 * [backup-simplify]: Simplify 0 into 0 30.706 * [backup-simplify]: Simplify 1 into 1 30.707 * [backup-simplify]: Simplify (/ 1 1) into 1 30.707 * [backup-simplify]: Simplify (log 1) into 0 30.708 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.708 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 30.708 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 30.708 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 30.708 * [taylor]: Taking taylor expansion of (cbrt -1) in n 30.708 * [taylor]: Taking taylor expansion of -1 in n 30.708 * [backup-simplify]: Simplify -1 into -1 30.709 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 30.709 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 30.709 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 30.710 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 30.710 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 30.710 * [taylor]: Taking taylor expansion of 1/3 in n 30.710 * [backup-simplify]: Simplify 1/3 into 1/3 30.710 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 30.710 * [taylor]: Taking taylor expansion of (/ 1 n) in n 30.710 * [taylor]: Taking taylor expansion of n in n 30.710 * [backup-simplify]: Simplify 0 into 0 30.710 * [backup-simplify]: Simplify 1 into 1 30.710 * [backup-simplify]: Simplify (/ 1 1) into 1 30.722 * [backup-simplify]: Simplify (log 1) into 0 30.723 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.723 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 30.723 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 30.724 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 30.725 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 30.726 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 30.727 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 30.727 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.728 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 30.729 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 30.730 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 30.730 * [backup-simplify]: Simplify 0 into 0 30.731 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.734 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 30.734 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.735 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 30.737 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.738 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 30.739 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 30.739 * [backup-simplify]: Simplify 0 into 0 30.740 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.745 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 30.746 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.747 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 30.749 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.750 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 30.752 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 30.752 * [backup-simplify]: Simplify 0 into 0 30.753 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.764 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 30.765 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.766 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 30.769 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.771 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 30.773 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 30.773 * [backup-simplify]: Simplify 0 into 0 30.774 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.793 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 30.794 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.796 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 30.800 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 30.801 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 30.803 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 30.803 * [backup-simplify]: Simplify 0 into 0 30.805 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.837 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 30.837 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 30.839 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 30.842 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 30.843 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 30.845 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 30.845 * [backup-simplify]: Simplify 0 into 0 30.845 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 30.845 * * * [progress]: simplifying candidates 30.848 * [simplify]: Simplifying: (expm1 (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (* (+ (log 2.0) (+ (+ (log (cbrt n)) (log (cbrt n))) (+ (log (cbrt n)) (log PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (+ (+ (log (cbrt n)) (log (cbrt n))) (log (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (+ (log (* (cbrt n) (cbrt n))) (+ (log (cbrt n)) (log PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (+ (log (* (cbrt n) (cbrt n))) (log (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (log (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1.0 2.0)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ k 2.0)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) 1) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)) (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) 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-1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) 30.852 * * [simplify]: Extracting # 0 : cost 0 30.852 * * [simplify]: Extracting # 1 : cost 0 30.852 * * [simplify]: Extracting # 2 : cost 0 30.853 * * [simplify]: Extracting # 3 : cost 0 30.853 * * [simplify]: Extracting # 4 : cost 0 30.854 * * [simplify]: Extracting # 5 : cost 0 30.854 * * [simplify]: Extracting # 6 : cost 0 30.855 * * [simplify]: Extracting # 7 : cost 0 30.862 * * [simplify]: Extracting # 8 : cost 0 30.863 * * [simplify]: Extracting # 9 : cost 0 30.863 * * [simplify]: Extracting # 10 : cost 0 30.864 * * [simplify]: Extracting # 11 : cost 0 30.864 * * [simplify]: Extracting # 12 : cost 0 30.865 * * [simplify]: iteration 0 : 323 enodes (cost 2686 ) 31.091 * * [simplify]: Extracting # 0 : cost 0 31.094 * * [simplify]: Extracting # 1 : cost 0 31.097 * * [simplify]: Extracting # 2 : cost 0 31.099 * * [simplify]: Extracting # 3 : cost 0 31.101 * * [simplify]: Extracting # 4 : cost 0 31.104 * * [simplify]: Extracting # 5 : cost 0 31.106 * * [simplify]: Extracting # 6 : cost 0 31.108 * * [simplify]: iteration 1 : 1701 enodes (cost 2496 ) 32.733 * * [simplify]: Extracting # 0 : cost 0 32.740 * * [simplify]: Extracting # 1 : cost 0 32.748 * * [simplify]: Extracting # 2 : cost 0 32.759 * * [simplify]: Extracting # 3 : cost 0 32.770 * * [simplify]: Extracting # 4 : cost 0 32.777 * * [simplify]: Extracting # 5 : cost 0 32.784 * * [simplify]: iteration done: 5001 enodes (cost 2132 ) 32.785 * [simplify]: Simplified to: (expm1 (pow (* n (* 2.0 PI)) (/ (- 1.0 k) 2.0))) (log1p (pow (* n (* 2.0 PI)) (/ (- 1.0 k) 2.0))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 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2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* n (* 2.0 PI)) (- 1.0 k)) (* n (* 2.0 PI)) (pow (* n (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* n (* 2.0 PI)) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* n (* 2.0 PI)) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) 1 (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) 1 (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (fma (* 0.125 (pow k 2)) (* (pow (* n (* 2.0 PI)) 0.5) (pow (log (* 2.0 PI)) 2)) (- (fma 0.125 (* (pow (log n) 2) (* (pow k 2) (pow (* n (* 2.0 PI)) 0.5))) (fma (* 0.25 (pow k 2)) (* (* (log n) (pow (* n (* 2.0 PI)) 0.5)) (log (* 2.0 PI))) (pow (* n (* 2.0 PI)) 0.5))) (* (fma (* k (log (* 2.0 PI))) (pow (* n (* 2.0 PI)) 0.5) (* (* k (pow (* n (* 2.0 PI)) 0.5)) (log n))) 0.5))) (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 0.0625 (* (* (log (* 2.0 PI)) (* (pow (* n (* 2.0 PI)) 0.25) (log n))) (pow k 2)) (* (* 0.03125 (pow k 2)) (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.25)))) (* (fma k (* (log (* 2.0 PI)) (pow (* n (* 2.0 PI)) 0.25)) (* k (* (pow (* n (* 2.0 PI)) 0.25) (log n)))) 0.25)) (fma (* (* (pow (log (* 2.0 PI)) 2) (pow (* n (* 2.0 PI)) 0.25)) (pow k 2)) 0.03125 (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)))))) (cbrt n) (pow (/ 1 n) -1/3) (* (cbrt (- n)) (cbrt -1)) (cbrt n) (pow (/ 1 n) -1/3) (* (cbrt (- n)) (cbrt -1)) 32.786 * * * [progress]: adding candidates to table 33.858 * [progress]: [Phase 3 of 3] Extracting. 33.858 * * [regime]: Finding splitpoints for: (# # # # # # #) 33.861 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 33.861 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 33.935 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # #) 33.972 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 34.021 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 34.080 * * * [regime]: Found split indices: #