11.673 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.085 * * * [progress]: [2/2] Setting up program. 0.088 * [progress]: [Phase 2 of 3] Improving. 0.088 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.088 * [simplify]: Sending expressions to egg_math: (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) 0.091 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.092 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.094 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.096 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.102 * * [simplify]: iteration 4 : 1044 enodes (cost 8 ) 0.124 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.125 * * [progress]: iteration 1 / 4 0.125 * * * [progress]: picking best candidate 0.127 * * * * [pick]: Picked # 0.127 * * * [progress]: localizing error 0.140 * * * [progress]: generating rewritten candidates 0.140 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.160 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.179 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.185 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.228 * * * [progress]: generating series expansions 0.228 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.229 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 0.229 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.229 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.229 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.229 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.229 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.229 * [taylor]: Taking taylor expansion of 0.5 in k 0.229 * [backup-simplify]: Simplify 0.5 into 0.5 0.229 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.229 * [taylor]: Taking taylor expansion of 1.0 in k 0.229 * [backup-simplify]: Simplify 1.0 into 1.0 0.229 * [taylor]: Taking taylor expansion of k in k 0.229 * [backup-simplify]: Simplify 0 into 0 0.229 * [backup-simplify]: Simplify 1 into 1 0.229 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.229 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.229 * [taylor]: Taking taylor expansion of 2.0 in k 0.229 * [backup-simplify]: Simplify 2.0 into 2.0 0.229 * [taylor]: Taking taylor expansion of (* n PI) in k 0.229 * [taylor]: Taking taylor expansion of n in k 0.229 * [backup-simplify]: Simplify n into n 0.229 * [taylor]: Taking taylor expansion of PI in k 0.229 * [backup-simplify]: Simplify PI into PI 0.230 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.230 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.230 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.230 * [backup-simplify]: Simplify (- 0) into 0 0.230 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.230 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.230 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.231 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.231 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.231 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.231 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.231 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.231 * [taylor]: Taking taylor expansion of 0.5 in n 0.231 * [backup-simplify]: Simplify 0.5 into 0.5 0.231 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.231 * [taylor]: Taking taylor expansion of 1.0 in n 0.231 * [backup-simplify]: Simplify 1.0 into 1.0 0.231 * [taylor]: Taking taylor expansion of k in n 0.231 * [backup-simplify]: Simplify k into k 0.231 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.231 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.231 * [taylor]: Taking taylor expansion of 2.0 in n 0.231 * [backup-simplify]: Simplify 2.0 into 2.0 0.231 * [taylor]: Taking taylor expansion of (* n PI) in n 0.231 * [taylor]: Taking taylor expansion of n in n 0.231 * [backup-simplify]: Simplify 0 into 0 0.231 * [backup-simplify]: Simplify 1 into 1 0.231 * [taylor]: Taking taylor expansion of PI in n 0.231 * [backup-simplify]: Simplify PI into PI 0.231 * [backup-simplify]: Simplify (* 0 PI) into 0 0.231 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.232 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.233 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.234 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.234 * [backup-simplify]: Simplify (- k) into (- k) 0.234 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.234 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.235 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.236 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.237 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.237 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.237 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.237 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.237 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.237 * [taylor]: Taking taylor expansion of 0.5 in n 0.237 * [backup-simplify]: Simplify 0.5 into 0.5 0.237 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.237 * [taylor]: Taking taylor expansion of 1.0 in n 0.237 * [backup-simplify]: Simplify 1.0 into 1.0 0.237 * [taylor]: Taking taylor expansion of k in n 0.237 * [backup-simplify]: Simplify k into k 0.237 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.237 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.237 * [taylor]: Taking taylor expansion of 2.0 in n 0.237 * [backup-simplify]: Simplify 2.0 into 2.0 0.237 * [taylor]: Taking taylor expansion of (* n PI) in n 0.237 * [taylor]: Taking taylor expansion of n in n 0.237 * [backup-simplify]: Simplify 0 into 0 0.237 * [backup-simplify]: Simplify 1 into 1 0.237 * [taylor]: Taking taylor expansion of PI in n 0.237 * [backup-simplify]: Simplify PI into PI 0.237 * [backup-simplify]: Simplify (* 0 PI) into 0 0.237 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.238 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.239 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.240 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.240 * [backup-simplify]: Simplify (- k) into (- k) 0.240 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.240 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.241 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.242 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.242 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.242 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.242 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.242 * [taylor]: Taking taylor expansion of 0.5 in k 0.242 * [backup-simplify]: Simplify 0.5 into 0.5 0.242 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.243 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.243 * [taylor]: Taking taylor expansion of 1.0 in k 0.243 * [backup-simplify]: Simplify 1.0 into 1.0 0.243 * [taylor]: Taking taylor expansion of k in k 0.243 * [backup-simplify]: Simplify 0 into 0 0.243 * [backup-simplify]: Simplify 1 into 1 0.243 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.243 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.243 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.243 * [taylor]: Taking taylor expansion of 2.0 in k 0.243 * [backup-simplify]: Simplify 2.0 into 2.0 0.243 * [taylor]: Taking taylor expansion of PI in k 0.243 * [backup-simplify]: Simplify PI into PI 0.243 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.244 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.244 * [taylor]: Taking taylor expansion of (log n) in k 0.244 * [taylor]: Taking taylor expansion of n in k 0.244 * [backup-simplify]: Simplify n into n 0.244 * [backup-simplify]: Simplify (log n) into (log n) 0.244 * [backup-simplify]: Simplify (- 0) into 0 0.244 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.245 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.245 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.246 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.247 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.247 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.248 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.249 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.249 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.250 * [backup-simplify]: Simplify (- 0) into 0 0.250 * [backup-simplify]: Simplify (+ 0 0) into 0 0.250 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 0.251 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.252 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.253 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.253 * [taylor]: Taking taylor expansion of 0 in k 0.253 * [backup-simplify]: Simplify 0 into 0 0.253 * [backup-simplify]: Simplify 0 into 0 0.253 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.254 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.255 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.255 * [backup-simplify]: Simplify (+ 0 0) into 0 0.255 * [backup-simplify]: Simplify (- 1) into -1 0.256 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.256 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.258 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 0.260 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0.261 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0.262 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.263 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.264 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.265 * [backup-simplify]: Simplify (- 0) into 0 0.265 * [backup-simplify]: Simplify (+ 0 0) into 0 0.265 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 0.266 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.267 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.268 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.268 * [taylor]: Taking taylor expansion of 0 in k 0.268 * [backup-simplify]: Simplify 0 into 0 0.268 * [backup-simplify]: Simplify 0 into 0 0.268 * [backup-simplify]: Simplify 0 into 0 0.269 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.271 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.272 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 0.272 * [backup-simplify]: Simplify (+ 0 0) into 0 0.272 * [backup-simplify]: Simplify (- 0) into 0 0.272 * [backup-simplify]: Simplify (+ 0 0) into 0 0.274 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.275 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 0.277 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0.280 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0.286 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 0.287 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 0.287 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.287 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.287 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.287 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.287 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.287 * [taylor]: Taking taylor expansion of 0.5 in k 0.287 * [backup-simplify]: Simplify 0.5 into 0.5 0.287 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.287 * [taylor]: Taking taylor expansion of 1.0 in k 0.287 * [backup-simplify]: Simplify 1.0 into 1.0 0.287 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.287 * [taylor]: Taking taylor expansion of k in k 0.287 * [backup-simplify]: Simplify 0 into 0 0.287 * [backup-simplify]: Simplify 1 into 1 0.287 * [backup-simplify]: Simplify (/ 1 1) into 1 0.287 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.287 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.287 * [taylor]: Taking taylor expansion of 2.0 in k 0.287 * [backup-simplify]: Simplify 2.0 into 2.0 0.287 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.287 * [taylor]: Taking taylor expansion of PI in k 0.287 * [backup-simplify]: Simplify PI into PI 0.287 * [taylor]: Taking taylor expansion of n in k 0.287 * [backup-simplify]: Simplify n into n 0.287 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.287 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.288 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.288 * [backup-simplify]: Simplify (- 1) into -1 0.288 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.288 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.288 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.289 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 0.289 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.289 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.289 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.289 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.289 * [taylor]: Taking taylor expansion of 0.5 in n 0.289 * [backup-simplify]: Simplify 0.5 into 0.5 0.289 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.289 * [taylor]: Taking taylor expansion of 1.0 in n 0.289 * [backup-simplify]: Simplify 1.0 into 1.0 0.289 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.289 * [taylor]: Taking taylor expansion of k in n 0.289 * [backup-simplify]: Simplify k into k 0.289 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.289 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.289 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.289 * [taylor]: Taking taylor expansion of 2.0 in n 0.289 * [backup-simplify]: Simplify 2.0 into 2.0 0.289 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.289 * [taylor]: Taking taylor expansion of PI in n 0.289 * [backup-simplify]: Simplify PI into PI 0.289 * [taylor]: Taking taylor expansion of n in n 0.289 * [backup-simplify]: Simplify 0 into 0 0.289 * [backup-simplify]: Simplify 1 into 1 0.289 * [backup-simplify]: Simplify (/ PI 1) into PI 0.290 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.290 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.290 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.290 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.290 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.291 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.292 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.292 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.293 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.293 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.293 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.293 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.293 * [taylor]: Taking taylor expansion of 0.5 in n 0.293 * [backup-simplify]: Simplify 0.5 into 0.5 0.293 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.293 * [taylor]: Taking taylor expansion of 1.0 in n 0.293 * [backup-simplify]: Simplify 1.0 into 1.0 0.293 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.293 * [taylor]: Taking taylor expansion of k in n 0.293 * [backup-simplify]: Simplify k into k 0.293 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.293 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.293 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.293 * [taylor]: Taking taylor expansion of 2.0 in n 0.293 * [backup-simplify]: Simplify 2.0 into 2.0 0.293 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.293 * [taylor]: Taking taylor expansion of PI in n 0.293 * [backup-simplify]: Simplify PI into PI 0.293 * [taylor]: Taking taylor expansion of n in n 0.293 * [backup-simplify]: Simplify 0 into 0 0.293 * [backup-simplify]: Simplify 1 into 1 0.293 * [backup-simplify]: Simplify (/ PI 1) into PI 0.293 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.294 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.294 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.294 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.294 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.295 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.296 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.296 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.297 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.297 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.297 * [taylor]: Taking taylor expansion of 0.5 in k 0.297 * [backup-simplify]: Simplify 0.5 into 0.5 0.297 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.297 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.297 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.297 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.297 * [taylor]: Taking taylor expansion of 2.0 in k 0.297 * [backup-simplify]: Simplify 2.0 into 2.0 0.297 * [taylor]: Taking taylor expansion of PI in k 0.297 * [backup-simplify]: Simplify PI into PI 0.297 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.298 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.298 * [taylor]: Taking taylor expansion of (log n) in k 0.298 * [taylor]: Taking taylor expansion of n in k 0.298 * [backup-simplify]: Simplify n into n 0.298 * [backup-simplify]: Simplify (log n) into (log n) 0.298 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.298 * [taylor]: Taking taylor expansion of 1.0 in k 0.298 * [backup-simplify]: Simplify 1.0 into 1.0 0.298 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.298 * [taylor]: Taking taylor expansion of k in k 0.298 * [backup-simplify]: Simplify 0 into 0 0.298 * [backup-simplify]: Simplify 1 into 1 0.298 * [backup-simplify]: Simplify (/ 1 1) into 1 0.298 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.299 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.299 * [backup-simplify]: Simplify (- 1) into -1 0.299 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.300 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.300 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 0.301 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.302 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.302 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.303 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.304 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.304 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.304 * [backup-simplify]: Simplify (- 0) into 0 0.304 * [backup-simplify]: Simplify (+ 0 0) into 0 0.305 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.305 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.306 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.307 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.307 * [taylor]: Taking taylor expansion of 0 in k 0.307 * [backup-simplify]: Simplify 0 into 0 0.307 * [backup-simplify]: Simplify 0 into 0 0.307 * [backup-simplify]: Simplify 0 into 0 0.308 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.309 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.316 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.316 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.316 * [backup-simplify]: Simplify (- 0) into 0 0.317 * [backup-simplify]: Simplify (+ 0 0) into 0 0.317 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 0.318 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.319 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 0.320 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.320 * [taylor]: Taking taylor expansion of 0 in k 0.320 * [backup-simplify]: Simplify 0 into 0 0.320 * [backup-simplify]: Simplify 0 into 0 0.320 * [backup-simplify]: Simplify 0 into 0 0.320 * [backup-simplify]: Simplify 0 into 0 0.321 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.321 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.324 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 0.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.325 * [backup-simplify]: Simplify (- 0) into 0 0.325 * [backup-simplify]: Simplify (+ 0 0) into 0 0.326 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 0.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.327 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 0.329 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 0.329 * [taylor]: Taking taylor expansion of 0 in k 0.329 * [backup-simplify]: Simplify 0 into 0 0.329 * [backup-simplify]: Simplify 0 into 0 0.330 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 0.330 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 0.330 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.330 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.330 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.330 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.330 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.330 * [taylor]: Taking taylor expansion of 0.5 in k 0.330 * [backup-simplify]: Simplify 0.5 into 0.5 0.330 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.330 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.330 * [taylor]: Taking taylor expansion of k in k 0.330 * [backup-simplify]: Simplify 0 into 0 0.330 * [backup-simplify]: Simplify 1 into 1 0.331 * [backup-simplify]: Simplify (/ 1 1) into 1 0.331 * [taylor]: Taking taylor expansion of 1.0 in k 0.331 * [backup-simplify]: Simplify 1.0 into 1.0 0.331 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.331 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.331 * [taylor]: Taking taylor expansion of -2.0 in k 0.331 * [backup-simplify]: Simplify -2.0 into -2.0 0.331 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.331 * [taylor]: Taking taylor expansion of PI in k 0.331 * [backup-simplify]: Simplify PI into PI 0.331 * [taylor]: Taking taylor expansion of n in k 0.331 * [backup-simplify]: Simplify n into n 0.331 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.331 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.331 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.331 * [backup-simplify]: Simplify (+ 1 0) into 1 0.331 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.332 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.332 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 0.332 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.332 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.332 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.332 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.332 * [taylor]: Taking taylor expansion of 0.5 in n 0.332 * [backup-simplify]: Simplify 0.5 into 0.5 0.332 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.332 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.332 * [taylor]: Taking taylor expansion of k in n 0.332 * [backup-simplify]: Simplify k into k 0.332 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.332 * [taylor]: Taking taylor expansion of 1.0 in n 0.332 * [backup-simplify]: Simplify 1.0 into 1.0 0.332 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.332 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.332 * [taylor]: Taking taylor expansion of -2.0 in n 0.332 * [backup-simplify]: Simplify -2.0 into -2.0 0.332 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.332 * [taylor]: Taking taylor expansion of PI in n 0.332 * [backup-simplify]: Simplify PI into PI 0.332 * [taylor]: Taking taylor expansion of n in n 0.332 * [backup-simplify]: Simplify 0 into 0 0.332 * [backup-simplify]: Simplify 1 into 1 0.332 * [backup-simplify]: Simplify (/ PI 1) into PI 0.333 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.333 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.333 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.333 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.334 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.335 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.336 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.336 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.336 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.336 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.336 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.336 * [taylor]: Taking taylor expansion of 0.5 in n 0.336 * [backup-simplify]: Simplify 0.5 into 0.5 0.336 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.336 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.336 * [taylor]: Taking taylor expansion of k in n 0.336 * [backup-simplify]: Simplify k into k 0.336 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.336 * [taylor]: Taking taylor expansion of 1.0 in n 0.336 * [backup-simplify]: Simplify 1.0 into 1.0 0.336 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.336 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.336 * [taylor]: Taking taylor expansion of -2.0 in n 0.336 * [backup-simplify]: Simplify -2.0 into -2.0 0.336 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.336 * [taylor]: Taking taylor expansion of PI in n 0.336 * [backup-simplify]: Simplify PI into PI 0.336 * [taylor]: Taking taylor expansion of n in n 0.336 * [backup-simplify]: Simplify 0 into 0 0.336 * [backup-simplify]: Simplify 1 into 1 0.337 * [backup-simplify]: Simplify (/ PI 1) into PI 0.337 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.337 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.338 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.338 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.338 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.339 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.340 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.340 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.340 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.340 * [taylor]: Taking taylor expansion of 0.5 in k 0.340 * [backup-simplify]: Simplify 0.5 into 0.5 0.340 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.340 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.340 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.340 * [taylor]: Taking taylor expansion of k in k 0.340 * [backup-simplify]: Simplify 0 into 0 0.340 * [backup-simplify]: Simplify 1 into 1 0.341 * [backup-simplify]: Simplify (/ 1 1) into 1 0.341 * [taylor]: Taking taylor expansion of 1.0 in k 0.341 * [backup-simplify]: Simplify 1.0 into 1.0 0.341 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.341 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.341 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.341 * [taylor]: Taking taylor expansion of -2.0 in k 0.341 * [backup-simplify]: Simplify -2.0 into -2.0 0.341 * [taylor]: Taking taylor expansion of PI in k 0.341 * [backup-simplify]: Simplify PI into PI 0.341 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.342 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.342 * [taylor]: Taking taylor expansion of (log n) in k 0.342 * [taylor]: Taking taylor expansion of n in k 0.342 * [backup-simplify]: Simplify n into n 0.342 * [backup-simplify]: Simplify (log n) into (log n) 0.342 * [backup-simplify]: Simplify (+ 1 0) into 1 0.342 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.343 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 0.343 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 0.344 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 0.345 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.346 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.346 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.347 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.348 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.348 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.348 * [backup-simplify]: Simplify (+ 0 0) into 0 0.348 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 0.349 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.350 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.351 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.351 * [taylor]: Taking taylor expansion of 0 in k 0.351 * [backup-simplify]: Simplify 0 into 0 0.351 * [backup-simplify]: Simplify 0 into 0 0.351 * [backup-simplify]: Simplify 0 into 0 0.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.352 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.354 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 0.354 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.354 * [backup-simplify]: Simplify (+ 0 0) into 0 0.355 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 0.355 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.356 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 0.358 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.358 * [taylor]: Taking taylor expansion of 0 in k 0.358 * [backup-simplify]: Simplify 0 into 0 0.358 * [backup-simplify]: Simplify 0 into 0 0.358 * [backup-simplify]: Simplify 0 into 0 0.358 * [backup-simplify]: Simplify 0 into 0 0.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.359 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.362 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 0.362 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.362 * [backup-simplify]: Simplify (+ 0 0) into 0 0.363 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.364 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.365 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 0.366 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 0.366 * [taylor]: Taking taylor expansion of 0 in k 0.366 * [backup-simplify]: Simplify 0 into 0 0.366 * [backup-simplify]: Simplify 0 into 0 0.367 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 0.367 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.367 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.368 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.368 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.368 * [taylor]: Taking taylor expansion of 2.0 in n 0.368 * [backup-simplify]: Simplify 2.0 into 2.0 0.368 * [taylor]: Taking taylor expansion of (* n PI) in n 0.368 * [taylor]: Taking taylor expansion of n in n 0.368 * [backup-simplify]: Simplify 0 into 0 0.368 * [backup-simplify]: Simplify 1 into 1 0.368 * [taylor]: Taking taylor expansion of PI in n 0.368 * [backup-simplify]: Simplify PI into PI 0.368 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.368 * [taylor]: Taking taylor expansion of 2.0 in n 0.368 * [backup-simplify]: Simplify 2.0 into 2.0 0.368 * [taylor]: Taking taylor expansion of (* n PI) in n 0.368 * [taylor]: Taking taylor expansion of n in n 0.368 * [backup-simplify]: Simplify 0 into 0 0.368 * [backup-simplify]: Simplify 1 into 1 0.368 * [taylor]: Taking taylor expansion of PI in n 0.368 * [backup-simplify]: Simplify PI into PI 0.368 * [backup-simplify]: Simplify (* 0 PI) into 0 0.368 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.368 * [backup-simplify]: Simplify 0 into 0 0.369 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.370 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.370 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.371 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.372 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.372 * [backup-simplify]: Simplify 0 into 0 0.372 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.373 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.373 * [backup-simplify]: Simplify 0 into 0 0.373 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.374 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.374 * [backup-simplify]: Simplify 0 into 0 0.375 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.376 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 0.376 * [backup-simplify]: Simplify 0 into 0 0.377 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.377 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.377 * [backup-simplify]: Simplify 0 into 0 0.378 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.379 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.379 * [backup-simplify]: Simplify 0 into 0 0.380 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.380 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 0.380 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.380 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.380 * [taylor]: Taking taylor expansion of 2.0 in n 0.380 * [backup-simplify]: Simplify 2.0 into 2.0 0.380 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.380 * [taylor]: Taking taylor expansion of PI in n 0.380 * [backup-simplify]: Simplify PI into PI 0.380 * [taylor]: Taking taylor expansion of n in n 0.380 * [backup-simplify]: Simplify 0 into 0 0.380 * [backup-simplify]: Simplify 1 into 1 0.381 * [backup-simplify]: Simplify (/ PI 1) into PI 0.381 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.381 * [taylor]: Taking taylor expansion of 2.0 in n 0.381 * [backup-simplify]: Simplify 2.0 into 2.0 0.381 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.381 * [taylor]: Taking taylor expansion of PI in n 0.381 * [backup-simplify]: Simplify PI into PI 0.381 * [taylor]: Taking taylor expansion of n in n 0.381 * [backup-simplify]: Simplify 0 into 0 0.381 * [backup-simplify]: Simplify 1 into 1 0.381 * [backup-simplify]: Simplify (/ PI 1) into PI 0.382 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.382 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.382 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.383 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.383 * [backup-simplify]: Simplify 0 into 0 0.383 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.384 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.384 * [backup-simplify]: Simplify 0 into 0 0.384 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.385 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.385 * [backup-simplify]: Simplify 0 into 0 0.386 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.386 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.386 * [backup-simplify]: Simplify 0 into 0 0.387 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.388 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.388 * [backup-simplify]: Simplify 0 into 0 0.388 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.389 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.389 * [backup-simplify]: Simplify 0 into 0 0.390 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.390 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.390 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.390 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.390 * [taylor]: Taking taylor expansion of -2.0 in n 0.390 * [backup-simplify]: Simplify -2.0 into -2.0 0.390 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.390 * [taylor]: Taking taylor expansion of PI in n 0.390 * [backup-simplify]: Simplify PI into PI 0.390 * [taylor]: Taking taylor expansion of n in n 0.390 * [backup-simplify]: Simplify 0 into 0 0.390 * [backup-simplify]: Simplify 1 into 1 0.390 * [backup-simplify]: Simplify (/ PI 1) into PI 0.390 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.390 * [taylor]: Taking taylor expansion of -2.0 in n 0.391 * [backup-simplify]: Simplify -2.0 into -2.0 0.391 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.391 * [taylor]: Taking taylor expansion of PI in n 0.391 * [backup-simplify]: Simplify PI into PI 0.391 * [taylor]: Taking taylor expansion of n in n 0.391 * [backup-simplify]: Simplify 0 into 0 0.391 * [backup-simplify]: Simplify 1 into 1 0.391 * [backup-simplify]: Simplify (/ PI 1) into PI 0.391 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.391 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.392 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.392 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.392 * [backup-simplify]: Simplify 0 into 0 0.393 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.393 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.393 * [backup-simplify]: Simplify 0 into 0 0.394 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.395 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.395 * [backup-simplify]: Simplify 0 into 0 0.395 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.396 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.396 * [backup-simplify]: Simplify 0 into 0 0.397 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.397 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.397 * [backup-simplify]: Simplify 0 into 0 0.398 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.399 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.399 * [backup-simplify]: Simplify 0 into 0 0.399 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.399 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.399 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.399 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.399 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.399 * [taylor]: Taking taylor expansion of 1.0 in k 0.399 * [backup-simplify]: Simplify 1.0 into 1.0 0.399 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.399 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.399 * [taylor]: Taking taylor expansion of k in k 0.399 * [backup-simplify]: Simplify 0 into 0 0.399 * [backup-simplify]: Simplify 1 into 1 0.400 * [backup-simplify]: Simplify (/ 1 1) into 1 0.400 * [backup-simplify]: Simplify (sqrt 0) into 0 0.401 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.401 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.401 * [taylor]: Taking taylor expansion of 1.0 in k 0.401 * [backup-simplify]: Simplify 1.0 into 1.0 0.401 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.401 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.401 * [taylor]: Taking taylor expansion of k in k 0.401 * [backup-simplify]: Simplify 0 into 0 0.401 * [backup-simplify]: Simplify 1 into 1 0.401 * [backup-simplify]: Simplify (/ 1 1) into 1 0.401 * [backup-simplify]: Simplify (sqrt 0) into 0 0.402 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.407 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.408 * [backup-simplify]: Simplify 0 into 0 0.408 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.409 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.409 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.411 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.412 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.412 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.413 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.414 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.416 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.416 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.417 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 0.417 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 0.417 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.417 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.417 * [taylor]: Taking taylor expansion of 1.0 in k 0.417 * [backup-simplify]: Simplify 1.0 into 1.0 0.417 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.417 * [taylor]: Taking taylor expansion of k in k 0.417 * [backup-simplify]: Simplify 0 into 0 0.417 * [backup-simplify]: Simplify 1 into 1 0.417 * [backup-simplify]: Simplify (sqrt 0) into 0 0.418 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.418 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.418 * [taylor]: Taking taylor expansion of 1.0 in k 0.418 * [backup-simplify]: Simplify 1.0 into 1.0 0.418 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.418 * [taylor]: Taking taylor expansion of k in k 0.418 * [backup-simplify]: Simplify 0 into 0 0.418 * [backup-simplify]: Simplify 1 into 1 0.418 * [backup-simplify]: Simplify (sqrt 0) into 0 0.419 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.419 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.419 * [backup-simplify]: Simplify 0 into 0 0.420 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.420 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.422 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.423 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.423 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.425 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.426 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.427 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.428 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 0.428 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.428 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.428 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.428 * [taylor]: Taking taylor expansion of 1.0 in k 0.428 * [backup-simplify]: Simplify 1.0 into 1.0 0.428 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.428 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.428 * [taylor]: Taking taylor expansion of -1 in k 0.428 * [backup-simplify]: Simplify -1 into -1 0.428 * [taylor]: Taking taylor expansion of k in k 0.428 * [backup-simplify]: Simplify 0 into 0 0.428 * [backup-simplify]: Simplify 1 into 1 0.428 * [backup-simplify]: Simplify (/ -1 1) into -1 0.428 * [backup-simplify]: Simplify (sqrt 0) into 0 0.429 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.429 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.429 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.429 * [taylor]: Taking taylor expansion of 1.0 in k 0.429 * [backup-simplify]: Simplify 1.0 into 1.0 0.429 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.429 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.429 * [taylor]: Taking taylor expansion of -1 in k 0.429 * [backup-simplify]: Simplify -1 into -1 0.429 * [taylor]: Taking taylor expansion of k in k 0.429 * [backup-simplify]: Simplify 0 into 0 0.430 * [backup-simplify]: Simplify 1 into 1 0.430 * [backup-simplify]: Simplify (/ -1 1) into -1 0.430 * [backup-simplify]: Simplify (sqrt 0) into 0 0.431 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.431 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.431 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.433 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.435 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 0.435 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.438 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.440 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 0.440 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.441 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 0.441 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.441 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 0.442 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 0.442 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.442 * [taylor]: Taking taylor expansion of 1.0 in n 0.442 * [backup-simplify]: Simplify 1.0 into 1.0 0.442 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.442 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.442 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.442 * [taylor]: Taking taylor expansion of k in n 0.442 * [backup-simplify]: Simplify k into k 0.442 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.442 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 0.442 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.442 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 0.442 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.442 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.442 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.442 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.442 * [taylor]: Taking taylor expansion of 0.5 in n 0.442 * [backup-simplify]: Simplify 0.5 into 0.5 0.442 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.442 * [taylor]: Taking taylor expansion of 1.0 in n 0.442 * [backup-simplify]: Simplify 1.0 into 1.0 0.442 * [taylor]: Taking taylor expansion of k in n 0.442 * [backup-simplify]: Simplify k into k 0.442 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.442 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.442 * [taylor]: Taking taylor expansion of 2.0 in n 0.442 * [backup-simplify]: Simplify 2.0 into 2.0 0.442 * [taylor]: Taking taylor expansion of (* n PI) in n 0.442 * [taylor]: Taking taylor expansion of n in n 0.442 * [backup-simplify]: Simplify 0 into 0 0.442 * [backup-simplify]: Simplify 1 into 1 0.442 * [taylor]: Taking taylor expansion of PI in n 0.442 * [backup-simplify]: Simplify PI into PI 0.443 * [backup-simplify]: Simplify (* 0 PI) into 0 0.443 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.444 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.445 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.445 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.445 * [backup-simplify]: Simplify (- k) into (- k) 0.445 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.445 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.446 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.447 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.448 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.448 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.448 * [taylor]: Taking taylor expansion of 1.0 in k 0.448 * [backup-simplify]: Simplify 1.0 into 1.0 0.448 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.448 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.448 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.448 * [taylor]: Taking taylor expansion of k in k 0.448 * [backup-simplify]: Simplify 0 into 0 0.448 * [backup-simplify]: Simplify 1 into 1 0.448 * [backup-simplify]: Simplify (/ 1 1) into 1 0.448 * [backup-simplify]: Simplify (sqrt 0) into 0 0.449 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.449 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.449 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.449 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.449 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.449 * [taylor]: Taking taylor expansion of 0.5 in k 0.449 * [backup-simplify]: Simplify 0.5 into 0.5 0.449 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.449 * [taylor]: Taking taylor expansion of 1.0 in k 0.449 * [backup-simplify]: Simplify 1.0 into 1.0 0.449 * [taylor]: Taking taylor expansion of k in k 0.449 * [backup-simplify]: Simplify 0 into 0 0.449 * [backup-simplify]: Simplify 1 into 1 0.449 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.449 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.449 * [taylor]: Taking taylor expansion of 2.0 in k 0.449 * [backup-simplify]: Simplify 2.0 into 2.0 0.449 * [taylor]: Taking taylor expansion of (* n PI) in k 0.449 * [taylor]: Taking taylor expansion of n in k 0.449 * [backup-simplify]: Simplify n into n 0.449 * [taylor]: Taking taylor expansion of PI in k 0.449 * [backup-simplify]: Simplify PI into PI 0.449 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.449 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.450 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.450 * [backup-simplify]: Simplify (- 0) into 0 0.450 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.450 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.450 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.450 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.450 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.450 * [taylor]: Taking taylor expansion of 1.0 in k 0.450 * [backup-simplify]: Simplify 1.0 into 1.0 0.450 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.450 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.451 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.451 * [taylor]: Taking taylor expansion of k in k 0.451 * [backup-simplify]: Simplify 0 into 0 0.451 * [backup-simplify]: Simplify 1 into 1 0.451 * [backup-simplify]: Simplify (/ 1 1) into 1 0.451 * [backup-simplify]: Simplify (sqrt 0) into 0 0.452 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.452 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.452 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.452 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.452 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.452 * [taylor]: Taking taylor expansion of 0.5 in k 0.452 * [backup-simplify]: Simplify 0.5 into 0.5 0.452 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.452 * [taylor]: Taking taylor expansion of 1.0 in k 0.452 * [backup-simplify]: Simplify 1.0 into 1.0 0.452 * [taylor]: Taking taylor expansion of k in k 0.452 * [backup-simplify]: Simplify 0 into 0 0.452 * [backup-simplify]: Simplify 1 into 1 0.452 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.452 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.452 * [taylor]: Taking taylor expansion of 2.0 in k 0.452 * [backup-simplify]: Simplify 2.0 into 2.0 0.452 * [taylor]: Taking taylor expansion of (* n PI) in k 0.452 * [taylor]: Taking taylor expansion of n in k 0.452 * [backup-simplify]: Simplify n into n 0.452 * [taylor]: Taking taylor expansion of PI in k 0.452 * [backup-simplify]: Simplify PI into PI 0.452 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.452 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.452 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.452 * [backup-simplify]: Simplify (- 0) into 0 0.453 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.453 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.453 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.453 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.453 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 0.454 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.454 * [taylor]: Taking taylor expansion of 0 in n 0.454 * [backup-simplify]: Simplify 0 into 0 0.454 * [backup-simplify]: Simplify 0 into 0 0.454 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 0.454 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 0.455 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 0.455 * [backup-simplify]: Simplify (- 1) into -1 0.455 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.456 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 0.457 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 0.457 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.458 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 0.459 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.459 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 0.459 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 0.459 * [taylor]: Taking taylor expansion of +nan.0 in n 0.459 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.459 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.459 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.459 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.459 * [taylor]: Taking taylor expansion of 0.5 in n 0.459 * [backup-simplify]: Simplify 0.5 into 0.5 0.459 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.459 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.459 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.459 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.459 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.459 * [taylor]: Taking taylor expansion of 1.0 in n 0.459 * [backup-simplify]: Simplify 1.0 into 1.0 0.459 * [taylor]: Taking taylor expansion of (log PI) in n 0.459 * [taylor]: Taking taylor expansion of PI in n 0.459 * [backup-simplify]: Simplify PI into PI 0.460 * [backup-simplify]: Simplify (log PI) into (log PI) 0.460 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.461 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.461 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.461 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.461 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.461 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.461 * [taylor]: Taking taylor expansion of 1.0 in n 0.461 * [backup-simplify]: Simplify 1.0 into 1.0 0.461 * [taylor]: Taking taylor expansion of (log n) in n 0.461 * [taylor]: Taking taylor expansion of n in n 0.461 * [backup-simplify]: Simplify 0 into 0 0.461 * [backup-simplify]: Simplify 1 into 1 0.461 * [backup-simplify]: Simplify (log 1) into 0 0.462 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.462 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.462 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.462 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.462 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.462 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.462 * [taylor]: Taking taylor expansion of 1.0 in n 0.462 * [backup-simplify]: Simplify 1.0 into 1.0 0.462 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.462 * [taylor]: Taking taylor expansion of 2.0 in n 0.462 * [backup-simplify]: Simplify 2.0 into 2.0 0.462 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.463 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.463 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.464 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 0.465 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 0.465 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 0.466 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 0.467 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.468 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 0.469 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 0.469 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.470 * [backup-simplify]: Simplify 0 into 0 0.470 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 0.470 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 0.471 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 0.472 * [backup-simplify]: Simplify (- 0) into 0 0.472 * [backup-simplify]: Simplify (+ 0 0) into 0 0.472 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.473 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 0.474 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.474 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.476 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.478 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 0.481 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 0.481 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 0.481 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 0.481 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 0.481 * [taylor]: Taking taylor expansion of +nan.0 in n 0.481 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.481 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.481 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.481 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.481 * [taylor]: Taking taylor expansion of 0.5 in n 0.481 * [backup-simplify]: Simplify 0.5 into 0.5 0.481 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.481 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.481 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.481 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.481 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.481 * [taylor]: Taking taylor expansion of 1.0 in n 0.481 * [backup-simplify]: Simplify 1.0 into 1.0 0.481 * [taylor]: Taking taylor expansion of (log PI) in n 0.481 * [taylor]: Taking taylor expansion of PI in n 0.481 * [backup-simplify]: Simplify PI into PI 0.481 * [backup-simplify]: Simplify (log PI) into (log PI) 0.482 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.483 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.483 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.483 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.483 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.483 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.483 * [taylor]: Taking taylor expansion of 1.0 in n 0.483 * [backup-simplify]: Simplify 1.0 into 1.0 0.483 * [taylor]: Taking taylor expansion of (log n) in n 0.483 * [taylor]: Taking taylor expansion of n in n 0.483 * [backup-simplify]: Simplify 0 into 0 0.483 * [backup-simplify]: Simplify 1 into 1 0.484 * [backup-simplify]: Simplify (log 1) into 0 0.484 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.484 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.484 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.484 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.484 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.484 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.484 * [taylor]: Taking taylor expansion of 1.0 in n 0.484 * [backup-simplify]: Simplify 1.0 into 1.0 0.484 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.484 * [taylor]: Taking taylor expansion of 2.0 in n 0.484 * [backup-simplify]: Simplify 2.0 into 2.0 0.484 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.485 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.486 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.486 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 0.487 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 0.488 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 0.489 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 0.489 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.489 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 0.489 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 0.489 * [taylor]: Taking taylor expansion of +nan.0 in n 0.489 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.489 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 0.489 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.490 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.490 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.490 * [taylor]: Taking taylor expansion of 0.5 in n 0.490 * [backup-simplify]: Simplify 0.5 into 0.5 0.490 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.490 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.490 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.490 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.490 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.490 * [taylor]: Taking taylor expansion of 1.0 in n 0.490 * [backup-simplify]: Simplify 1.0 into 1.0 0.490 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.490 * [taylor]: Taking taylor expansion of 2.0 in n 0.490 * [backup-simplify]: Simplify 2.0 into 2.0 0.490 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.491 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.491 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.491 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.491 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.491 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.491 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.491 * [taylor]: Taking taylor expansion of 1.0 in n 0.492 * [backup-simplify]: Simplify 1.0 into 1.0 0.492 * [taylor]: Taking taylor expansion of (log PI) in n 0.492 * [taylor]: Taking taylor expansion of PI in n 0.492 * [backup-simplify]: Simplify PI into PI 0.492 * [backup-simplify]: Simplify (log PI) into (log PI) 0.492 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.493 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.493 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.493 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.493 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.493 * [taylor]: Taking taylor expansion of 1.0 in n 0.493 * [backup-simplify]: Simplify 1.0 into 1.0 0.493 * [taylor]: Taking taylor expansion of (log n) in n 0.493 * [taylor]: Taking taylor expansion of n in n 0.493 * [backup-simplify]: Simplify 0 into 0 0.493 * [backup-simplify]: Simplify 1 into 1 0.494 * [backup-simplify]: Simplify (log 1) into 0 0.494 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.494 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.494 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.494 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.495 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.496 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.497 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.498 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.498 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.498 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.498 * [taylor]: Taking taylor expansion of 2.0 in n 0.498 * [backup-simplify]: Simplify 2.0 into 2.0 0.498 * [taylor]: Taking taylor expansion of (* n PI) in n 0.498 * [taylor]: Taking taylor expansion of n in n 0.498 * [backup-simplify]: Simplify 0 into 0 0.498 * [backup-simplify]: Simplify 1 into 1 0.498 * [taylor]: Taking taylor expansion of PI in n 0.498 * [backup-simplify]: Simplify PI into PI 0.498 * [backup-simplify]: Simplify (* 0 PI) into 0 0.498 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.499 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.505 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.506 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.507 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 0.508 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.509 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.511 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.512 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))) 0.516 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.519 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.523 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.524 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 0.524 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 0.525 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 0.525 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 0.526 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.526 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.527 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 0.527 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 0.528 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 0.528 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 0.529 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 0.530 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 0.531 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 0.532 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 0.533 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 0.534 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 0.535 * [backup-simplify]: Simplify (- 0) into 0 0.535 * [backup-simplify]: Simplify 0 into 0 0.535 * [backup-simplify]: Simplify 0 into 0 0.535 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.536 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 0.538 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 0.538 * [backup-simplify]: Simplify (- 0) into 0 0.538 * [backup-simplify]: Simplify (+ 0 0) into 0 0.539 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 0.540 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 0.541 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.541 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.543 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.547 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 0.553 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 0.553 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 0.553 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 0.553 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 0.553 * [taylor]: Taking taylor expansion of +nan.0 in n 0.553 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.553 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.553 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.553 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.553 * [taylor]: Taking taylor expansion of 0.5 in n 0.553 * [backup-simplify]: Simplify 0.5 into 0.5 0.553 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.553 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.553 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.553 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.553 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.553 * [taylor]: Taking taylor expansion of 1.0 in n 0.553 * [backup-simplify]: Simplify 1.0 into 1.0 0.553 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.553 * [taylor]: Taking taylor expansion of 2.0 in n 0.553 * [backup-simplify]: Simplify 2.0 into 2.0 0.554 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.554 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.555 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.555 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.555 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.555 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.555 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.555 * [taylor]: Taking taylor expansion of 1.0 in n 0.555 * [backup-simplify]: Simplify 1.0 into 1.0 0.555 * [taylor]: Taking taylor expansion of (log n) in n 0.555 * [taylor]: Taking taylor expansion of n in n 0.555 * [backup-simplify]: Simplify 0 into 0 0.555 * [backup-simplify]: Simplify 1 into 1 0.555 * [backup-simplify]: Simplify (log 1) into 0 0.556 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.556 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.556 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.556 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.556 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.556 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.556 * [taylor]: Taking taylor expansion of 1.0 in n 0.556 * [backup-simplify]: Simplify 1.0 into 1.0 0.556 * [taylor]: Taking taylor expansion of (log PI) in n 0.556 * [taylor]: Taking taylor expansion of PI in n 0.556 * [backup-simplify]: Simplify PI into PI 0.556 * [backup-simplify]: Simplify (log PI) into (log PI) 0.557 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.558 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.558 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.559 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.559 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.560 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.561 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.561 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 0.561 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 0.561 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 0.561 * [taylor]: Taking taylor expansion of +nan.0 in n 0.561 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.561 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 0.561 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.561 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.561 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.561 * [taylor]: Taking taylor expansion of 0.5 in n 0.561 * [backup-simplify]: Simplify 0.5 into 0.5 0.561 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.561 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.561 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.561 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.561 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.561 * [taylor]: Taking taylor expansion of 1.0 in n 0.561 * [backup-simplify]: Simplify 1.0 into 1.0 0.561 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.561 * [taylor]: Taking taylor expansion of 2.0 in n 0.561 * [backup-simplify]: Simplify 2.0 into 2.0 0.562 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.562 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.563 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.563 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.563 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.563 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.563 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.563 * [taylor]: Taking taylor expansion of 1.0 in n 0.563 * [backup-simplify]: Simplify 1.0 into 1.0 0.563 * [taylor]: Taking taylor expansion of (log PI) in n 0.563 * [taylor]: Taking taylor expansion of PI in n 0.563 * [backup-simplify]: Simplify PI into PI 0.563 * [backup-simplify]: Simplify (log PI) into (log PI) 0.564 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.565 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.565 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.565 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.565 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.565 * [taylor]: Taking taylor expansion of 1.0 in n 0.565 * [backup-simplify]: Simplify 1.0 into 1.0 0.565 * [taylor]: Taking taylor expansion of (log n) in n 0.565 * [taylor]: Taking taylor expansion of n in n 0.565 * [backup-simplify]: Simplify 0 into 0 0.565 * [backup-simplify]: Simplify 1 into 1 0.565 * [backup-simplify]: Simplify (log 1) into 0 0.566 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.566 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.566 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.566 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.567 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.568 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.568 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.569 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.569 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.569 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.569 * [taylor]: Taking taylor expansion of 2.0 in n 0.569 * [backup-simplify]: Simplify 2.0 into 2.0 0.569 * [taylor]: Taking taylor expansion of (* n PI) in n 0.569 * [taylor]: Taking taylor expansion of n in n 0.569 * [backup-simplify]: Simplify 0 into 0 0.569 * [backup-simplify]: Simplify 1 into 1 0.569 * [taylor]: Taking taylor expansion of PI in n 0.569 * [backup-simplify]: Simplify PI into PI 0.570 * [backup-simplify]: Simplify (* 0 PI) into 0 0.570 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.571 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.572 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.572 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.572 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 0.572 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 0.572 * [taylor]: Taking taylor expansion of +nan.0 in n 0.572 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.572 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 0.572 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.572 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.572 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.572 * [taylor]: Taking taylor expansion of 0.5 in n 0.572 * [backup-simplify]: Simplify 0.5 into 0.5 0.572 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.572 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.572 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.572 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.572 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.572 * [taylor]: Taking taylor expansion of 1.0 in n 0.572 * [backup-simplify]: Simplify 1.0 into 1.0 0.572 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.572 * [taylor]: Taking taylor expansion of 2.0 in n 0.572 * [backup-simplify]: Simplify 2.0 into 2.0 0.573 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.573 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.574 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.574 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.574 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.574 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.574 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.574 * [taylor]: Taking taylor expansion of 1.0 in n 0.574 * [backup-simplify]: Simplify 1.0 into 1.0 0.574 * [taylor]: Taking taylor expansion of (log PI) in n 0.574 * [taylor]: Taking taylor expansion of PI in n 0.574 * [backup-simplify]: Simplify PI into PI 0.574 * [backup-simplify]: Simplify (log PI) into (log PI) 0.575 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.576 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.576 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.576 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.576 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.576 * [taylor]: Taking taylor expansion of 1.0 in n 0.576 * [backup-simplify]: Simplify 1.0 into 1.0 0.576 * [taylor]: Taking taylor expansion of (log n) in n 0.576 * [taylor]: Taking taylor expansion of n in n 0.576 * [backup-simplify]: Simplify 0 into 0 0.576 * [backup-simplify]: Simplify 1 into 1 0.576 * [backup-simplify]: Simplify (log 1) into 0 0.577 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.577 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.577 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.577 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.578 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.579 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.579 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.580 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.580 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.580 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.580 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.580 * [taylor]: Taking taylor expansion of 2.0 in n 0.580 * [backup-simplify]: Simplify 2.0 into 2.0 0.580 * [taylor]: Taking taylor expansion of (* n PI) in n 0.580 * [taylor]: Taking taylor expansion of n in n 0.580 * [backup-simplify]: Simplify 0 into 0 0.580 * [backup-simplify]: Simplify 1 into 1 0.580 * [taylor]: Taking taylor expansion of PI in n 0.580 * [backup-simplify]: Simplify PI into PI 0.581 * [backup-simplify]: Simplify (* 0 PI) into 0 0.581 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.582 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.583 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.583 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.584 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.585 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.586 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.587 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.589 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.590 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.591 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.592 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 0.594 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.595 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.602 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.608 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))))))))))) 0.616 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))) 0.626 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 0.635 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 0.644 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 0.659 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) 0.660 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 0.660 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 0.660 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.660 * [taylor]: Taking taylor expansion of 1.0 in n 0.660 * [backup-simplify]: Simplify 1.0 into 1.0 0.660 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.660 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.660 * [taylor]: Taking taylor expansion of k in n 0.660 * [backup-simplify]: Simplify k into k 0.660 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 0.660 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 0.660 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.660 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.660 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.660 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.660 * [taylor]: Taking taylor expansion of 0.5 in n 0.660 * [backup-simplify]: Simplify 0.5 into 0.5 0.660 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.660 * [taylor]: Taking taylor expansion of 1.0 in n 0.660 * [backup-simplify]: Simplify 1.0 into 1.0 0.660 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.660 * [taylor]: Taking taylor expansion of k in n 0.660 * [backup-simplify]: Simplify k into k 0.660 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.660 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.660 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.660 * [taylor]: Taking taylor expansion of 2.0 in n 0.660 * [backup-simplify]: Simplify 2.0 into 2.0 0.660 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.660 * [taylor]: Taking taylor expansion of PI in n 0.660 * [backup-simplify]: Simplify PI into PI 0.660 * [taylor]: Taking taylor expansion of n in n 0.660 * [backup-simplify]: Simplify 0 into 0 0.660 * [backup-simplify]: Simplify 1 into 1 0.661 * [backup-simplify]: Simplify (/ PI 1) into PI 0.661 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.662 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.662 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.662 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.662 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.663 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.663 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.664 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.664 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.664 * [taylor]: Taking taylor expansion of 1.0 in k 0.664 * [backup-simplify]: Simplify 1.0 into 1.0 0.664 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.664 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.664 * [taylor]: Taking taylor expansion of k in k 0.664 * [backup-simplify]: Simplify 0 into 0 0.664 * [backup-simplify]: Simplify 1 into 1 0.664 * [backup-simplify]: Simplify (sqrt 0) into 0 0.665 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.665 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.665 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.665 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.665 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.665 * [taylor]: Taking taylor expansion of 0.5 in k 0.665 * [backup-simplify]: Simplify 0.5 into 0.5 0.665 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.665 * [taylor]: Taking taylor expansion of 1.0 in k 0.665 * [backup-simplify]: Simplify 1.0 into 1.0 0.665 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.665 * [taylor]: Taking taylor expansion of k in k 0.665 * [backup-simplify]: Simplify 0 into 0 0.665 * [backup-simplify]: Simplify 1 into 1 0.666 * [backup-simplify]: Simplify (/ 1 1) into 1 0.666 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.666 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.666 * [taylor]: Taking taylor expansion of 2.0 in k 0.666 * [backup-simplify]: Simplify 2.0 into 2.0 0.666 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.666 * [taylor]: Taking taylor expansion of PI in k 0.666 * [backup-simplify]: Simplify PI into PI 0.666 * [taylor]: Taking taylor expansion of n in k 0.666 * [backup-simplify]: Simplify n into n 0.666 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.666 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.666 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.666 * [backup-simplify]: Simplify (- 1) into -1 0.666 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.667 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.667 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.667 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 0.667 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.667 * [taylor]: Taking taylor expansion of 1.0 in k 0.667 * [backup-simplify]: Simplify 1.0 into 1.0 0.667 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.667 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.667 * [taylor]: Taking taylor expansion of k in k 0.667 * [backup-simplify]: Simplify 0 into 0 0.667 * [backup-simplify]: Simplify 1 into 1 0.667 * [backup-simplify]: Simplify (sqrt 0) into 0 0.668 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.668 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.668 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.668 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.668 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.668 * [taylor]: Taking taylor expansion of 0.5 in k 0.668 * [backup-simplify]: Simplify 0.5 into 0.5 0.668 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.668 * [taylor]: Taking taylor expansion of 1.0 in k 0.668 * [backup-simplify]: Simplify 1.0 into 1.0 0.668 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.668 * [taylor]: Taking taylor expansion of k in k 0.668 * [backup-simplify]: Simplify 0 into 0 0.668 * [backup-simplify]: Simplify 1 into 1 0.668 * [backup-simplify]: Simplify (/ 1 1) into 1 0.668 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.668 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.668 * [taylor]: Taking taylor expansion of 2.0 in k 0.668 * [backup-simplify]: Simplify 2.0 into 2.0 0.668 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.668 * [taylor]: Taking taylor expansion of PI in k 0.668 * [backup-simplify]: Simplify PI into PI 0.668 * [taylor]: Taking taylor expansion of n in k 0.668 * [backup-simplify]: Simplify n into n 0.669 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.669 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.669 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.669 * [backup-simplify]: Simplify (- 1) into -1 0.669 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.669 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.669 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.670 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 0.670 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 0.670 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.670 * [taylor]: Taking taylor expansion of 0 in n 0.670 * [backup-simplify]: Simplify 0 into 0 0.670 * [backup-simplify]: Simplify 0 into 0 0.671 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 0.671 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 0.671 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.671 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.671 * [taylor]: Taking taylor expansion of +nan.0 in n 0.671 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.671 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.671 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.671 * [taylor]: Taking taylor expansion of 0.5 in n 0.671 * [backup-simplify]: Simplify 0.5 into 0.5 0.671 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.671 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.671 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.671 * [taylor]: Taking taylor expansion of 2.0 in n 0.671 * [backup-simplify]: Simplify 2.0 into 2.0 0.671 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.671 * [taylor]: Taking taylor expansion of PI in n 0.671 * [backup-simplify]: Simplify PI into PI 0.671 * [taylor]: Taking taylor expansion of n in n 0.671 * [backup-simplify]: Simplify 0 into 0 0.671 * [backup-simplify]: Simplify 1 into 1 0.672 * [backup-simplify]: Simplify (/ PI 1) into PI 0.672 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.672 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.672 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.672 * [taylor]: Taking taylor expansion of 1.0 in n 0.672 * [backup-simplify]: Simplify 1.0 into 1.0 0.672 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.672 * [taylor]: Taking taylor expansion of k in n 0.673 * [backup-simplify]: Simplify k into k 0.673 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.673 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.673 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.673 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.674 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.675 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.675 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.676 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 0.677 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.678 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.678 * [backup-simplify]: Simplify 0 into 0 0.679 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.680 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 0.681 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 0.681 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.681 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.681 * [taylor]: Taking taylor expansion of +nan.0 in n 0.681 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.681 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.681 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.681 * [taylor]: Taking taylor expansion of 0.5 in n 0.681 * [backup-simplify]: Simplify 0.5 into 0.5 0.681 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.681 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.681 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.681 * [taylor]: Taking taylor expansion of 2.0 in n 0.681 * [backup-simplify]: Simplify 2.0 into 2.0 0.681 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.681 * [taylor]: Taking taylor expansion of PI in n 0.681 * [backup-simplify]: Simplify PI into PI 0.681 * [taylor]: Taking taylor expansion of n in n 0.681 * [backup-simplify]: Simplify 0 into 0 0.681 * [backup-simplify]: Simplify 1 into 1 0.681 * [backup-simplify]: Simplify (/ PI 1) into PI 0.682 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.682 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.682 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.682 * [taylor]: Taking taylor expansion of 1.0 in n 0.682 * [backup-simplify]: Simplify 1.0 into 1.0 0.682 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.682 * [taylor]: Taking taylor expansion of k in n 0.682 * [backup-simplify]: Simplify k into k 0.682 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.683 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.683 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.683 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.684 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.685 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.685 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.686 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 0.687 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.687 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.688 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.689 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.693 * [backup-simplify]: Simplify (- 0) into 0 0.693 * [backup-simplify]: Simplify (+ 0 0) into 0 0.694 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.694 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.695 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.696 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.697 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 0.699 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.700 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 0.700 * [backup-simplify]: Simplify (- 0) into 0 0.700 * [backup-simplify]: Simplify 0 into 0 0.700 * [backup-simplify]: Simplify 0 into 0 0.702 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.703 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 0.704 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 0.704 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.704 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.704 * [taylor]: Taking taylor expansion of +nan.0 in n 0.704 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.704 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.704 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.704 * [taylor]: Taking taylor expansion of 0.5 in n 0.704 * [backup-simplify]: Simplify 0.5 into 0.5 0.704 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.704 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.704 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.704 * [taylor]: Taking taylor expansion of 2.0 in n 0.704 * [backup-simplify]: Simplify 2.0 into 2.0 0.704 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.704 * [taylor]: Taking taylor expansion of PI in n 0.704 * [backup-simplify]: Simplify PI into PI 0.704 * [taylor]: Taking taylor expansion of n in n 0.704 * [backup-simplify]: Simplify 0 into 0 0.704 * [backup-simplify]: Simplify 1 into 1 0.704 * [backup-simplify]: Simplify (/ PI 1) into PI 0.704 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.705 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.705 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.705 * [taylor]: Taking taylor expansion of 1.0 in n 0.705 * [backup-simplify]: Simplify 1.0 into 1.0 0.705 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.705 * [taylor]: Taking taylor expansion of k in n 0.705 * [backup-simplify]: Simplify k into k 0.705 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.706 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.706 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.706 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.707 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.707 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.708 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.709 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 0.710 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.710 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.713 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 0.714 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 0.714 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 0.714 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.714 * [taylor]: Taking taylor expansion of 1.0 in n 0.714 * [backup-simplify]: Simplify 1.0 into 1.0 0.714 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.714 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.714 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.714 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.714 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.714 * [taylor]: Taking taylor expansion of 0.5 in n 0.714 * [backup-simplify]: Simplify 0.5 into 0.5 0.714 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.714 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.714 * [taylor]: Taking taylor expansion of k in n 0.714 * [backup-simplify]: Simplify k into k 0.714 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.714 * [taylor]: Taking taylor expansion of 1.0 in n 0.714 * [backup-simplify]: Simplify 1.0 into 1.0 0.714 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.714 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.714 * [taylor]: Taking taylor expansion of -2.0 in n 0.714 * [backup-simplify]: Simplify -2.0 into -2.0 0.714 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.714 * [taylor]: Taking taylor expansion of PI in n 0.714 * [backup-simplify]: Simplify PI into PI 0.714 * [taylor]: Taking taylor expansion of n in n 0.714 * [backup-simplify]: Simplify 0 into 0 0.714 * [backup-simplify]: Simplify 1 into 1 0.714 * [backup-simplify]: Simplify (/ PI 1) into PI 0.715 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.715 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.715 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.715 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.716 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.717 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.717 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.718 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.718 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.718 * [taylor]: Taking taylor expansion of -1 in n 0.718 * [backup-simplify]: Simplify -1 into -1 0.718 * [taylor]: Taking taylor expansion of k in n 0.718 * [backup-simplify]: Simplify k into k 0.718 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 0.718 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 0.718 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 0.718 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 0.719 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 0.719 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.719 * [taylor]: Taking taylor expansion of 1.0 in k 0.719 * [backup-simplify]: Simplify 1.0 into 1.0 0.719 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.719 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.719 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.719 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.719 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.719 * [taylor]: Taking taylor expansion of 0.5 in k 0.719 * [backup-simplify]: Simplify 0.5 into 0.5 0.719 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.719 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.719 * [taylor]: Taking taylor expansion of k in k 0.719 * [backup-simplify]: Simplify 0 into 0 0.719 * [backup-simplify]: Simplify 1 into 1 0.719 * [backup-simplify]: Simplify (/ 1 1) into 1 0.719 * [taylor]: Taking taylor expansion of 1.0 in k 0.719 * [backup-simplify]: Simplify 1.0 into 1.0 0.719 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.719 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.719 * [taylor]: Taking taylor expansion of -2.0 in k 0.719 * [backup-simplify]: Simplify -2.0 into -2.0 0.719 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.719 * [taylor]: Taking taylor expansion of PI in k 0.719 * [backup-simplify]: Simplify PI into PI 0.719 * [taylor]: Taking taylor expansion of n in k 0.719 * [backup-simplify]: Simplify n into n 0.719 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.719 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.719 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.720 * [backup-simplify]: Simplify (+ 1 0) into 1 0.720 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.720 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.720 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 0.720 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.720 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.720 * [taylor]: Taking taylor expansion of -1 in k 0.720 * [backup-simplify]: Simplify -1 into -1 0.720 * [taylor]: Taking taylor expansion of k in k 0.720 * [backup-simplify]: Simplify 0 into 0 0.720 * [backup-simplify]: Simplify 1 into 1 0.720 * [backup-simplify]: Simplify (/ -1 1) into -1 0.721 * [backup-simplify]: Simplify (sqrt 0) into 0 0.721 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.722 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 0.722 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.722 * [taylor]: Taking taylor expansion of 1.0 in k 0.722 * [backup-simplify]: Simplify 1.0 into 1.0 0.722 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.722 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.722 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.722 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.722 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.722 * [taylor]: Taking taylor expansion of 0.5 in k 0.722 * [backup-simplify]: Simplify 0.5 into 0.5 0.722 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.722 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.722 * [taylor]: Taking taylor expansion of k in k 0.722 * [backup-simplify]: Simplify 0 into 0 0.722 * [backup-simplify]: Simplify 1 into 1 0.722 * [backup-simplify]: Simplify (/ 1 1) into 1 0.722 * [taylor]: Taking taylor expansion of 1.0 in k 0.722 * [backup-simplify]: Simplify 1.0 into 1.0 0.722 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.722 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.722 * [taylor]: Taking taylor expansion of -2.0 in k 0.722 * [backup-simplify]: Simplify -2.0 into -2.0 0.722 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.722 * [taylor]: Taking taylor expansion of PI in k 0.722 * [backup-simplify]: Simplify PI into PI 0.722 * [taylor]: Taking taylor expansion of n in k 0.722 * [backup-simplify]: Simplify n into n 0.722 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.722 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.722 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.723 * [backup-simplify]: Simplify (+ 1 0) into 1 0.723 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.723 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.723 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 0.723 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.723 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.723 * [taylor]: Taking taylor expansion of -1 in k 0.723 * [backup-simplify]: Simplify -1 into -1 0.723 * [taylor]: Taking taylor expansion of k in k 0.723 * [backup-simplify]: Simplify 0 into 0 0.723 * [backup-simplify]: Simplify 1 into 1 0.723 * [backup-simplify]: Simplify (/ -1 1) into -1 0.724 * [backup-simplify]: Simplify (sqrt 0) into 0 0.724 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.725 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 0.725 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 0.725 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.725 * [taylor]: Taking taylor expansion of +nan.0 in n 0.725 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.725 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.725 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.725 * [taylor]: Taking taylor expansion of 0.5 in n 0.725 * [backup-simplify]: Simplify 0.5 into 0.5 0.725 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.725 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.725 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.725 * [taylor]: Taking taylor expansion of k in n 0.725 * [backup-simplify]: Simplify k into k 0.725 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.725 * [taylor]: Taking taylor expansion of 1.0 in n 0.725 * [backup-simplify]: Simplify 1.0 into 1.0 0.725 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.725 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.725 * [taylor]: Taking taylor expansion of -2.0 in n 0.725 * [backup-simplify]: Simplify -2.0 into -2.0 0.725 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.725 * [taylor]: Taking taylor expansion of PI in n 0.725 * [backup-simplify]: Simplify PI into PI 0.725 * [taylor]: Taking taylor expansion of n in n 0.725 * [backup-simplify]: Simplify 0 into 0 0.725 * [backup-simplify]: Simplify 1 into 1 0.725 * [backup-simplify]: Simplify (/ PI 1) into PI 0.726 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.726 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.726 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.727 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.728 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.729 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.729 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.730 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.731 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.731 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.733 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.733 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 0.734 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 0.734 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.734 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.734 * [taylor]: Taking taylor expansion of +nan.0 in n 0.734 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.734 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.734 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.734 * [taylor]: Taking taylor expansion of 0.5 in n 0.734 * [backup-simplify]: Simplify 0.5 into 0.5 0.734 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.734 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.734 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.734 * [taylor]: Taking taylor expansion of k in n 0.734 * [backup-simplify]: Simplify k into k 0.734 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.734 * [taylor]: Taking taylor expansion of 1.0 in n 0.734 * [backup-simplify]: Simplify 1.0 into 1.0 0.734 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.734 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.734 * [taylor]: Taking taylor expansion of -2.0 in n 0.734 * [backup-simplify]: Simplify -2.0 into -2.0 0.734 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.734 * [taylor]: Taking taylor expansion of PI in n 0.734 * [backup-simplify]: Simplify PI into PI 0.734 * [taylor]: Taking taylor expansion of n in n 0.734 * [backup-simplify]: Simplify 0 into 0 0.734 * [backup-simplify]: Simplify 1 into 1 0.735 * [backup-simplify]: Simplify (/ PI 1) into PI 0.735 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.735 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.735 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.736 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.737 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.738 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.739 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.739 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.740 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 0.741 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 0.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.742 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.743 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.743 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.743 * [backup-simplify]: Simplify (+ 0 0) into 0 0.744 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.745 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.746 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 0.747 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.748 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 0.748 * [backup-simplify]: Simplify 0 into 0 0.748 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.751 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.752 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 0.752 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 0.752 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.752 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.752 * [taylor]: Taking taylor expansion of +nan.0 in n 0.752 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.752 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.752 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.752 * [taylor]: Taking taylor expansion of 0.5 in n 0.752 * [backup-simplify]: Simplify 0.5 into 0.5 0.752 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.752 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.752 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.752 * [taylor]: Taking taylor expansion of k in n 0.752 * [backup-simplify]: Simplify k into k 0.752 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.752 * [taylor]: Taking taylor expansion of 1.0 in n 0.752 * [backup-simplify]: Simplify 1.0 into 1.0 0.752 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.753 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.753 * [taylor]: Taking taylor expansion of -2.0 in n 0.753 * [backup-simplify]: Simplify -2.0 into -2.0 0.753 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.753 * [taylor]: Taking taylor expansion of PI in n 0.753 * [backup-simplify]: Simplify PI into PI 0.753 * [taylor]: Taking taylor expansion of n in n 0.753 * [backup-simplify]: Simplify 0 into 0 0.753 * [backup-simplify]: Simplify 1 into 1 0.753 * [backup-simplify]: Simplify (/ PI 1) into PI 0.753 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.754 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.754 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.755 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.755 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.756 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.757 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.757 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.758 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 0.759 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 0.762 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 0.762 * * * [progress]: simplifying candidates 0.764 * [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 (* (* 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))) (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 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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)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +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))))) (- (+ (* +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))) (- 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(sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (expm1 (* (* h0 h4) h3)) (log1p (* (* h0 h4) h3)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (expm1 (/ h2 (sqrt h1))) (log1p (/ h2 (sqrt h1))) (- (log h2) (log (sqrt h1))) (log (/ h2 (sqrt h1))) (exp (/ h2 (sqrt h1))) (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (cbrt (/ h2 (sqrt h1))) (cbrt (/ h2 (sqrt 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(sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (cbrt (sqrt h1))) (/ 1 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (cbrt h1))) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 (sqrt 1)) (/ h2 (sqrt h1)) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 1) (/ h2 (sqrt h1)) (/ 1 (sqrt h1)) (/ (sqrt h1) h2) (/ h2 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (sqrt h1))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h1))) (/ h2 1) (/ (sqrt h1) (cbrt h2)) (/ (sqrt h1) (sqrt h2)) (/ (sqrt h1) h2) (expm1 (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (log1p (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (+ (- (log h2) (log (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (+ (log (/ h2 (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (log (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (exp (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (* (* (/ h2 (sqrt h1)) (/ h2 (sqrt h1))) (/ h2 (sqrt h1))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (* (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (sqrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (sqrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* h2 (pow (* (* h0 h4) h3) (/ h2 h0))) (* (sqrt h1) (pow (* (* h0 h4) h3) (/ h1 h0))) (* (sqrt (/ h2 (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (sqrt (/ h2 (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ h2 (sqrt h1)) (pow (* h0 h4) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (* (/ h2 (sqrt h1)) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ h2 (sqrt h1)) 1) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ 1 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ h2 h0))) (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (- (+ (* h7 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h7 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (+ (* h6 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (- (+ (* h9 h1) (- (+ (* h9 (pow h1 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- (* h9 (/ 1 (pow h1 3)))))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- h9))))) (- (+ (* h9 (* (* (pow h1 2) (pow (log (* h0 h4)) 2)) (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log (* h0 h4))) (pow (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (* (log (* h0 h4)) (log h3))) (pow (* (pow h4 h2) (* (pow h0 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log h3)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* h1 (log (* h0 h4))) (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (pow (log h3) 2)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* h1 (log h3)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5)) (- (+ (* h9 (* (pow h1 2) (pow (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2))) h5))) (- (* h9 (* h1 (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5)))))))))))))))))))))) (- (+ (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (pow h1 3))) (- (+ (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) h1)) (- (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (pow h1 2)))))))) (- (+ (* h9 (/ (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) h1)) (- (+ (* h9 (/ (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (pow h1 2))) (- (* h9 (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))))))))) 0.773 * * [simplify]: iteration 0 : 981 enodes (cost 1502 ) 0.790 * * [simplify]: iteration 1 : 4021 enodes (cost 1398 ) 0.852 * * [simplify]: iteration 2 : 5003 enodes (cost 1383 ) 0.858 * * * [progress]: adding candidates to table 1.286 * * [progress]: iteration 2 / 4 1.286 * * * [progress]: picking best candidate 1.310 * * * * [pick]: Picked # 1.310 * * * [progress]: localizing error 1.325 * * * [progress]: generating rewritten candidates 1.325 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 1.350 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 1.377 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1) 1.393 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1) 1.420 * * * [progress]: generating series expansions 1.420 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 1.421 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 1.421 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 1.421 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 1.421 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.421 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.421 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 1.421 * [taylor]: Taking taylor expansion of 0.25 in k 1.421 * [backup-simplify]: Simplify 0.25 into 0.25 1.421 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.421 * [taylor]: Taking taylor expansion of 1.0 in k 1.421 * [backup-simplify]: Simplify 1.0 into 1.0 1.421 * [taylor]: Taking taylor expansion of k in k 1.421 * [backup-simplify]: Simplify 0 into 0 1.421 * [backup-simplify]: Simplify 1 into 1 1.421 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.421 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.421 * [taylor]: Taking taylor expansion of 2.0 in k 1.421 * [backup-simplify]: Simplify 2.0 into 2.0 1.421 * [taylor]: Taking taylor expansion of (* n PI) in k 1.421 * [taylor]: Taking taylor expansion of n in k 1.421 * [backup-simplify]: Simplify n into n 1.421 * [taylor]: Taking taylor expansion of PI in k 1.421 * [backup-simplify]: Simplify PI into PI 1.421 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.422 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.422 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.422 * [backup-simplify]: Simplify (- 0) into 0 1.422 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.422 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 1.423 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 1.423 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 1.423 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.423 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.423 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.423 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.423 * [taylor]: Taking taylor expansion of 0.25 in n 1.423 * [backup-simplify]: Simplify 0.25 into 0.25 1.423 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.423 * [taylor]: Taking taylor expansion of 1.0 in n 1.423 * [backup-simplify]: Simplify 1.0 into 1.0 1.423 * [taylor]: Taking taylor expansion of k in n 1.423 * [backup-simplify]: Simplify k into k 1.423 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.423 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.423 * [taylor]: Taking taylor expansion of 2.0 in n 1.423 * [backup-simplify]: Simplify 2.0 into 2.0 1.423 * [taylor]: Taking taylor expansion of (* n PI) in n 1.423 * [taylor]: Taking taylor expansion of n in n 1.423 * [backup-simplify]: Simplify 0 into 0 1.423 * [backup-simplify]: Simplify 1 into 1 1.423 * [taylor]: Taking taylor expansion of PI in n 1.423 * [backup-simplify]: Simplify PI into PI 1.423 * [backup-simplify]: Simplify (* 0 PI) into 0 1.424 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.425 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.426 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.426 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.426 * [backup-simplify]: Simplify (- k) into (- k) 1.426 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.427 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.432 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.432 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.433 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.433 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.433 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.433 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.433 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.433 * [taylor]: Taking taylor expansion of 0.25 in n 1.433 * [backup-simplify]: Simplify 0.25 into 0.25 1.433 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.433 * [taylor]: Taking taylor expansion of 1.0 in n 1.433 * [backup-simplify]: Simplify 1.0 into 1.0 1.433 * [taylor]: Taking taylor expansion of k in n 1.433 * [backup-simplify]: Simplify k into k 1.433 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.433 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.433 * [taylor]: Taking taylor expansion of 2.0 in n 1.433 * [backup-simplify]: Simplify 2.0 into 2.0 1.433 * [taylor]: Taking taylor expansion of (* n PI) in n 1.433 * [taylor]: Taking taylor expansion of n in n 1.433 * [backup-simplify]: Simplify 0 into 0 1.433 * [backup-simplify]: Simplify 1 into 1 1.433 * [taylor]: Taking taylor expansion of PI in n 1.433 * [backup-simplify]: Simplify PI into PI 1.434 * [backup-simplify]: Simplify (* 0 PI) into 0 1.434 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.435 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.436 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.436 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.436 * [backup-simplify]: Simplify (- k) into (- k) 1.436 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.436 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.437 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.438 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.439 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.439 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.439 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.439 * [taylor]: Taking taylor expansion of 0.25 in k 1.439 * [backup-simplify]: Simplify 0.25 into 0.25 1.439 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.439 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.439 * [taylor]: Taking taylor expansion of 1.0 in k 1.439 * [backup-simplify]: Simplify 1.0 into 1.0 1.439 * [taylor]: Taking taylor expansion of k in k 1.439 * [backup-simplify]: Simplify 0 into 0 1.439 * [backup-simplify]: Simplify 1 into 1 1.439 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.439 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.439 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.439 * [taylor]: Taking taylor expansion of 2.0 in k 1.439 * [backup-simplify]: Simplify 2.0 into 2.0 1.439 * [taylor]: Taking taylor expansion of PI in k 1.439 * [backup-simplify]: Simplify PI into PI 1.439 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.440 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.440 * [taylor]: Taking taylor expansion of (log n) in k 1.440 * [taylor]: Taking taylor expansion of n in k 1.440 * [backup-simplify]: Simplify n into n 1.440 * [backup-simplify]: Simplify (log n) into (log n) 1.440 * [backup-simplify]: Simplify (- 0) into 0 1.440 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.441 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.442 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.442 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 1.443 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.444 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.444 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.445 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.446 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.446 * [backup-simplify]: Simplify (- 0) into 0 1.446 * [backup-simplify]: Simplify (+ 0 0) into 0 1.447 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 1.447 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.448 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.449 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.449 * [taylor]: Taking taylor expansion of 0 in k 1.449 * [backup-simplify]: Simplify 0 into 0 1.449 * [backup-simplify]: Simplify 0 into 0 1.450 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.451 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.451 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.451 * [backup-simplify]: Simplify (+ 0 0) into 0 1.452 * [backup-simplify]: Simplify (- 1) into -1 1.452 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.453 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.454 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1.456 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.458 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.458 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.459 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.460 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.461 * [backup-simplify]: Simplify (- 0) into 0 1.461 * [backup-simplify]: Simplify (+ 0 0) into 0 1.461 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.462 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.463 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.464 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.464 * [taylor]: Taking taylor expansion of 0 in k 1.464 * [backup-simplify]: Simplify 0 into 0 1.464 * [backup-simplify]: Simplify 0 into 0 1.465 * [backup-simplify]: Simplify 0 into 0 1.465 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.467 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.468 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.468 * [backup-simplify]: Simplify (+ 0 0) into 0 1.468 * [backup-simplify]: Simplify (- 0) into 0 1.469 * [backup-simplify]: Simplify (+ 0 0) into 0 1.470 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.471 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.473 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.476 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.482 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 1.483 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 1.483 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 1.483 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 1.483 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.483 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.483 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 1.483 * [taylor]: Taking taylor expansion of 0.25 in k 1.483 * [backup-simplify]: Simplify 0.25 into 0.25 1.483 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.483 * [taylor]: Taking taylor expansion of 1.0 in k 1.483 * [backup-simplify]: Simplify 1.0 into 1.0 1.483 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.483 * [taylor]: Taking taylor expansion of k in k 1.483 * [backup-simplify]: Simplify 0 into 0 1.483 * [backup-simplify]: Simplify 1 into 1 1.483 * [backup-simplify]: Simplify (/ 1 1) into 1 1.483 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.484 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.484 * [taylor]: Taking taylor expansion of 2.0 in k 1.484 * [backup-simplify]: Simplify 2.0 into 2.0 1.484 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.484 * [taylor]: Taking taylor expansion of PI in k 1.484 * [backup-simplify]: Simplify PI into PI 1.484 * [taylor]: Taking taylor expansion of n in k 1.484 * [backup-simplify]: Simplify n into n 1.484 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.484 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.484 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.484 * [backup-simplify]: Simplify (- 1) into -1 1.484 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.484 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 1.485 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 1.485 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.485 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.485 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.485 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.485 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.485 * [taylor]: Taking taylor expansion of 0.25 in n 1.485 * [backup-simplify]: Simplify 0.25 into 0.25 1.485 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.485 * [taylor]: Taking taylor expansion of 1.0 in n 1.485 * [backup-simplify]: Simplify 1.0 into 1.0 1.485 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.485 * [taylor]: Taking taylor expansion of k in n 1.485 * [backup-simplify]: Simplify k into k 1.485 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.485 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.485 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.485 * [taylor]: Taking taylor expansion of 2.0 in n 1.485 * [backup-simplify]: Simplify 2.0 into 2.0 1.485 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.485 * [taylor]: Taking taylor expansion of PI in n 1.485 * [backup-simplify]: Simplify PI into PI 1.485 * [taylor]: Taking taylor expansion of n in n 1.485 * [backup-simplify]: Simplify 0 into 0 1.485 * [backup-simplify]: Simplify 1 into 1 1.485 * [backup-simplify]: Simplify (/ PI 1) into PI 1.486 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.486 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.486 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.486 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.486 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.487 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.488 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.489 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.489 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.489 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.489 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.489 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.489 * [taylor]: Taking taylor expansion of 0.25 in n 1.489 * [backup-simplify]: Simplify 0.25 into 0.25 1.489 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.489 * [taylor]: Taking taylor expansion of 1.0 in n 1.489 * [backup-simplify]: Simplify 1.0 into 1.0 1.489 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.489 * [taylor]: Taking taylor expansion of k in n 1.489 * [backup-simplify]: Simplify k into k 1.489 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.489 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.489 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.489 * [taylor]: Taking taylor expansion of 2.0 in n 1.489 * [backup-simplify]: Simplify 2.0 into 2.0 1.489 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.489 * [taylor]: Taking taylor expansion of PI in n 1.489 * [backup-simplify]: Simplify PI into PI 1.489 * [taylor]: Taking taylor expansion of n in n 1.489 * [backup-simplify]: Simplify 0 into 0 1.489 * [backup-simplify]: Simplify 1 into 1 1.489 * [backup-simplify]: Simplify (/ PI 1) into PI 1.490 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.490 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.490 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.490 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.490 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.491 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.492 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.492 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.493 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.493 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.493 * [taylor]: Taking taylor expansion of 0.25 in k 1.493 * [backup-simplify]: Simplify 0.25 into 0.25 1.493 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.493 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.493 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.493 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.493 * [taylor]: Taking taylor expansion of 2.0 in k 1.493 * [backup-simplify]: Simplify 2.0 into 2.0 1.493 * [taylor]: Taking taylor expansion of PI in k 1.493 * [backup-simplify]: Simplify PI into PI 1.493 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.494 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.494 * [taylor]: Taking taylor expansion of (log n) in k 1.494 * [taylor]: Taking taylor expansion of n in k 1.494 * [backup-simplify]: Simplify n into n 1.494 * [backup-simplify]: Simplify (log n) into (log n) 1.494 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.494 * [taylor]: Taking taylor expansion of 1.0 in k 1.494 * [backup-simplify]: Simplify 1.0 into 1.0 1.494 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.494 * [taylor]: Taking taylor expansion of k in k 1.494 * [backup-simplify]: Simplify 0 into 0 1.494 * [backup-simplify]: Simplify 1 into 1 1.494 * [backup-simplify]: Simplify (/ 1 1) into 1 1.494 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.495 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.495 * [backup-simplify]: Simplify (- 1) into -1 1.495 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.496 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.496 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 1.497 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.498 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.498 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.499 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.500 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.500 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.500 * [backup-simplify]: Simplify (- 0) into 0 1.500 * [backup-simplify]: Simplify (+ 0 0) into 0 1.501 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.501 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.502 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.503 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.503 * [taylor]: Taking taylor expansion of 0 in k 1.503 * [backup-simplify]: Simplify 0 into 0 1.503 * [backup-simplify]: Simplify 0 into 0 1.503 * [backup-simplify]: Simplify 0 into 0 1.504 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.504 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.506 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.506 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.506 * [backup-simplify]: Simplify (- 0) into 0 1.507 * [backup-simplify]: Simplify (+ 0 0) into 0 1.507 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.508 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.509 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.510 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.510 * [taylor]: Taking taylor expansion of 0 in k 1.510 * [backup-simplify]: Simplify 0 into 0 1.510 * [backup-simplify]: Simplify 0 into 0 1.510 * [backup-simplify]: Simplify 0 into 0 1.510 * [backup-simplify]: Simplify 0 into 0 1.511 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.511 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.514 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 1.514 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.515 * [backup-simplify]: Simplify (- 0) into 0 1.515 * [backup-simplify]: Simplify (+ 0 0) into 0 1.516 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.517 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.518 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.525 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.525 * [taylor]: Taking taylor expansion of 0 in k 1.525 * [backup-simplify]: Simplify 0 into 0 1.525 * [backup-simplify]: Simplify 0 into 0 1.526 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 1.527 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 1.527 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 1.527 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 1.527 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.527 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.527 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 1.527 * [taylor]: Taking taylor expansion of 0.25 in k 1.527 * [backup-simplify]: Simplify 0.25 into 0.25 1.527 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.527 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.527 * [taylor]: Taking taylor expansion of k in k 1.527 * [backup-simplify]: Simplify 0 into 0 1.527 * [backup-simplify]: Simplify 1 into 1 1.527 * [backup-simplify]: Simplify (/ 1 1) into 1 1.527 * [taylor]: Taking taylor expansion of 1.0 in k 1.527 * [backup-simplify]: Simplify 1.0 into 1.0 1.527 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.527 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.527 * [taylor]: Taking taylor expansion of -2.0 in k 1.528 * [backup-simplify]: Simplify -2.0 into -2.0 1.528 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.528 * [taylor]: Taking taylor expansion of PI in k 1.528 * [backup-simplify]: Simplify PI into PI 1.528 * [taylor]: Taking taylor expansion of n in k 1.528 * [backup-simplify]: Simplify n into n 1.528 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.528 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.528 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.528 * [backup-simplify]: Simplify (+ 1 0) into 1 1.528 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 1.528 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 1.528 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.528 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.528 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.529 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.529 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.529 * [taylor]: Taking taylor expansion of 0.25 in n 1.529 * [backup-simplify]: Simplify 0.25 into 0.25 1.529 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.529 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.529 * [taylor]: Taking taylor expansion of k in n 1.529 * [backup-simplify]: Simplify k into k 1.529 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.529 * [taylor]: Taking taylor expansion of 1.0 in n 1.529 * [backup-simplify]: Simplify 1.0 into 1.0 1.529 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.529 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.529 * [taylor]: Taking taylor expansion of -2.0 in n 1.529 * [backup-simplify]: Simplify -2.0 into -2.0 1.529 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.529 * [taylor]: Taking taylor expansion of PI in n 1.529 * [backup-simplify]: Simplify PI into PI 1.529 * [taylor]: Taking taylor expansion of n in n 1.529 * [backup-simplify]: Simplify 0 into 0 1.529 * [backup-simplify]: Simplify 1 into 1 1.529 * [backup-simplify]: Simplify (/ PI 1) into PI 1.529 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.530 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.530 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.530 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.531 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.532 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.532 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.532 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.532 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.532 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.532 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.532 * [taylor]: Taking taylor expansion of 0.25 in n 1.532 * [backup-simplify]: Simplify 0.25 into 0.25 1.532 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.532 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.532 * [taylor]: Taking taylor expansion of k in n 1.532 * [backup-simplify]: Simplify k into k 1.533 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.533 * [taylor]: Taking taylor expansion of 1.0 in n 1.533 * [backup-simplify]: Simplify 1.0 into 1.0 1.533 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.533 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.533 * [taylor]: Taking taylor expansion of -2.0 in n 1.533 * [backup-simplify]: Simplify -2.0 into -2.0 1.533 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.533 * [taylor]: Taking taylor expansion of PI in n 1.533 * [backup-simplify]: Simplify PI into PI 1.533 * [taylor]: Taking taylor expansion of n in n 1.533 * [backup-simplify]: Simplify 0 into 0 1.533 * [backup-simplify]: Simplify 1 into 1 1.533 * [backup-simplify]: Simplify (/ PI 1) into PI 1.533 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.534 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.534 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.534 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.535 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.535 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.536 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.536 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.536 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.536 * [taylor]: Taking taylor expansion of 0.25 in k 1.536 * [backup-simplify]: Simplify 0.25 into 0.25 1.536 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.536 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.536 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.536 * [taylor]: Taking taylor expansion of k in k 1.536 * [backup-simplify]: Simplify 0 into 0 1.536 * [backup-simplify]: Simplify 1 into 1 1.537 * [backup-simplify]: Simplify (/ 1 1) into 1 1.537 * [taylor]: Taking taylor expansion of 1.0 in k 1.537 * [backup-simplify]: Simplify 1.0 into 1.0 1.537 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.537 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.537 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.537 * [taylor]: Taking taylor expansion of -2.0 in k 1.537 * [backup-simplify]: Simplify -2.0 into -2.0 1.537 * [taylor]: Taking taylor expansion of PI in k 1.537 * [backup-simplify]: Simplify PI into PI 1.537 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.538 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.538 * [taylor]: Taking taylor expansion of (log n) in k 1.538 * [taylor]: Taking taylor expansion of n in k 1.538 * [backup-simplify]: Simplify n into n 1.538 * [backup-simplify]: Simplify (log n) into (log n) 1.538 * [backup-simplify]: Simplify (+ 1 0) into 1 1.538 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.539 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.539 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.540 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 1.541 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.541 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.542 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.542 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.543 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.543 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.544 * [backup-simplify]: Simplify (+ 0 0) into 0 1.544 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.545 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.545 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.546 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.546 * [taylor]: Taking taylor expansion of 0 in k 1.546 * [backup-simplify]: Simplify 0 into 0 1.547 * [backup-simplify]: Simplify 0 into 0 1.547 * [backup-simplify]: Simplify 0 into 0 1.547 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.548 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.549 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 1.549 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.550 * [backup-simplify]: Simplify (+ 0 0) into 0 1.550 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.551 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.552 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.553 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.553 * [taylor]: Taking taylor expansion of 0 in k 1.553 * [backup-simplify]: Simplify 0 into 0 1.553 * [backup-simplify]: Simplify 0 into 0 1.553 * [backup-simplify]: Simplify 0 into 0 1.553 * [backup-simplify]: Simplify 0 into 0 1.554 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.554 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.557 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 1.557 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.558 * [backup-simplify]: Simplify (+ 0 0) into 0 1.558 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.560 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.562 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.562 * [taylor]: Taking taylor expansion of 0 in k 1.562 * [backup-simplify]: Simplify 0 into 0 1.562 * [backup-simplify]: Simplify 0 into 0 1.563 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 1.563 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 1.563 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 1.563 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 1.563 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 1.563 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.563 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.563 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 1.563 * [taylor]: Taking taylor expansion of 0.25 in k 1.563 * [backup-simplify]: Simplify 0.25 into 0.25 1.563 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.563 * [taylor]: Taking taylor expansion of 1.0 in k 1.563 * [backup-simplify]: Simplify 1.0 into 1.0 1.563 * [taylor]: Taking taylor expansion of k in k 1.563 * [backup-simplify]: Simplify 0 into 0 1.563 * [backup-simplify]: Simplify 1 into 1 1.563 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.563 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.563 * [taylor]: Taking taylor expansion of 2.0 in k 1.563 * [backup-simplify]: Simplify 2.0 into 2.0 1.563 * [taylor]: Taking taylor expansion of (* n PI) in k 1.563 * [taylor]: Taking taylor expansion of n in k 1.563 * [backup-simplify]: Simplify n into n 1.563 * [taylor]: Taking taylor expansion of PI in k 1.563 * [backup-simplify]: Simplify PI into PI 1.563 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.564 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.564 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.564 * [backup-simplify]: Simplify (- 0) into 0 1.564 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.564 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 1.564 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 1.564 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 1.564 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.565 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.565 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.565 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.565 * [taylor]: Taking taylor expansion of 0.25 in n 1.565 * [backup-simplify]: Simplify 0.25 into 0.25 1.565 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.565 * [taylor]: Taking taylor expansion of 1.0 in n 1.565 * [backup-simplify]: Simplify 1.0 into 1.0 1.565 * [taylor]: Taking taylor expansion of k in n 1.565 * [backup-simplify]: Simplify k into k 1.565 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.565 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.565 * [taylor]: Taking taylor expansion of 2.0 in n 1.565 * [backup-simplify]: Simplify 2.0 into 2.0 1.565 * [taylor]: Taking taylor expansion of (* n PI) in n 1.565 * [taylor]: Taking taylor expansion of n in n 1.565 * [backup-simplify]: Simplify 0 into 0 1.565 * [backup-simplify]: Simplify 1 into 1 1.565 * [taylor]: Taking taylor expansion of PI in n 1.565 * [backup-simplify]: Simplify PI into PI 1.565 * [backup-simplify]: Simplify (* 0 PI) into 0 1.565 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.566 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.567 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.568 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.568 * [backup-simplify]: Simplify (- k) into (- k) 1.568 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.568 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.569 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.569 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.570 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.570 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.570 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.570 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.570 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.570 * [taylor]: Taking taylor expansion of 0.25 in n 1.570 * [backup-simplify]: Simplify 0.25 into 0.25 1.570 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.570 * [taylor]: Taking taylor expansion of 1.0 in n 1.570 * [backup-simplify]: Simplify 1.0 into 1.0 1.570 * [taylor]: Taking taylor expansion of k in n 1.570 * [backup-simplify]: Simplify k into k 1.570 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.570 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.570 * [taylor]: Taking taylor expansion of 2.0 in n 1.570 * [backup-simplify]: Simplify 2.0 into 2.0 1.570 * [taylor]: Taking taylor expansion of (* n PI) in n 1.570 * [taylor]: Taking taylor expansion of n in n 1.570 * [backup-simplify]: Simplify 0 into 0 1.570 * [backup-simplify]: Simplify 1 into 1 1.570 * [taylor]: Taking taylor expansion of PI in n 1.570 * [backup-simplify]: Simplify PI into PI 1.571 * [backup-simplify]: Simplify (* 0 PI) into 0 1.571 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.572 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.573 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.574 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.574 * [backup-simplify]: Simplify (- k) into (- k) 1.574 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.574 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.575 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.575 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.576 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.576 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.576 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.576 * [taylor]: Taking taylor expansion of 0.25 in k 1.576 * [backup-simplify]: Simplify 0.25 into 0.25 1.576 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.576 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.576 * [taylor]: Taking taylor expansion of 1.0 in k 1.576 * [backup-simplify]: Simplify 1.0 into 1.0 1.576 * [taylor]: Taking taylor expansion of k in k 1.576 * [backup-simplify]: Simplify 0 into 0 1.576 * [backup-simplify]: Simplify 1 into 1 1.576 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.576 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.576 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.576 * [taylor]: Taking taylor expansion of 2.0 in k 1.576 * [backup-simplify]: Simplify 2.0 into 2.0 1.576 * [taylor]: Taking taylor expansion of PI in k 1.576 * [backup-simplify]: Simplify PI into PI 1.577 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.577 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.577 * [taylor]: Taking taylor expansion of (log n) in k 1.577 * [taylor]: Taking taylor expansion of n in k 1.577 * [backup-simplify]: Simplify n into n 1.577 * [backup-simplify]: Simplify (log n) into (log n) 1.577 * [backup-simplify]: Simplify (- 0) into 0 1.578 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.578 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.579 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.580 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 1.580 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.581 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.581 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.582 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.583 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.583 * [backup-simplify]: Simplify (- 0) into 0 1.583 * [backup-simplify]: Simplify (+ 0 0) into 0 1.584 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 1.584 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.585 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.586 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.586 * [taylor]: Taking taylor expansion of 0 in k 1.586 * [backup-simplify]: Simplify 0 into 0 1.586 * [backup-simplify]: Simplify 0 into 0 1.587 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.588 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.588 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.588 * [backup-simplify]: Simplify (+ 0 0) into 0 1.589 * [backup-simplify]: Simplify (- 1) into -1 1.589 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.590 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.591 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1.593 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.594 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.595 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.596 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.597 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.598 * [backup-simplify]: Simplify (- 0) into 0 1.598 * [backup-simplify]: Simplify (+ 0 0) into 0 1.598 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.599 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.600 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.601 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.601 * [taylor]: Taking taylor expansion of 0 in k 1.601 * [backup-simplify]: Simplify 0 into 0 1.601 * [backup-simplify]: Simplify 0 into 0 1.601 * [backup-simplify]: Simplify 0 into 0 1.602 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.604 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.605 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.605 * [backup-simplify]: Simplify (+ 0 0) into 0 1.605 * [backup-simplify]: Simplify (- 0) into 0 1.605 * [backup-simplify]: Simplify (+ 0 0) into 0 1.606 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.608 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.610 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.619 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.625 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 1.625 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 1.625 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 1.625 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 1.625 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.625 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.625 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 1.625 * [taylor]: Taking taylor expansion of 0.25 in k 1.625 * [backup-simplify]: Simplify 0.25 into 0.25 1.625 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.625 * [taylor]: Taking taylor expansion of 1.0 in k 1.625 * [backup-simplify]: Simplify 1.0 into 1.0 1.625 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.626 * [taylor]: Taking taylor expansion of k in k 1.626 * [backup-simplify]: Simplify 0 into 0 1.626 * [backup-simplify]: Simplify 1 into 1 1.626 * [backup-simplify]: Simplify (/ 1 1) into 1 1.626 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.626 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.626 * [taylor]: Taking taylor expansion of 2.0 in k 1.626 * [backup-simplify]: Simplify 2.0 into 2.0 1.626 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.626 * [taylor]: Taking taylor expansion of PI in k 1.626 * [backup-simplify]: Simplify PI into PI 1.626 * [taylor]: Taking taylor expansion of n in k 1.626 * [backup-simplify]: Simplify n into n 1.626 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.626 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.626 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.626 * [backup-simplify]: Simplify (- 1) into -1 1.627 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.627 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 1.627 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 1.627 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.627 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.627 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.627 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.627 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.627 * [taylor]: Taking taylor expansion of 0.25 in n 1.627 * [backup-simplify]: Simplify 0.25 into 0.25 1.627 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.627 * [taylor]: Taking taylor expansion of 1.0 in n 1.627 * [backup-simplify]: Simplify 1.0 into 1.0 1.627 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.627 * [taylor]: Taking taylor expansion of k in n 1.627 * [backup-simplify]: Simplify k into k 1.627 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.627 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.627 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.627 * [taylor]: Taking taylor expansion of 2.0 in n 1.627 * [backup-simplify]: Simplify 2.0 into 2.0 1.627 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.627 * [taylor]: Taking taylor expansion of PI in n 1.627 * [backup-simplify]: Simplify PI into PI 1.627 * [taylor]: Taking taylor expansion of n in n 1.627 * [backup-simplify]: Simplify 0 into 0 1.627 * [backup-simplify]: Simplify 1 into 1 1.628 * [backup-simplify]: Simplify (/ PI 1) into PI 1.628 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.629 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.629 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.629 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.629 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.630 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.630 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.631 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.631 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.631 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.631 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.631 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.631 * [taylor]: Taking taylor expansion of 0.25 in n 1.631 * [backup-simplify]: Simplify 0.25 into 0.25 1.631 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.631 * [taylor]: Taking taylor expansion of 1.0 in n 1.631 * [backup-simplify]: Simplify 1.0 into 1.0 1.631 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.631 * [taylor]: Taking taylor expansion of k in n 1.631 * [backup-simplify]: Simplify k into k 1.631 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.631 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.631 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.631 * [taylor]: Taking taylor expansion of 2.0 in n 1.631 * [backup-simplify]: Simplify 2.0 into 2.0 1.631 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.631 * [taylor]: Taking taylor expansion of PI in n 1.631 * [backup-simplify]: Simplify PI into PI 1.631 * [taylor]: Taking taylor expansion of n in n 1.631 * [backup-simplify]: Simplify 0 into 0 1.631 * [backup-simplify]: Simplify 1 into 1 1.632 * [backup-simplify]: Simplify (/ PI 1) into PI 1.632 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.632 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.633 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.633 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.633 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.633 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.634 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.635 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.635 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.635 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.635 * [taylor]: Taking taylor expansion of 0.25 in k 1.635 * [backup-simplify]: Simplify 0.25 into 0.25 1.635 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.635 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.635 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.635 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.635 * [taylor]: Taking taylor expansion of 2.0 in k 1.635 * [backup-simplify]: Simplify 2.0 into 2.0 1.635 * [taylor]: Taking taylor expansion of PI in k 1.635 * [backup-simplify]: Simplify PI into PI 1.635 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.636 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.636 * [taylor]: Taking taylor expansion of (log n) in k 1.636 * [taylor]: Taking taylor expansion of n in k 1.636 * [backup-simplify]: Simplify n into n 1.636 * [backup-simplify]: Simplify (log n) into (log n) 1.636 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.636 * [taylor]: Taking taylor expansion of 1.0 in k 1.636 * [backup-simplify]: Simplify 1.0 into 1.0 1.636 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.636 * [taylor]: Taking taylor expansion of k in k 1.636 * [backup-simplify]: Simplify 0 into 0 1.636 * [backup-simplify]: Simplify 1 into 1 1.636 * [backup-simplify]: Simplify (/ 1 1) into 1 1.636 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.637 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.637 * [backup-simplify]: Simplify (- 1) into -1 1.638 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.638 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.639 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 1.639 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.640 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.641 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.641 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.642 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.642 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.642 * [backup-simplify]: Simplify (- 0) into 0 1.643 * [backup-simplify]: Simplify (+ 0 0) into 0 1.643 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.644 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.644 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.645 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.646 * [taylor]: Taking taylor expansion of 0 in k 1.646 * [backup-simplify]: Simplify 0 into 0 1.646 * [backup-simplify]: Simplify 0 into 0 1.646 * [backup-simplify]: Simplify 0 into 0 1.646 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.647 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.648 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.648 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.649 * [backup-simplify]: Simplify (- 0) into 0 1.649 * [backup-simplify]: Simplify (+ 0 0) into 0 1.649 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.650 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.651 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.652 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.652 * [taylor]: Taking taylor expansion of 0 in k 1.652 * [backup-simplify]: Simplify 0 into 0 1.653 * [backup-simplify]: Simplify 0 into 0 1.653 * [backup-simplify]: Simplify 0 into 0 1.653 * [backup-simplify]: Simplify 0 into 0 1.653 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.654 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.657 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 1.657 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.657 * [backup-simplify]: Simplify (- 0) into 0 1.658 * [backup-simplify]: Simplify (+ 0 0) into 0 1.658 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.659 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.660 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.662 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.662 * [taylor]: Taking taylor expansion of 0 in k 1.662 * [backup-simplify]: Simplify 0 into 0 1.662 * [backup-simplify]: Simplify 0 into 0 1.663 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 1.663 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 1.663 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 1.663 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 1.663 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.663 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.663 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 1.663 * [taylor]: Taking taylor expansion of 0.25 in k 1.663 * [backup-simplify]: Simplify 0.25 into 0.25 1.663 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.663 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.663 * [taylor]: Taking taylor expansion of k in k 1.663 * [backup-simplify]: Simplify 0 into 0 1.663 * [backup-simplify]: Simplify 1 into 1 1.663 * [backup-simplify]: Simplify (/ 1 1) into 1 1.663 * [taylor]: Taking taylor expansion of 1.0 in k 1.664 * [backup-simplify]: Simplify 1.0 into 1.0 1.664 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.664 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.664 * [taylor]: Taking taylor expansion of -2.0 in k 1.664 * [backup-simplify]: Simplify -2.0 into -2.0 1.664 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.664 * [taylor]: Taking taylor expansion of PI in k 1.664 * [backup-simplify]: Simplify PI into PI 1.664 * [taylor]: Taking taylor expansion of n in k 1.664 * [backup-simplify]: Simplify n into n 1.664 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.664 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.664 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.664 * [backup-simplify]: Simplify (+ 1 0) into 1 1.664 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 1.664 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 1.665 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.665 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.665 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.665 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.665 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.665 * [taylor]: Taking taylor expansion of 0.25 in n 1.665 * [backup-simplify]: Simplify 0.25 into 0.25 1.665 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.665 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.665 * [taylor]: Taking taylor expansion of k in n 1.665 * [backup-simplify]: Simplify k into k 1.665 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.665 * [taylor]: Taking taylor expansion of 1.0 in n 1.665 * [backup-simplify]: Simplify 1.0 into 1.0 1.665 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.665 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.665 * [taylor]: Taking taylor expansion of -2.0 in n 1.665 * [backup-simplify]: Simplify -2.0 into -2.0 1.665 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.665 * [taylor]: Taking taylor expansion of PI in n 1.665 * [backup-simplify]: Simplify PI into PI 1.665 * [taylor]: Taking taylor expansion of n in n 1.665 * [backup-simplify]: Simplify 0 into 0 1.665 * [backup-simplify]: Simplify 1 into 1 1.665 * [backup-simplify]: Simplify (/ PI 1) into PI 1.665 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.666 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.666 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.666 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.667 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.668 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.668 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.668 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.668 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.668 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.668 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.668 * [taylor]: Taking taylor expansion of 0.25 in n 1.669 * [backup-simplify]: Simplify 0.25 into 0.25 1.669 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.669 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.669 * [taylor]: Taking taylor expansion of k in n 1.669 * [backup-simplify]: Simplify k into k 1.669 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.669 * [taylor]: Taking taylor expansion of 1.0 in n 1.669 * [backup-simplify]: Simplify 1.0 into 1.0 1.669 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.669 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.669 * [taylor]: Taking taylor expansion of -2.0 in n 1.669 * [backup-simplify]: Simplify -2.0 into -2.0 1.669 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.669 * [taylor]: Taking taylor expansion of PI in n 1.669 * [backup-simplify]: Simplify PI into PI 1.669 * [taylor]: Taking taylor expansion of n in n 1.669 * [backup-simplify]: Simplify 0 into 0 1.669 * [backup-simplify]: Simplify 1 into 1 1.669 * [backup-simplify]: Simplify (/ PI 1) into PI 1.669 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.670 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.670 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.670 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.671 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.672 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.672 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.672 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.672 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.672 * [taylor]: Taking taylor expansion of 0.25 in k 1.672 * [backup-simplify]: Simplify 0.25 into 0.25 1.672 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.672 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.672 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.672 * [taylor]: Taking taylor expansion of k in k 1.672 * [backup-simplify]: Simplify 0 into 0 1.672 * [backup-simplify]: Simplify 1 into 1 1.673 * [backup-simplify]: Simplify (/ 1 1) into 1 1.673 * [taylor]: Taking taylor expansion of 1.0 in k 1.673 * [backup-simplify]: Simplify 1.0 into 1.0 1.673 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.673 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.673 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.673 * [taylor]: Taking taylor expansion of -2.0 in k 1.673 * [backup-simplify]: Simplify -2.0 into -2.0 1.673 * [taylor]: Taking taylor expansion of PI in k 1.673 * [backup-simplify]: Simplify PI into PI 1.673 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.674 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.674 * [taylor]: Taking taylor expansion of (log n) in k 1.674 * [taylor]: Taking taylor expansion of n in k 1.674 * [backup-simplify]: Simplify n into n 1.674 * [backup-simplify]: Simplify (log n) into (log n) 1.674 * [backup-simplify]: Simplify (+ 1 0) into 1 1.674 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.675 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.675 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.676 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 1.677 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.678 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.678 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.679 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.679 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.680 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.680 * [backup-simplify]: Simplify (+ 0 0) into 0 1.680 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.681 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.682 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.683 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.683 * [taylor]: Taking taylor expansion of 0 in k 1.683 * [backup-simplify]: Simplify 0 into 0 1.683 * [backup-simplify]: Simplify 0 into 0 1.683 * [backup-simplify]: Simplify 0 into 0 1.683 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.684 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.685 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 1.686 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.686 * [backup-simplify]: Simplify (+ 0 0) into 0 1.686 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.687 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.688 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.689 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.689 * [taylor]: Taking taylor expansion of 0 in k 1.689 * [backup-simplify]: Simplify 0 into 0 1.689 * [backup-simplify]: Simplify 0 into 0 1.689 * [backup-simplify]: Simplify 0 into 0 1.689 * [backup-simplify]: Simplify 0 into 0 1.690 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.691 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.693 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 1.694 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.694 * [backup-simplify]: Simplify (+ 0 0) into 0 1.694 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.695 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.696 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.698 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.698 * [taylor]: Taking taylor expansion of 0 in k 1.698 * [backup-simplify]: Simplify 0 into 0 1.698 * [backup-simplify]: Simplify 0 into 0 1.699 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 1.699 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1) 1.699 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.699 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.699 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.699 * [taylor]: Taking taylor expansion of 2.0 in n 1.699 * [backup-simplify]: Simplify 2.0 into 2.0 1.699 * [taylor]: Taking taylor expansion of (* n PI) in n 1.699 * [taylor]: Taking taylor expansion of n in n 1.699 * [backup-simplify]: Simplify 0 into 0 1.699 * [backup-simplify]: Simplify 1 into 1 1.699 * [taylor]: Taking taylor expansion of PI in n 1.699 * [backup-simplify]: Simplify PI into PI 1.699 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.699 * [taylor]: Taking taylor expansion of 2.0 in n 1.699 * [backup-simplify]: Simplify 2.0 into 2.0 1.699 * [taylor]: Taking taylor expansion of (* n PI) in n 1.699 * [taylor]: Taking taylor expansion of n in n 1.699 * [backup-simplify]: Simplify 0 into 0 1.699 * [backup-simplify]: Simplify 1 into 1 1.699 * [taylor]: Taking taylor expansion of PI in n 1.699 * [backup-simplify]: Simplify PI into PI 1.700 * [backup-simplify]: Simplify (* 0 PI) into 0 1.700 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.700 * [backup-simplify]: Simplify 0 into 0 1.701 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.702 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.702 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.702 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.703 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.703 * [backup-simplify]: Simplify 0 into 0 1.704 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.704 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.704 * [backup-simplify]: Simplify 0 into 0 1.705 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.706 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.706 * [backup-simplify]: Simplify 0 into 0 1.712 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.712 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.713 * [backup-simplify]: Simplify 0 into 0 1.713 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.714 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.714 * [backup-simplify]: Simplify 0 into 0 1.715 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.716 * [backup-simplify]: Simplify 0 into 0 1.717 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.717 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.717 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.717 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.717 * [taylor]: Taking taylor expansion of 2.0 in n 1.717 * [backup-simplify]: Simplify 2.0 into 2.0 1.717 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.717 * [taylor]: Taking taylor expansion of PI in n 1.717 * [backup-simplify]: Simplify PI into PI 1.717 * [taylor]: Taking taylor expansion of n in n 1.717 * [backup-simplify]: Simplify 0 into 0 1.717 * [backup-simplify]: Simplify 1 into 1 1.717 * [backup-simplify]: Simplify (/ PI 1) into PI 1.717 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.717 * [taylor]: Taking taylor expansion of 2.0 in n 1.717 * [backup-simplify]: Simplify 2.0 into 2.0 1.717 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.717 * [taylor]: Taking taylor expansion of PI in n 1.717 * [backup-simplify]: Simplify PI into PI 1.717 * [taylor]: Taking taylor expansion of n in n 1.717 * [backup-simplify]: Simplify 0 into 0 1.717 * [backup-simplify]: Simplify 1 into 1 1.718 * [backup-simplify]: Simplify (/ PI 1) into PI 1.718 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.718 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.719 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.719 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.719 * [backup-simplify]: Simplify 0 into 0 1.720 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.720 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.720 * [backup-simplify]: Simplify 0 into 0 1.721 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.722 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.722 * [backup-simplify]: Simplify 0 into 0 1.722 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.723 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.723 * [backup-simplify]: Simplify 0 into 0 1.724 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.724 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.724 * [backup-simplify]: Simplify 0 into 0 1.725 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.726 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.726 * [backup-simplify]: Simplify 0 into 0 1.726 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.727 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.727 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.727 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.727 * [taylor]: Taking taylor expansion of -2.0 in n 1.727 * [backup-simplify]: Simplify -2.0 into -2.0 1.727 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.727 * [taylor]: Taking taylor expansion of PI in n 1.727 * [backup-simplify]: Simplify PI into PI 1.727 * [taylor]: Taking taylor expansion of n in n 1.727 * [backup-simplify]: Simplify 0 into 0 1.727 * [backup-simplify]: Simplify 1 into 1 1.727 * [backup-simplify]: Simplify (/ PI 1) into PI 1.727 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.727 * [taylor]: Taking taylor expansion of -2.0 in n 1.728 * [backup-simplify]: Simplify -2.0 into -2.0 1.728 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.728 * [taylor]: Taking taylor expansion of PI in n 1.728 * [backup-simplify]: Simplify PI into PI 1.728 * [taylor]: Taking taylor expansion of n in n 1.728 * [backup-simplify]: Simplify 0 into 0 1.728 * [backup-simplify]: Simplify 1 into 1 1.728 * [backup-simplify]: Simplify (/ PI 1) into PI 1.728 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.728 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.729 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.729 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.729 * [backup-simplify]: Simplify 0 into 0 1.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.731 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.731 * [backup-simplify]: Simplify 0 into 0 1.731 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.732 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.732 * [backup-simplify]: Simplify 0 into 0 1.733 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.733 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.733 * [backup-simplify]: Simplify 0 into 0 1.734 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.735 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.735 * [backup-simplify]: Simplify 0 into 0 1.735 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.736 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.736 * [backup-simplify]: Simplify 0 into 0 1.737 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.737 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1) 1.737 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.737 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.737 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.737 * [taylor]: Taking taylor expansion of 2.0 in n 1.737 * [backup-simplify]: Simplify 2.0 into 2.0 1.737 * [taylor]: Taking taylor expansion of (* n PI) in n 1.737 * [taylor]: Taking taylor expansion of n in n 1.737 * [backup-simplify]: Simplify 0 into 0 1.737 * [backup-simplify]: Simplify 1 into 1 1.737 * [taylor]: Taking taylor expansion of PI in n 1.737 * [backup-simplify]: Simplify PI into PI 1.737 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.737 * [taylor]: Taking taylor expansion of 2.0 in n 1.737 * [backup-simplify]: Simplify 2.0 into 2.0 1.737 * [taylor]: Taking taylor expansion of (* n PI) in n 1.737 * [taylor]: Taking taylor expansion of n in n 1.737 * [backup-simplify]: Simplify 0 into 0 1.737 * [backup-simplify]: Simplify 1 into 1 1.737 * [taylor]: Taking taylor expansion of PI in n 1.737 * [backup-simplify]: Simplify PI into PI 1.738 * [backup-simplify]: Simplify (* 0 PI) into 0 1.738 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.738 * [backup-simplify]: Simplify 0 into 0 1.739 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.740 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.740 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.740 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.741 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.741 * [backup-simplify]: Simplify 0 into 0 1.742 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.743 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.743 * [backup-simplify]: Simplify 0 into 0 1.743 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.744 * [backup-simplify]: Simplify 0 into 0 1.745 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.746 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.746 * [backup-simplify]: Simplify 0 into 0 1.747 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.747 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.747 * [backup-simplify]: Simplify 0 into 0 1.748 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.749 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.749 * [backup-simplify]: Simplify 0 into 0 1.750 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.750 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.750 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.750 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.750 * [taylor]: Taking taylor expansion of 2.0 in n 1.750 * [backup-simplify]: Simplify 2.0 into 2.0 1.750 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.750 * [taylor]: Taking taylor expansion of PI in n 1.750 * [backup-simplify]: Simplify PI into PI 1.750 * [taylor]: Taking taylor expansion of n in n 1.750 * [backup-simplify]: Simplify 0 into 0 1.750 * [backup-simplify]: Simplify 1 into 1 1.750 * [backup-simplify]: Simplify (/ PI 1) into PI 1.750 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.750 * [taylor]: Taking taylor expansion of 2.0 in n 1.750 * [backup-simplify]: Simplify 2.0 into 2.0 1.750 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.750 * [taylor]: Taking taylor expansion of PI in n 1.751 * [backup-simplify]: Simplify PI into PI 1.751 * [taylor]: Taking taylor expansion of n in n 1.751 * [backup-simplify]: Simplify 0 into 0 1.751 * [backup-simplify]: Simplify 1 into 1 1.751 * [backup-simplify]: Simplify (/ PI 1) into PI 1.751 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.751 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.752 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.752 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.752 * [backup-simplify]: Simplify 0 into 0 1.753 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.753 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.753 * [backup-simplify]: Simplify 0 into 0 1.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.755 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.755 * [backup-simplify]: Simplify 0 into 0 1.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.756 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.756 * [backup-simplify]: Simplify 0 into 0 1.756 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.757 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.757 * [backup-simplify]: Simplify 0 into 0 1.758 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.759 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.759 * [backup-simplify]: Simplify 0 into 0 1.759 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.759 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.759 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.759 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.759 * [taylor]: Taking taylor expansion of -2.0 in n 1.760 * [backup-simplify]: Simplify -2.0 into -2.0 1.760 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.760 * [taylor]: Taking taylor expansion of PI in n 1.760 * [backup-simplify]: Simplify PI into PI 1.760 * [taylor]: Taking taylor expansion of n in n 1.760 * [backup-simplify]: Simplify 0 into 0 1.760 * [backup-simplify]: Simplify 1 into 1 1.760 * [backup-simplify]: Simplify (/ PI 1) into PI 1.760 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.760 * [taylor]: Taking taylor expansion of -2.0 in n 1.760 * [backup-simplify]: Simplify -2.0 into -2.0 1.760 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.760 * [taylor]: Taking taylor expansion of PI in n 1.760 * [backup-simplify]: Simplify PI into PI 1.760 * [taylor]: Taking taylor expansion of n in n 1.760 * [backup-simplify]: Simplify 0 into 0 1.760 * [backup-simplify]: Simplify 1 into 1 1.760 * [backup-simplify]: Simplify (/ PI 1) into PI 1.761 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.761 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.762 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.762 * [backup-simplify]: Simplify 0 into 0 1.762 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.763 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.763 * [backup-simplify]: Simplify 0 into 0 1.763 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.764 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.764 * [backup-simplify]: Simplify 0 into 0 1.765 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.765 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.765 * [backup-simplify]: Simplify 0 into 0 1.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.767 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.767 * [backup-simplify]: Simplify 0 into 0 1.767 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.768 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.768 * [backup-simplify]: Simplify 0 into 0 1.769 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.769 * * * [progress]: simplifying candidates 1.772 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (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) 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(* 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)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 1.772 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (log1p (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (/ (- h2 h1) h0) 2)) (* (+ (log (* h0 h4)) (log h3)) (/ (/ (- h2 h1) h0) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (- h2 h1) h0) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ h2 h0) 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(sqrt h2) (sqrt h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ 1 (sqrt 2))) (pow (* (* h0 h4) h3) (/ 1 1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (- h2 h1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (- h2 h1) 1)) (pow (* (* h0 h4) h3) 1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* h0 h4) (/ (/ (- h2 h1) h0) 2)) (pow h3 (/ (/ (- h2 h1) h0) 2)) (log (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (exp (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (expm1 (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (log1p (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (/ (- h2 h1) h0) 2)) (* (+ (log (* h0 h4)) (log h3)) (/ (/ (- h2 h1) h0) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (- h2 h1) h0) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ h2 h0) 2)) (pow (* (* h0 h4) h3) (/ (/ h1 h0) 2)) (pow (* (* h0 h4) h3) (* (cbrt (/ (/ (- h2 h1) h0) 2)) (cbrt (/ (/ (- h2 h1) h0) 2)))) (pow (* (* h0 h4) h3) (sqrt (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) 1)) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ 1 (sqrt 2))) (pow (* (* h0 h4) h3) (/ 1 1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (- h2 h1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (- h2 h1) 1)) (pow (* (* h0 h4) h3) 1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* h0 h4) (/ (/ (- h2 h1) h0) 2)) (pow h3 (/ (/ (- h2 h1) h0) 2)) (log (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (exp (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (expm1 (* (* h0 h4) h3)) (log1p (* (* h0 h4) h3)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (expm1 (* (* h0 h4) h3)) (log1p (* (* h0 h4) h3)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) 1.780 * * [simplify]: iteration 0 : 703 enodes (cost 1718 ) 1.791 * * [simplify]: iteration 1 : 2797 enodes (cost 1652 ) 1.832 * * [simplify]: iteration 2 : 5001 enodes (cost 1636 ) 1.840 * * * [progress]: adding candidates to table 2.506 * * [progress]: iteration 3 / 4 2.506 * * * [progress]: picking best candidate 2.528 * * * * [pick]: Picked # 2.528 * * * [progress]: localizing error 2.544 * * * [progress]: generating rewritten candidates 2.544 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.572 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 2.596 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 2.602 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 2.631 * * * [progress]: generating series expansions 2.631 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.632 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2.632 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.632 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.632 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.632 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.632 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.632 * [taylor]: Taking taylor expansion of 0.25 in k 2.632 * [backup-simplify]: Simplify 0.25 into 0.25 2.632 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.632 * [taylor]: Taking taylor expansion of 1.0 in k 2.632 * [backup-simplify]: Simplify 1.0 into 1.0 2.632 * [taylor]: Taking taylor expansion of k in k 2.632 * [backup-simplify]: Simplify 0 into 0 2.632 * [backup-simplify]: Simplify 1 into 1 2.632 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.633 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.633 * [taylor]: Taking taylor expansion of 2.0 in k 2.633 * [backup-simplify]: Simplify 2.0 into 2.0 2.633 * [taylor]: Taking taylor expansion of (* n PI) in k 2.633 * [taylor]: Taking taylor expansion of n in k 2.633 * [backup-simplify]: Simplify n into n 2.633 * [taylor]: Taking taylor expansion of PI in k 2.633 * [backup-simplify]: Simplify PI into PI 2.633 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.633 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.633 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.633 * [backup-simplify]: Simplify (- 0) into 0 2.633 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.634 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.634 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.634 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.634 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.634 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.634 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.634 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.634 * [taylor]: Taking taylor expansion of 0.25 in n 2.634 * [backup-simplify]: Simplify 0.25 into 0.25 2.634 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.634 * [taylor]: Taking taylor expansion of 1.0 in n 2.634 * [backup-simplify]: Simplify 1.0 into 1.0 2.634 * [taylor]: Taking taylor expansion of k in n 2.634 * [backup-simplify]: Simplify k into k 2.634 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.634 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.634 * [taylor]: Taking taylor expansion of 2.0 in n 2.634 * [backup-simplify]: Simplify 2.0 into 2.0 2.634 * [taylor]: Taking taylor expansion of (* n PI) in n 2.634 * [taylor]: Taking taylor expansion of n in n 2.634 * [backup-simplify]: Simplify 0 into 0 2.634 * [backup-simplify]: Simplify 1 into 1 2.634 * [taylor]: Taking taylor expansion of PI in n 2.634 * [backup-simplify]: Simplify PI into PI 2.634 * [backup-simplify]: Simplify (* 0 PI) into 0 2.635 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.636 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.636 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.637 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.637 * [backup-simplify]: Simplify (- k) into (- k) 2.637 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.637 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.638 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.639 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.639 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.639 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.639 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.639 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.640 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.640 * [taylor]: Taking taylor expansion of 0.25 in n 2.640 * [backup-simplify]: Simplify 0.25 into 0.25 2.640 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.640 * [taylor]: Taking taylor expansion of 1.0 in n 2.640 * [backup-simplify]: Simplify 1.0 into 1.0 2.640 * [taylor]: Taking taylor expansion of k in n 2.640 * [backup-simplify]: Simplify k into k 2.640 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.640 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.640 * [taylor]: Taking taylor expansion of 2.0 in n 2.640 * [backup-simplify]: Simplify 2.0 into 2.0 2.640 * [taylor]: Taking taylor expansion of (* n PI) in n 2.640 * [taylor]: Taking taylor expansion of n in n 2.640 * [backup-simplify]: Simplify 0 into 0 2.640 * [backup-simplify]: Simplify 1 into 1 2.640 * [taylor]: Taking taylor expansion of PI in n 2.640 * [backup-simplify]: Simplify PI into PI 2.640 * [backup-simplify]: Simplify (* 0 PI) into 0 2.640 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.641 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.642 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.643 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.643 * [backup-simplify]: Simplify (- k) into (- k) 2.643 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.643 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.644 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.644 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.645 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.645 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.645 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.645 * [taylor]: Taking taylor expansion of 0.25 in k 2.645 * [backup-simplify]: Simplify 0.25 into 0.25 2.645 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.645 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.645 * [taylor]: Taking taylor expansion of 1.0 in k 2.645 * [backup-simplify]: Simplify 1.0 into 1.0 2.645 * [taylor]: Taking taylor expansion of k in k 2.645 * [backup-simplify]: Simplify 0 into 0 2.645 * [backup-simplify]: Simplify 1 into 1 2.645 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.645 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.645 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.645 * [taylor]: Taking taylor expansion of 2.0 in k 2.645 * [backup-simplify]: Simplify 2.0 into 2.0 2.645 * [taylor]: Taking taylor expansion of PI in k 2.645 * [backup-simplify]: Simplify PI into PI 2.646 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.646 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.646 * [taylor]: Taking taylor expansion of (log n) in k 2.646 * [taylor]: Taking taylor expansion of n in k 2.646 * [backup-simplify]: Simplify n into n 2.646 * [backup-simplify]: Simplify (log n) into (log n) 2.646 * [backup-simplify]: Simplify (- 0) into 0 2.647 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.647 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.648 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.649 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.649 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.650 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.651 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.651 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.652 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.652 * [backup-simplify]: Simplify (- 0) into 0 2.652 * [backup-simplify]: Simplify (+ 0 0) into 0 2.653 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.654 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.654 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.655 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.655 * [taylor]: Taking taylor expansion of 0 in k 2.655 * [backup-simplify]: Simplify 0 into 0 2.655 * [backup-simplify]: Simplify 0 into 0 2.656 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.657 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.657 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.658 * [backup-simplify]: Simplify (+ 0 0) into 0 2.658 * [backup-simplify]: Simplify (- 1) into -1 2.658 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.659 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.660 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2.662 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.664 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.664 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.665 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.667 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.667 * [backup-simplify]: Simplify (- 0) into 0 2.667 * [backup-simplify]: Simplify (+ 0 0) into 0 2.668 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.669 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.669 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.671 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.671 * [taylor]: Taking taylor expansion of 0 in k 2.671 * [backup-simplify]: Simplify 0 into 0 2.671 * [backup-simplify]: Simplify 0 into 0 2.671 * [backup-simplify]: Simplify 0 into 0 2.671 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.673 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.674 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.674 * [backup-simplify]: Simplify (+ 0 0) into 0 2.674 * [backup-simplify]: Simplify (- 0) into 0 2.675 * [backup-simplify]: Simplify (+ 0 0) into 0 2.676 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.677 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.680 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.683 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.689 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.689 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2.689 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.689 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.689 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.689 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.689 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.689 * [taylor]: Taking taylor expansion of 0.25 in k 2.689 * [backup-simplify]: Simplify 0.25 into 0.25 2.689 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.689 * [taylor]: Taking taylor expansion of 1.0 in k 2.689 * [backup-simplify]: Simplify 1.0 into 1.0 2.689 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.689 * [taylor]: Taking taylor expansion of k in k 2.689 * [backup-simplify]: Simplify 0 into 0 2.689 * [backup-simplify]: Simplify 1 into 1 2.690 * [backup-simplify]: Simplify (/ 1 1) into 1 2.690 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.690 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.690 * [taylor]: Taking taylor expansion of 2.0 in k 2.690 * [backup-simplify]: Simplify 2.0 into 2.0 2.690 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.690 * [taylor]: Taking taylor expansion of PI in k 2.690 * [backup-simplify]: Simplify PI into PI 2.690 * [taylor]: Taking taylor expansion of n in k 2.690 * [backup-simplify]: Simplify n into n 2.690 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.690 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.690 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.690 * [backup-simplify]: Simplify (- 1) into -1 2.690 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.691 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.691 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.691 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.691 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.691 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.691 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.691 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.691 * [taylor]: Taking taylor expansion of 0.25 in n 2.691 * [backup-simplify]: Simplify 0.25 into 0.25 2.691 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.691 * [taylor]: Taking taylor expansion of 1.0 in n 2.691 * [backup-simplify]: Simplify 1.0 into 1.0 2.691 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.691 * [taylor]: Taking taylor expansion of k in n 2.691 * [backup-simplify]: Simplify k into k 2.691 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.691 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.691 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.691 * [taylor]: Taking taylor expansion of 2.0 in n 2.691 * [backup-simplify]: Simplify 2.0 into 2.0 2.691 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.691 * [taylor]: Taking taylor expansion of PI in n 2.691 * [backup-simplify]: Simplify PI into PI 2.691 * [taylor]: Taking taylor expansion of n in n 2.691 * [backup-simplify]: Simplify 0 into 0 2.691 * [backup-simplify]: Simplify 1 into 1 2.692 * [backup-simplify]: Simplify (/ PI 1) into PI 2.692 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.692 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.693 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.693 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.693 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.693 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.694 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.695 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.695 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.695 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.695 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.695 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.695 * [taylor]: Taking taylor expansion of 0.25 in n 2.695 * [backup-simplify]: Simplify 0.25 into 0.25 2.695 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.695 * [taylor]: Taking taylor expansion of 1.0 in n 2.695 * [backup-simplify]: Simplify 1.0 into 1.0 2.695 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.695 * [taylor]: Taking taylor expansion of k in n 2.695 * [backup-simplify]: Simplify k into k 2.695 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.695 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.695 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.695 * [taylor]: Taking taylor expansion of 2.0 in n 2.695 * [backup-simplify]: Simplify 2.0 into 2.0 2.695 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.695 * [taylor]: Taking taylor expansion of PI in n 2.695 * [backup-simplify]: Simplify PI into PI 2.695 * [taylor]: Taking taylor expansion of n in n 2.695 * [backup-simplify]: Simplify 0 into 0 2.695 * [backup-simplify]: Simplify 1 into 1 2.696 * [backup-simplify]: Simplify (/ PI 1) into PI 2.696 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.696 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.696 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.697 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.697 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.697 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.698 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.699 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.699 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.699 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.699 * [taylor]: Taking taylor expansion of 0.25 in k 2.699 * [backup-simplify]: Simplify 0.25 into 0.25 2.699 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.699 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.699 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.699 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.699 * [taylor]: Taking taylor expansion of 2.0 in k 2.699 * [backup-simplify]: Simplify 2.0 into 2.0 2.699 * [taylor]: Taking taylor expansion of PI in k 2.699 * [backup-simplify]: Simplify PI into PI 2.699 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.706 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.706 * [taylor]: Taking taylor expansion of (log n) in k 2.706 * [taylor]: Taking taylor expansion of n in k 2.707 * [backup-simplify]: Simplify n into n 2.707 * [backup-simplify]: Simplify (log n) into (log n) 2.707 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.707 * [taylor]: Taking taylor expansion of 1.0 in k 2.707 * [backup-simplify]: Simplify 1.0 into 1.0 2.707 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.707 * [taylor]: Taking taylor expansion of k in k 2.707 * [backup-simplify]: Simplify 0 into 0 2.707 * [backup-simplify]: Simplify 1 into 1 2.707 * [backup-simplify]: Simplify (/ 1 1) into 1 2.707 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.708 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.708 * [backup-simplify]: Simplify (- 1) into -1 2.708 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.709 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.709 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.710 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.711 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.712 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.713 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.713 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.713 * [backup-simplify]: Simplify (- 0) into 0 2.713 * [backup-simplify]: Simplify (+ 0 0) into 0 2.714 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.714 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.715 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.716 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.716 * [taylor]: Taking taylor expansion of 0 in k 2.716 * [backup-simplify]: Simplify 0 into 0 2.716 * [backup-simplify]: Simplify 0 into 0 2.716 * [backup-simplify]: Simplify 0 into 0 2.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.717 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.719 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.719 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.719 * [backup-simplify]: Simplify (- 0) into 0 2.720 * [backup-simplify]: Simplify (+ 0 0) into 0 2.720 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.721 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.722 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.723 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.723 * [taylor]: Taking taylor expansion of 0 in k 2.723 * [backup-simplify]: Simplify 0 into 0 2.723 * [backup-simplify]: Simplify 0 into 0 2.723 * [backup-simplify]: Simplify 0 into 0 2.723 * [backup-simplify]: Simplify 0 into 0 2.724 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.724 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.728 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 2.728 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.728 * [backup-simplify]: Simplify (- 0) into 0 2.728 * [backup-simplify]: Simplify (+ 0 0) into 0 2.729 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.730 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.731 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.733 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.733 * [taylor]: Taking taylor expansion of 0 in k 2.733 * [backup-simplify]: Simplify 0 into 0 2.733 * [backup-simplify]: Simplify 0 into 0 2.733 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.734 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2.734 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.734 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.734 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.734 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.734 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.734 * [taylor]: Taking taylor expansion of 0.25 in k 2.734 * [backup-simplify]: Simplify 0.25 into 0.25 2.734 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.734 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.734 * [taylor]: Taking taylor expansion of k in k 2.734 * [backup-simplify]: Simplify 0 into 0 2.734 * [backup-simplify]: Simplify 1 into 1 2.734 * [backup-simplify]: Simplify (/ 1 1) into 1 2.734 * [taylor]: Taking taylor expansion of 1.0 in k 2.734 * [backup-simplify]: Simplify 1.0 into 1.0 2.734 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.734 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.734 * [taylor]: Taking taylor expansion of -2.0 in k 2.734 * [backup-simplify]: Simplify -2.0 into -2.0 2.734 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.734 * [taylor]: Taking taylor expansion of PI in k 2.734 * [backup-simplify]: Simplify PI into PI 2.734 * [taylor]: Taking taylor expansion of n in k 2.734 * [backup-simplify]: Simplify n into n 2.734 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.735 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.735 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.735 * [backup-simplify]: Simplify (+ 1 0) into 1 2.735 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.735 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.735 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.735 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.735 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.735 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.735 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.735 * [taylor]: Taking taylor expansion of 0.25 in n 2.735 * [backup-simplify]: Simplify 0.25 into 0.25 2.735 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.735 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.735 * [taylor]: Taking taylor expansion of k in n 2.736 * [backup-simplify]: Simplify k into k 2.736 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.736 * [taylor]: Taking taylor expansion of 1.0 in n 2.736 * [backup-simplify]: Simplify 1.0 into 1.0 2.736 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.736 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.736 * [taylor]: Taking taylor expansion of -2.0 in n 2.736 * [backup-simplify]: Simplify -2.0 into -2.0 2.736 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.736 * [taylor]: Taking taylor expansion of PI in n 2.736 * [backup-simplify]: Simplify PI into PI 2.736 * [taylor]: Taking taylor expansion of n in n 2.736 * [backup-simplify]: Simplify 0 into 0 2.736 * [backup-simplify]: Simplify 1 into 1 2.736 * [backup-simplify]: Simplify (/ PI 1) into PI 2.736 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.737 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.737 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.737 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.738 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.739 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.739 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.739 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.739 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.739 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.739 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.739 * [taylor]: Taking taylor expansion of 0.25 in n 2.739 * [backup-simplify]: Simplify 0.25 into 0.25 2.739 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.739 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.739 * [taylor]: Taking taylor expansion of k in n 2.739 * [backup-simplify]: Simplify k into k 2.739 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.739 * [taylor]: Taking taylor expansion of 1.0 in n 2.740 * [backup-simplify]: Simplify 1.0 into 1.0 2.740 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.740 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.740 * [taylor]: Taking taylor expansion of -2.0 in n 2.740 * [backup-simplify]: Simplify -2.0 into -2.0 2.740 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.740 * [taylor]: Taking taylor expansion of PI in n 2.740 * [backup-simplify]: Simplify PI into PI 2.740 * [taylor]: Taking taylor expansion of n in n 2.740 * [backup-simplify]: Simplify 0 into 0 2.740 * [backup-simplify]: Simplify 1 into 1 2.740 * [backup-simplify]: Simplify (/ PI 1) into PI 2.740 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.741 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.741 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.741 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.742 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.742 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.743 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.743 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.743 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.743 * [taylor]: Taking taylor expansion of 0.25 in k 2.743 * [backup-simplify]: Simplify 0.25 into 0.25 2.743 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.743 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.743 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.743 * [taylor]: Taking taylor expansion of k in k 2.743 * [backup-simplify]: Simplify 0 into 0 2.743 * [backup-simplify]: Simplify 1 into 1 2.744 * [backup-simplify]: Simplify (/ 1 1) into 1 2.744 * [taylor]: Taking taylor expansion of 1.0 in k 2.744 * [backup-simplify]: Simplify 1.0 into 1.0 2.744 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.744 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.744 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.744 * [taylor]: Taking taylor expansion of -2.0 in k 2.744 * [backup-simplify]: Simplify -2.0 into -2.0 2.744 * [taylor]: Taking taylor expansion of PI in k 2.744 * [backup-simplify]: Simplify PI into PI 2.744 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.745 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.745 * [taylor]: Taking taylor expansion of (log n) in k 2.745 * [taylor]: Taking taylor expansion of n in k 2.745 * [backup-simplify]: Simplify n into n 2.745 * [backup-simplify]: Simplify (log n) into (log n) 2.745 * [backup-simplify]: Simplify (+ 1 0) into 1 2.745 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.746 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.746 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.747 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.748 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.748 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.749 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.750 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.750 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.751 * [backup-simplify]: Simplify (+ 0 0) into 0 2.751 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.752 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.752 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.754 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.754 * [taylor]: Taking taylor expansion of 0 in k 2.754 * [backup-simplify]: Simplify 0 into 0 2.754 * [backup-simplify]: Simplify 0 into 0 2.754 * [backup-simplify]: Simplify 0 into 0 2.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.755 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.756 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 2.757 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.757 * [backup-simplify]: Simplify (+ 0 0) into 0 2.757 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.758 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.759 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.760 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.760 * [taylor]: Taking taylor expansion of 0 in k 2.760 * [backup-simplify]: Simplify 0 into 0 2.760 * [backup-simplify]: Simplify 0 into 0 2.760 * [backup-simplify]: Simplify 0 into 0 2.760 * [backup-simplify]: Simplify 0 into 0 2.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.762 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.765 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 2.765 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.765 * [backup-simplify]: Simplify (+ 0 0) into 0 2.766 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.766 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.768 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.769 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.769 * [taylor]: Taking taylor expansion of 0 in k 2.769 * [backup-simplify]: Simplify 0 into 0 2.769 * [backup-simplify]: Simplify 0 into 0 2.770 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.770 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 2.770 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2.770 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.770 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.770 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.770 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.771 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.771 * [taylor]: Taking taylor expansion of 0.25 in k 2.771 * [backup-simplify]: Simplify 0.25 into 0.25 2.771 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.771 * [taylor]: Taking taylor expansion of 1.0 in k 2.771 * [backup-simplify]: Simplify 1.0 into 1.0 2.771 * [taylor]: Taking taylor expansion of k in k 2.771 * [backup-simplify]: Simplify 0 into 0 2.771 * [backup-simplify]: Simplify 1 into 1 2.771 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.771 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.771 * [taylor]: Taking taylor expansion of 2.0 in k 2.771 * [backup-simplify]: Simplify 2.0 into 2.0 2.771 * [taylor]: Taking taylor expansion of (* n PI) in k 2.771 * [taylor]: Taking taylor expansion of n in k 2.771 * [backup-simplify]: Simplify n into n 2.771 * [taylor]: Taking taylor expansion of PI in k 2.771 * [backup-simplify]: Simplify PI into PI 2.771 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.771 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.771 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.771 * [backup-simplify]: Simplify (- 0) into 0 2.771 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.772 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.772 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.772 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.772 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.772 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.772 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.772 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.772 * [taylor]: Taking taylor expansion of 0.25 in n 2.772 * [backup-simplify]: Simplify 0.25 into 0.25 2.772 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.772 * [taylor]: Taking taylor expansion of 1.0 in n 2.772 * [backup-simplify]: Simplify 1.0 into 1.0 2.772 * [taylor]: Taking taylor expansion of k in n 2.772 * [backup-simplify]: Simplify k into k 2.772 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.772 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.772 * [taylor]: Taking taylor expansion of 2.0 in n 2.772 * [backup-simplify]: Simplify 2.0 into 2.0 2.772 * [taylor]: Taking taylor expansion of (* n PI) in n 2.772 * [taylor]: Taking taylor expansion of n in n 2.772 * [backup-simplify]: Simplify 0 into 0 2.772 * [backup-simplify]: Simplify 1 into 1 2.772 * [taylor]: Taking taylor expansion of PI in n 2.772 * [backup-simplify]: Simplify PI into PI 2.772 * [backup-simplify]: Simplify (* 0 PI) into 0 2.773 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.773 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.774 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.775 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.775 * [backup-simplify]: Simplify (- k) into (- k) 2.775 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.775 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.776 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.777 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.777 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.777 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.777 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.777 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.777 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.778 * [taylor]: Taking taylor expansion of 0.25 in n 2.778 * [backup-simplify]: Simplify 0.25 into 0.25 2.778 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.778 * [taylor]: Taking taylor expansion of 1.0 in n 2.778 * [backup-simplify]: Simplify 1.0 into 1.0 2.778 * [taylor]: Taking taylor expansion of k in n 2.778 * [backup-simplify]: Simplify k into k 2.778 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.778 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.778 * [taylor]: Taking taylor expansion of 2.0 in n 2.778 * [backup-simplify]: Simplify 2.0 into 2.0 2.778 * [taylor]: Taking taylor expansion of (* n PI) in n 2.778 * [taylor]: Taking taylor expansion of n in n 2.778 * [backup-simplify]: Simplify 0 into 0 2.778 * [backup-simplify]: Simplify 1 into 1 2.778 * [taylor]: Taking taylor expansion of PI in n 2.778 * [backup-simplify]: Simplify PI into PI 2.778 * [backup-simplify]: Simplify (* 0 PI) into 0 2.778 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.779 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.780 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.781 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.781 * [backup-simplify]: Simplify (- k) into (- k) 2.781 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.781 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.782 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.782 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.783 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.783 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.783 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.783 * [taylor]: Taking taylor expansion of 0.25 in k 2.783 * [backup-simplify]: Simplify 0.25 into 0.25 2.783 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.783 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.783 * [taylor]: Taking taylor expansion of 1.0 in k 2.783 * [backup-simplify]: Simplify 1.0 into 1.0 2.783 * [taylor]: Taking taylor expansion of k in k 2.783 * [backup-simplify]: Simplify 0 into 0 2.783 * [backup-simplify]: Simplify 1 into 1 2.783 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.783 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.783 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.783 * [taylor]: Taking taylor expansion of 2.0 in k 2.783 * [backup-simplify]: Simplify 2.0 into 2.0 2.783 * [taylor]: Taking taylor expansion of PI in k 2.783 * [backup-simplify]: Simplify PI into PI 2.784 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.784 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.784 * [taylor]: Taking taylor expansion of (log n) in k 2.784 * [taylor]: Taking taylor expansion of n in k 2.784 * [backup-simplify]: Simplify n into n 2.784 * [backup-simplify]: Simplify (log n) into (log n) 2.784 * [backup-simplify]: Simplify (- 0) into 0 2.785 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.785 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.786 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.787 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.787 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.788 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.788 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.789 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.790 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.790 * [backup-simplify]: Simplify (- 0) into 0 2.790 * [backup-simplify]: Simplify (+ 0 0) into 0 2.791 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.791 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.792 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.793 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.793 * [taylor]: Taking taylor expansion of 0 in k 2.793 * [backup-simplify]: Simplify 0 into 0 2.793 * [backup-simplify]: Simplify 0 into 0 2.794 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.801 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.801 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.802 * [backup-simplify]: Simplify (+ 0 0) into 0 2.802 * [backup-simplify]: Simplify (- 1) into -1 2.802 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.803 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.804 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2.806 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.808 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.808 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.809 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.811 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.811 * [backup-simplify]: Simplify (- 0) into 0 2.811 * [backup-simplify]: Simplify (+ 0 0) into 0 2.812 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.812 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.813 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.815 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.815 * [taylor]: Taking taylor expansion of 0 in k 2.815 * [backup-simplify]: Simplify 0 into 0 2.815 * [backup-simplify]: Simplify 0 into 0 2.815 * [backup-simplify]: Simplify 0 into 0 2.815 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.817 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.818 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.818 * [backup-simplify]: Simplify (+ 0 0) into 0 2.819 * [backup-simplify]: Simplify (- 0) into 0 2.819 * [backup-simplify]: Simplify (+ 0 0) into 0 2.820 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.821 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.824 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.827 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.833 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.833 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2.833 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.833 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.833 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.833 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.833 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.833 * [taylor]: Taking taylor expansion of 0.25 in k 2.834 * [backup-simplify]: Simplify 0.25 into 0.25 2.834 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.834 * [taylor]: Taking taylor expansion of 1.0 in k 2.834 * [backup-simplify]: Simplify 1.0 into 1.0 2.834 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.834 * [taylor]: Taking taylor expansion of k in k 2.834 * [backup-simplify]: Simplify 0 into 0 2.834 * [backup-simplify]: Simplify 1 into 1 2.834 * [backup-simplify]: Simplify (/ 1 1) into 1 2.834 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.834 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.834 * [taylor]: Taking taylor expansion of 2.0 in k 2.834 * [backup-simplify]: Simplify 2.0 into 2.0 2.834 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.834 * [taylor]: Taking taylor expansion of PI in k 2.834 * [backup-simplify]: Simplify PI into PI 2.834 * [taylor]: Taking taylor expansion of n in k 2.834 * [backup-simplify]: Simplify n into n 2.834 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.834 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.834 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.834 * [backup-simplify]: Simplify (- 1) into -1 2.835 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.835 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.835 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.835 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.835 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.835 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.835 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.835 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.835 * [taylor]: Taking taylor expansion of 0.25 in n 2.835 * [backup-simplify]: Simplify 0.25 into 0.25 2.835 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.835 * [taylor]: Taking taylor expansion of 1.0 in n 2.835 * [backup-simplify]: Simplify 1.0 into 1.0 2.835 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.835 * [taylor]: Taking taylor expansion of k in n 2.835 * [backup-simplify]: Simplify k into k 2.835 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.835 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.835 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.835 * [taylor]: Taking taylor expansion of 2.0 in n 2.835 * [backup-simplify]: Simplify 2.0 into 2.0 2.835 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.835 * [taylor]: Taking taylor expansion of PI in n 2.835 * [backup-simplify]: Simplify PI into PI 2.835 * [taylor]: Taking taylor expansion of n in n 2.835 * [backup-simplify]: Simplify 0 into 0 2.835 * [backup-simplify]: Simplify 1 into 1 2.836 * [backup-simplify]: Simplify (/ PI 1) into PI 2.836 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.837 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.837 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.837 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.837 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.838 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.838 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.839 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.839 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.839 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.839 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.839 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.839 * [taylor]: Taking taylor expansion of 0.25 in n 2.839 * [backup-simplify]: Simplify 0.25 into 0.25 2.839 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.839 * [taylor]: Taking taylor expansion of 1.0 in n 2.839 * [backup-simplify]: Simplify 1.0 into 1.0 2.839 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.839 * [taylor]: Taking taylor expansion of k in n 2.839 * [backup-simplify]: Simplify k into k 2.839 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.839 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.839 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.839 * [taylor]: Taking taylor expansion of 2.0 in n 2.839 * [backup-simplify]: Simplify 2.0 into 2.0 2.839 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.839 * [taylor]: Taking taylor expansion of PI in n 2.839 * [backup-simplify]: Simplify PI into PI 2.839 * [taylor]: Taking taylor expansion of n in n 2.839 * [backup-simplify]: Simplify 0 into 0 2.840 * [backup-simplify]: Simplify 1 into 1 2.840 * [backup-simplify]: Simplify (/ PI 1) into PI 2.840 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.841 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.841 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.841 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.841 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.842 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.843 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.844 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.844 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.844 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.844 * [taylor]: Taking taylor expansion of 0.25 in k 2.844 * [backup-simplify]: Simplify 0.25 into 0.25 2.844 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.844 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.844 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.844 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.844 * [taylor]: Taking taylor expansion of 2.0 in k 2.844 * [backup-simplify]: Simplify 2.0 into 2.0 2.844 * [taylor]: Taking taylor expansion of PI in k 2.844 * [backup-simplify]: Simplify PI into PI 2.844 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.845 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.845 * [taylor]: Taking taylor expansion of (log n) in k 2.845 * [taylor]: Taking taylor expansion of n in k 2.845 * [backup-simplify]: Simplify n into n 2.845 * [backup-simplify]: Simplify (log n) into (log n) 2.845 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.845 * [taylor]: Taking taylor expansion of 1.0 in k 2.845 * [backup-simplify]: Simplify 1.0 into 1.0 2.845 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.845 * [taylor]: Taking taylor expansion of k in k 2.845 * [backup-simplify]: Simplify 0 into 0 2.845 * [backup-simplify]: Simplify 1 into 1 2.845 * [backup-simplify]: Simplify (/ 1 1) into 1 2.845 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.846 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.846 * [backup-simplify]: Simplify (- 1) into -1 2.847 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.847 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.848 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.849 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.849 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.850 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.850 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.851 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.851 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.851 * [backup-simplify]: Simplify (- 0) into 0 2.852 * [backup-simplify]: Simplify (+ 0 0) into 0 2.852 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.853 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.853 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.855 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.855 * [taylor]: Taking taylor expansion of 0 in k 2.855 * [backup-simplify]: Simplify 0 into 0 2.855 * [backup-simplify]: Simplify 0 into 0 2.855 * [backup-simplify]: Simplify 0 into 0 2.855 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.856 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.857 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.857 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.858 * [backup-simplify]: Simplify (- 0) into 0 2.858 * [backup-simplify]: Simplify (+ 0 0) into 0 2.858 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.859 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.860 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.861 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.862 * [taylor]: Taking taylor expansion of 0 in k 2.862 * [backup-simplify]: Simplify 0 into 0 2.862 * [backup-simplify]: Simplify 0 into 0 2.862 * [backup-simplify]: Simplify 0 into 0 2.862 * [backup-simplify]: Simplify 0 into 0 2.862 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.863 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.866 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 2.866 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.866 * [backup-simplify]: Simplify (- 0) into 0 2.866 * [backup-simplify]: Simplify (+ 0 0) into 0 2.867 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.868 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.869 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.870 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.870 * [taylor]: Taking taylor expansion of 0 in k 2.870 * [backup-simplify]: Simplify 0 into 0 2.870 * [backup-simplify]: Simplify 0 into 0 2.871 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.872 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2.872 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.872 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.872 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.872 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.872 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.872 * [taylor]: Taking taylor expansion of 0.25 in k 2.872 * [backup-simplify]: Simplify 0.25 into 0.25 2.872 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.872 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.872 * [taylor]: Taking taylor expansion of k in k 2.872 * [backup-simplify]: Simplify 0 into 0 2.872 * [backup-simplify]: Simplify 1 into 1 2.872 * [backup-simplify]: Simplify (/ 1 1) into 1 2.872 * [taylor]: Taking taylor expansion of 1.0 in k 2.872 * [backup-simplify]: Simplify 1.0 into 1.0 2.872 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.872 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.872 * [taylor]: Taking taylor expansion of -2.0 in k 2.872 * [backup-simplify]: Simplify -2.0 into -2.0 2.872 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.872 * [taylor]: Taking taylor expansion of PI in k 2.872 * [backup-simplify]: Simplify PI into PI 2.872 * [taylor]: Taking taylor expansion of n in k 2.872 * [backup-simplify]: Simplify n into n 2.872 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.872 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.872 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.873 * [backup-simplify]: Simplify (+ 1 0) into 1 2.873 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.873 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.873 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.873 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.873 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.873 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.873 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.873 * [taylor]: Taking taylor expansion of 0.25 in n 2.873 * [backup-simplify]: Simplify 0.25 into 0.25 2.873 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.873 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.873 * [taylor]: Taking taylor expansion of k in n 2.873 * [backup-simplify]: Simplify k into k 2.873 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.873 * [taylor]: Taking taylor expansion of 1.0 in n 2.873 * [backup-simplify]: Simplify 1.0 into 1.0 2.873 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.873 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.873 * [taylor]: Taking taylor expansion of -2.0 in n 2.873 * [backup-simplify]: Simplify -2.0 into -2.0 2.873 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.873 * [taylor]: Taking taylor expansion of PI in n 2.873 * [backup-simplify]: Simplify PI into PI 2.873 * [taylor]: Taking taylor expansion of n in n 2.873 * [backup-simplify]: Simplify 0 into 0 2.873 * [backup-simplify]: Simplify 1 into 1 2.874 * [backup-simplify]: Simplify (/ PI 1) into PI 2.874 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.875 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.875 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.875 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.876 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.876 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.877 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.877 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.877 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.877 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.877 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.877 * [taylor]: Taking taylor expansion of 0.25 in n 2.877 * [backup-simplify]: Simplify 0.25 into 0.25 2.877 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.877 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.877 * [taylor]: Taking taylor expansion of k in n 2.877 * [backup-simplify]: Simplify k into k 2.877 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.877 * [taylor]: Taking taylor expansion of 1.0 in n 2.877 * [backup-simplify]: Simplify 1.0 into 1.0 2.877 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.877 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.877 * [taylor]: Taking taylor expansion of -2.0 in n 2.877 * [backup-simplify]: Simplify -2.0 into -2.0 2.877 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.877 * [taylor]: Taking taylor expansion of PI in n 2.877 * [backup-simplify]: Simplify PI into PI 2.877 * [taylor]: Taking taylor expansion of n in n 2.877 * [backup-simplify]: Simplify 0 into 0 2.877 * [backup-simplify]: Simplify 1 into 1 2.878 * [backup-simplify]: Simplify (/ PI 1) into PI 2.878 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.879 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.879 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.879 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.880 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.880 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.881 * [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))))) 2.881 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.881 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.881 * [taylor]: Taking taylor expansion of 0.25 in k 2.881 * [backup-simplify]: Simplify 0.25 into 0.25 2.881 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.881 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.881 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.881 * [taylor]: Taking taylor expansion of k in k 2.881 * [backup-simplify]: Simplify 0 into 0 2.881 * [backup-simplify]: Simplify 1 into 1 2.881 * [backup-simplify]: Simplify (/ 1 1) into 1 2.882 * [taylor]: Taking taylor expansion of 1.0 in k 2.882 * [backup-simplify]: Simplify 1.0 into 1.0 2.882 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.882 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.882 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.882 * [taylor]: Taking taylor expansion of -2.0 in k 2.882 * [backup-simplify]: Simplify -2.0 into -2.0 2.882 * [taylor]: Taking taylor expansion of PI in k 2.882 * [backup-simplify]: Simplify PI into PI 2.882 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.882 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.883 * [taylor]: Taking taylor expansion of (log n) in k 2.883 * [taylor]: Taking taylor expansion of n in k 2.883 * [backup-simplify]: Simplify n into n 2.883 * [backup-simplify]: Simplify (log n) into (log n) 2.883 * [backup-simplify]: Simplify (+ 1 0) into 1 2.883 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.884 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.884 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.885 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.885 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.886 * [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))))) 2.887 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.887 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.888 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.888 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.888 * [backup-simplify]: Simplify (+ 0 0) into 0 2.889 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.895 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.896 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.897 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.897 * [taylor]: Taking taylor expansion of 0 in k 2.897 * [backup-simplify]: Simplify 0 into 0 2.897 * [backup-simplify]: Simplify 0 into 0 2.897 * [backup-simplify]: Simplify 0 into 0 2.898 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.898 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.900 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 2.900 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.900 * [backup-simplify]: Simplify (+ 0 0) into 0 2.901 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.901 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.902 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.904 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.904 * [taylor]: Taking taylor expansion of 0 in k 2.904 * [backup-simplify]: Simplify 0 into 0 2.904 * [backup-simplify]: Simplify 0 into 0 2.904 * [backup-simplify]: Simplify 0 into 0 2.904 * [backup-simplify]: Simplify 0 into 0 2.904 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.905 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.908 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 2.908 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.908 * [backup-simplify]: Simplify (+ 0 0) into 0 2.909 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.910 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.911 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.912 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.912 * [taylor]: Taking taylor expansion of 0 in k 2.912 * [backup-simplify]: Simplify 0 into 0 2.912 * [backup-simplify]: Simplify 0 into 0 2.913 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.913 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 2.913 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 2.913 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.913 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.913 * [taylor]: Taking taylor expansion of 1.0 in k 2.913 * [backup-simplify]: Simplify 1.0 into 1.0 2.913 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.913 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.913 * [taylor]: Taking taylor expansion of k in k 2.913 * [backup-simplify]: Simplify 0 into 0 2.913 * [backup-simplify]: Simplify 1 into 1 2.914 * [backup-simplify]: Simplify (/ 1 1) into 1 2.914 * [backup-simplify]: Simplify (sqrt 0) into 0 2.915 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.915 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.915 * [taylor]: Taking taylor expansion of 1.0 in k 2.915 * [backup-simplify]: Simplify 1.0 into 1.0 2.915 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.915 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.915 * [taylor]: Taking taylor expansion of k in k 2.915 * [backup-simplify]: Simplify 0 into 0 2.915 * [backup-simplify]: Simplify 1 into 1 2.915 * [backup-simplify]: Simplify (/ 1 1) into 1 2.915 * [backup-simplify]: Simplify (sqrt 0) into 0 2.916 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.916 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.916 * [backup-simplify]: Simplify 0 into 0 2.917 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.917 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.918 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.919 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.920 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.921 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.921 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.923 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.924 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.925 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.925 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 2.925 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 2.925 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.925 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.925 * [taylor]: Taking taylor expansion of 1.0 in k 2.926 * [backup-simplify]: Simplify 1.0 into 1.0 2.926 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.926 * [taylor]: Taking taylor expansion of k in k 2.926 * [backup-simplify]: Simplify 0 into 0 2.926 * [backup-simplify]: Simplify 1 into 1 2.926 * [backup-simplify]: Simplify (sqrt 0) into 0 2.927 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.927 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.927 * [taylor]: Taking taylor expansion of 1.0 in k 2.927 * [backup-simplify]: Simplify 1.0 into 1.0 2.927 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.927 * [taylor]: Taking taylor expansion of k in k 2.927 * [backup-simplify]: Simplify 0 into 0 2.927 * [backup-simplify]: Simplify 1 into 1 2.927 * [backup-simplify]: Simplify (sqrt 0) into 0 2.928 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.928 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.928 * [backup-simplify]: Simplify 0 into 0 2.929 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.929 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.931 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.932 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.932 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.934 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.936 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.936 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.937 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 2.937 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 2.937 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.937 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.937 * [taylor]: Taking taylor expansion of 1.0 in k 2.937 * [backup-simplify]: Simplify 1.0 into 1.0 2.937 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.937 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.937 * [taylor]: Taking taylor expansion of -1 in k 2.937 * [backup-simplify]: Simplify -1 into -1 2.937 * [taylor]: Taking taylor expansion of k in k 2.937 * [backup-simplify]: Simplify 0 into 0 2.937 * [backup-simplify]: Simplify 1 into 1 2.937 * [backup-simplify]: Simplify (/ -1 1) into -1 2.938 * [backup-simplify]: Simplify (sqrt 0) into 0 2.938 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.939 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.939 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.939 * [taylor]: Taking taylor expansion of 1.0 in k 2.939 * [backup-simplify]: Simplify 1.0 into 1.0 2.939 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.939 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.939 * [taylor]: Taking taylor expansion of -1 in k 2.939 * [backup-simplify]: Simplify -1 into -1 2.939 * [taylor]: Taking taylor expansion of k in k 2.939 * [backup-simplify]: Simplify 0 into 0 2.939 * [backup-simplify]: Simplify 1 into 1 2.939 * [backup-simplify]: Simplify (/ -1 1) into -1 2.939 * [backup-simplify]: Simplify (sqrt 0) into 0 2.940 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.940 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.940 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.941 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.942 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.944 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 2.944 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.944 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.946 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.949 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 2.949 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.950 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 2.950 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 2.950 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.950 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.950 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.950 * [taylor]: Taking taylor expansion of 2.0 in n 2.950 * [backup-simplify]: Simplify 2.0 into 2.0 2.950 * [taylor]: Taking taylor expansion of (* n PI) in n 2.950 * [taylor]: Taking taylor expansion of n in n 2.950 * [backup-simplify]: Simplify 0 into 0 2.950 * [backup-simplify]: Simplify 1 into 1 2.950 * [taylor]: Taking taylor expansion of PI in n 2.950 * [backup-simplify]: Simplify PI into PI 2.950 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.950 * [taylor]: Taking taylor expansion of 2.0 in n 2.950 * [backup-simplify]: Simplify 2.0 into 2.0 2.950 * [taylor]: Taking taylor expansion of (* n PI) in n 2.950 * [taylor]: Taking taylor expansion of n in n 2.950 * [backup-simplify]: Simplify 0 into 0 2.950 * [backup-simplify]: Simplify 1 into 1 2.950 * [taylor]: Taking taylor expansion of PI in n 2.950 * [backup-simplify]: Simplify PI into PI 2.950 * [backup-simplify]: Simplify (* 0 PI) into 0 2.951 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.951 * [backup-simplify]: Simplify 0 into 0 2.952 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.952 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.953 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.953 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.954 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.954 * [backup-simplify]: Simplify 0 into 0 2.954 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.955 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.955 * [backup-simplify]: Simplify 0 into 0 2.956 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.957 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.957 * [backup-simplify]: Simplify 0 into 0 2.958 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.958 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.958 * [backup-simplify]: Simplify 0 into 0 2.959 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.960 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.960 * [backup-simplify]: Simplify 0 into 0 2.961 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.962 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.962 * [backup-simplify]: Simplify 0 into 0 2.962 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.963 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.963 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.963 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.963 * [taylor]: Taking taylor expansion of 2.0 in n 2.963 * [backup-simplify]: Simplify 2.0 into 2.0 2.963 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.963 * [taylor]: Taking taylor expansion of PI in n 2.963 * [backup-simplify]: Simplify PI into PI 2.963 * [taylor]: Taking taylor expansion of n in n 2.963 * [backup-simplify]: Simplify 0 into 0 2.963 * [backup-simplify]: Simplify 1 into 1 2.963 * [backup-simplify]: Simplify (/ PI 1) into PI 2.963 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.963 * [taylor]: Taking taylor expansion of 2.0 in n 2.963 * [backup-simplify]: Simplify 2.0 into 2.0 2.963 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.963 * [taylor]: Taking taylor expansion of PI in n 2.963 * [backup-simplify]: Simplify PI into PI 2.963 * [taylor]: Taking taylor expansion of n in n 2.963 * [backup-simplify]: Simplify 0 into 0 2.963 * [backup-simplify]: Simplify 1 into 1 2.964 * [backup-simplify]: Simplify (/ PI 1) into PI 2.964 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.964 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.965 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.965 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.965 * [backup-simplify]: Simplify 0 into 0 2.966 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.966 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.966 * [backup-simplify]: Simplify 0 into 0 2.967 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.967 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.967 * [backup-simplify]: Simplify 0 into 0 2.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.969 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.969 * [backup-simplify]: Simplify 0 into 0 2.969 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.970 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.970 * [backup-simplify]: Simplify 0 into 0 2.971 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.971 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.971 * [backup-simplify]: Simplify 0 into 0 2.972 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.972 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.972 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.972 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.972 * [taylor]: Taking taylor expansion of -2.0 in n 2.972 * [backup-simplify]: Simplify -2.0 into -2.0 2.972 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.972 * [taylor]: Taking taylor expansion of PI in n 2.972 * [backup-simplify]: Simplify PI into PI 2.972 * [taylor]: Taking taylor expansion of n in n 2.972 * [backup-simplify]: Simplify 0 into 0 2.972 * [backup-simplify]: Simplify 1 into 1 2.973 * [backup-simplify]: Simplify (/ PI 1) into PI 2.973 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.973 * [taylor]: Taking taylor expansion of -2.0 in n 2.973 * [backup-simplify]: Simplify -2.0 into -2.0 2.973 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.973 * [taylor]: Taking taylor expansion of PI in n 2.973 * [backup-simplify]: Simplify PI into PI 2.973 * [taylor]: Taking taylor expansion of n in n 2.973 * [backup-simplify]: Simplify 0 into 0 2.973 * [backup-simplify]: Simplify 1 into 1 2.973 * [backup-simplify]: Simplify (/ PI 1) into PI 2.973 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.974 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.974 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.975 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.975 * [backup-simplify]: Simplify 0 into 0 2.975 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.976 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.976 * [backup-simplify]: Simplify 0 into 0 2.976 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.977 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.977 * [backup-simplify]: Simplify 0 into 0 2.977 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.978 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.978 * [backup-simplify]: Simplify 0 into 0 2.985 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.985 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.986 * [backup-simplify]: Simplify 0 into 0 2.986 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.987 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.987 * [backup-simplify]: Simplify 0 into 0 2.987 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.987 * * * [progress]: simplifying candidates 2.991 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (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 (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 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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 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 2.992 * [simplify]: Sending expressions to egg_math: (expm1 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(pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* 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(cbrt 2)))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) 1)) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ 1 (sqrt 2))) (pow (* (* h0 h4) h3) (/ 1 1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (- h2 h1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (- h2 h1) 1)) (pow (* (* h0 h4) h3) 1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* h0 h4) (/ (/ (- h2 h1) h0) 2)) (pow h3 (/ (/ (- h2 h1) h0) 2)) (log (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (exp (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (expm1 (/ h2 (sqrt h1))) (log1p (/ h2 (sqrt h1))) (- (log h2) (log (sqrt h1))) (log (/ h2 (sqrt h1))) (exp (/ h2 (sqrt h1))) (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (cbrt (/ h2 (sqrt h1))) (cbrt (/ h2 (sqrt h1)))) (cbrt (/ h2 (sqrt h1))) (* (* (/ h2 (sqrt h1)) (/ h2 (sqrt h1))) (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (- h2) (- (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (cbrt h2) (cbrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (cbrt h2) (sqrt (cbrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt 1)) (/ (cbrt h2) (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) 1) (/ (cbrt h2) (sqrt h1)) (/ (sqrt h2) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (sqrt h2) (cbrt (sqrt h1))) (/ (sqrt h2) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (sqrt h2) (sqrt (cbrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt 1)) (/ (sqrt h2) (sqrt h1)) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) 1) (/ (sqrt h2) (sqrt h1)) (/ 1 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (cbrt (sqrt h1))) (/ 1 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (cbrt h1))) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 (sqrt 1)) (/ h2 (sqrt h1)) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 1) (/ h2 (sqrt h1)) (/ 1 (sqrt h1)) (/ (sqrt h1) h2) (/ h2 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (sqrt h1))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h1))) (/ h2 1) (/ (sqrt h1) (cbrt h2)) (/ (sqrt h1) (sqrt h2)) (/ (sqrt h1) h2) (expm1 (* (* h0 h4) h3)) (log1p (* (* h0 h4) h3)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h9 h1) (- (+ (* h9 (pow h1 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- (* h9 (/ 1 (pow h1 3)))))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- h9))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) 3.000 * * [simplify]: iteration 0 : 874 enodes (cost 1888 ) 3.014 * * [simplify]: iteration 1 : 3432 enodes (cost 1810 ) 3.062 * * [simplify]: iteration 2 : 5001 enodes (cost 1792 ) 3.071 * * * [progress]: adding candidates to table 3.793 * * [progress]: iteration 4 / 4 3.793 * * * [progress]: picking best candidate 3.818 * * * * [pick]: Picked # 3.818 * * * [progress]: localizing error 3.839 * * * [progress]: generating rewritten candidates 3.839 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.863 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 2) 3.903 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2 1) 3.943 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 3.991 * * * [progress]: generating series expansions 3.991 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.992 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 3.992 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 3.992 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 3.992 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.992 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.992 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 3.992 * [taylor]: Taking taylor expansion of 0.25 in k 3.992 * [backup-simplify]: Simplify 0.25 into 0.25 3.992 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.992 * [taylor]: Taking taylor expansion of 1.0 in k 3.992 * [backup-simplify]: Simplify 1.0 into 1.0 3.992 * [taylor]: Taking taylor expansion of k in k 3.992 * [backup-simplify]: Simplify 0 into 0 3.992 * [backup-simplify]: Simplify 1 into 1 3.992 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.992 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.992 * [taylor]: Taking taylor expansion of 2.0 in k 3.992 * [backup-simplify]: Simplify 2.0 into 2.0 3.992 * [taylor]: Taking taylor expansion of (* n PI) in k 3.992 * [taylor]: Taking taylor expansion of n in k 3.992 * [backup-simplify]: Simplify n into n 3.992 * [taylor]: Taking taylor expansion of PI in k 3.992 * [backup-simplify]: Simplify PI into PI 3.992 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.992 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.992 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.993 * [backup-simplify]: Simplify (- 0) into 0 3.993 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.993 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 3.993 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 3.993 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 3.993 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 3.993 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.993 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.993 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 3.993 * [taylor]: Taking taylor expansion of 0.25 in n 3.993 * [backup-simplify]: Simplify 0.25 into 0.25 3.993 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.994 * [taylor]: Taking taylor expansion of 1.0 in n 3.994 * [backup-simplify]: Simplify 1.0 into 1.0 3.994 * [taylor]: Taking taylor expansion of k in n 3.994 * [backup-simplify]: Simplify k into k 3.994 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.994 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.994 * [taylor]: Taking taylor expansion of 2.0 in n 3.994 * [backup-simplify]: Simplify 2.0 into 2.0 3.994 * [taylor]: Taking taylor expansion of (* n PI) in n 3.994 * [taylor]: Taking taylor expansion of n in n 3.994 * [backup-simplify]: Simplify 0 into 0 3.994 * [backup-simplify]: Simplify 1 into 1 3.994 * [taylor]: Taking taylor expansion of PI in n 3.994 * [backup-simplify]: Simplify PI into PI 3.994 * [backup-simplify]: Simplify (* 0 PI) into 0 3.994 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.995 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.005 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.006 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.006 * [backup-simplify]: Simplify (- k) into (- k) 4.006 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.006 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.007 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.008 * [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)))) 4.008 * [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))))) 4.008 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.008 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.008 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.008 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.008 * [taylor]: Taking taylor expansion of 0.25 in n 4.008 * [backup-simplify]: Simplify 0.25 into 0.25 4.008 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.009 * [taylor]: Taking taylor expansion of 1.0 in n 4.009 * [backup-simplify]: Simplify 1.0 into 1.0 4.009 * [taylor]: Taking taylor expansion of k in n 4.009 * [backup-simplify]: Simplify k into k 4.009 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.009 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.009 * [taylor]: Taking taylor expansion of 2.0 in n 4.009 * [backup-simplify]: Simplify 2.0 into 2.0 4.009 * [taylor]: Taking taylor expansion of (* n PI) in n 4.009 * [taylor]: Taking taylor expansion of n in n 4.009 * [backup-simplify]: Simplify 0 into 0 4.009 * [backup-simplify]: Simplify 1 into 1 4.009 * [taylor]: Taking taylor expansion of PI in n 4.009 * [backup-simplify]: Simplify PI into PI 4.009 * [backup-simplify]: Simplify (* 0 PI) into 0 4.009 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.010 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.011 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.012 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.012 * [backup-simplify]: Simplify (- k) into (- k) 4.012 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.012 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.012 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.013 * [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)))) 4.014 * [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))))) 4.014 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.014 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.014 * [taylor]: Taking taylor expansion of 0.25 in k 4.014 * [backup-simplify]: Simplify 0.25 into 0.25 4.014 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.014 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.014 * [taylor]: Taking taylor expansion of 1.0 in k 4.014 * [backup-simplify]: Simplify 1.0 into 1.0 4.014 * [taylor]: Taking taylor expansion of k in k 4.014 * [backup-simplify]: Simplify 0 into 0 4.014 * [backup-simplify]: Simplify 1 into 1 4.014 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.014 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.014 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.014 * [taylor]: Taking taylor expansion of 2.0 in k 4.014 * [backup-simplify]: Simplify 2.0 into 2.0 4.014 * [taylor]: Taking taylor expansion of PI in k 4.014 * [backup-simplify]: Simplify PI into PI 4.014 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.015 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.015 * [taylor]: Taking taylor expansion of (log n) in k 4.015 * [taylor]: Taking taylor expansion of n in k 4.015 * [backup-simplify]: Simplify n into n 4.015 * [backup-simplify]: Simplify (log n) into (log n) 4.015 * [backup-simplify]: Simplify (- 0) into 0 4.016 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.016 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.017 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.018 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 4.018 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.019 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.019 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.020 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.021 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.021 * [backup-simplify]: Simplify (- 0) into 0 4.021 * [backup-simplify]: Simplify (+ 0 0) into 0 4.022 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 4.022 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.023 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.024 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.024 * [taylor]: Taking taylor expansion of 0 in k 4.024 * [backup-simplify]: Simplify 0 into 0 4.024 * [backup-simplify]: Simplify 0 into 0 4.025 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.026 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.026 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.027 * [backup-simplify]: Simplify (+ 0 0) into 0 4.027 * [backup-simplify]: Simplify (- 1) into -1 4.027 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.028 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.029 * [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)))) 4.031 * [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)))))) 4.033 * [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)))))) 4.034 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.034 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.036 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.036 * [backup-simplify]: Simplify (- 0) into 0 4.036 * [backup-simplify]: Simplify (+ 0 0) into 0 4.037 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.038 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.038 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.040 * [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 4.040 * [taylor]: Taking taylor expansion of 0 in k 4.040 * [backup-simplify]: Simplify 0 into 0 4.040 * [backup-simplify]: Simplify 0 into 0 4.040 * [backup-simplify]: Simplify 0 into 0 4.041 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.042 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.043 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.043 * [backup-simplify]: Simplify (+ 0 0) into 0 4.044 * [backup-simplify]: Simplify (- 0) into 0 4.044 * [backup-simplify]: Simplify (+ 0 0) into 0 4.045 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.046 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.049 * [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))))) 4.052 * [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))))) 4.057 * [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)))))) 4.058 * [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)))) 4.058 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 4.058 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 4.058 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.058 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.058 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 4.058 * [taylor]: Taking taylor expansion of 0.25 in k 4.058 * [backup-simplify]: Simplify 0.25 into 0.25 4.058 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.058 * [taylor]: Taking taylor expansion of 1.0 in k 4.058 * [backup-simplify]: Simplify 1.0 into 1.0 4.058 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.058 * [taylor]: Taking taylor expansion of k in k 4.058 * [backup-simplify]: Simplify 0 into 0 4.058 * [backup-simplify]: Simplify 1 into 1 4.058 * [backup-simplify]: Simplify (/ 1 1) into 1 4.058 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.058 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.058 * [taylor]: Taking taylor expansion of 2.0 in k 4.058 * [backup-simplify]: Simplify 2.0 into 2.0 4.058 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.058 * [taylor]: Taking taylor expansion of PI in k 4.058 * [backup-simplify]: Simplify PI into PI 4.058 * [taylor]: Taking taylor expansion of n in k 4.058 * [backup-simplify]: Simplify n into n 4.059 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.059 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.059 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.059 * [backup-simplify]: Simplify (- 1) into -1 4.059 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.059 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 4.059 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 4.060 * [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))))) 4.060 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.060 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.060 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.060 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.060 * [taylor]: Taking taylor expansion of 0.25 in n 4.060 * [backup-simplify]: Simplify 0.25 into 0.25 4.060 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.060 * [taylor]: Taking taylor expansion of 1.0 in n 4.060 * [backup-simplify]: Simplify 1.0 into 1.0 4.060 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.060 * [taylor]: Taking taylor expansion of k in n 4.060 * [backup-simplify]: Simplify k into k 4.060 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.060 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.060 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.060 * [taylor]: Taking taylor expansion of 2.0 in n 4.060 * [backup-simplify]: Simplify 2.0 into 2.0 4.060 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.060 * [taylor]: Taking taylor expansion of PI in n 4.060 * [backup-simplify]: Simplify PI into PI 4.060 * [taylor]: Taking taylor expansion of n in n 4.060 * [backup-simplify]: Simplify 0 into 0 4.060 * [backup-simplify]: Simplify 1 into 1 4.060 * [backup-simplify]: Simplify (/ PI 1) into PI 4.061 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.061 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.061 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.061 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.061 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.062 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.063 * [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)))) 4.064 * [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))))) 4.064 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.064 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.064 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.064 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.064 * [taylor]: Taking taylor expansion of 0.25 in n 4.064 * [backup-simplify]: Simplify 0.25 into 0.25 4.064 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.064 * [taylor]: Taking taylor expansion of 1.0 in n 4.064 * [backup-simplify]: Simplify 1.0 into 1.0 4.064 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.064 * [taylor]: Taking taylor expansion of k in n 4.064 * [backup-simplify]: Simplify k into k 4.064 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.064 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.064 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.064 * [taylor]: Taking taylor expansion of 2.0 in n 4.064 * [backup-simplify]: Simplify 2.0 into 2.0 4.064 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.064 * [taylor]: Taking taylor expansion of PI in n 4.064 * [backup-simplify]: Simplify PI into PI 4.064 * [taylor]: Taking taylor expansion of n in n 4.064 * [backup-simplify]: Simplify 0 into 0 4.064 * [backup-simplify]: Simplify 1 into 1 4.064 * [backup-simplify]: Simplify (/ PI 1) into PI 4.064 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.065 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.065 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.065 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.065 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.066 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.067 * [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)))) 4.067 * [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))))) 4.068 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.068 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.068 * [taylor]: Taking taylor expansion of 0.25 in k 4.068 * [backup-simplify]: Simplify 0.25 into 0.25 4.068 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.068 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.068 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.068 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.068 * [taylor]: Taking taylor expansion of 2.0 in k 4.068 * [backup-simplify]: Simplify 2.0 into 2.0 4.068 * [taylor]: Taking taylor expansion of PI in k 4.068 * [backup-simplify]: Simplify PI into PI 4.068 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.069 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.069 * [taylor]: Taking taylor expansion of (log n) in k 4.069 * [taylor]: Taking taylor expansion of n in k 4.069 * [backup-simplify]: Simplify n into n 4.069 * [backup-simplify]: Simplify (log n) into (log n) 4.069 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.069 * [taylor]: Taking taylor expansion of 1.0 in k 4.069 * [backup-simplify]: Simplify 1.0 into 1.0 4.069 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.069 * [taylor]: Taking taylor expansion of k in k 4.069 * [backup-simplify]: Simplify 0 into 0 4.069 * [backup-simplify]: Simplify 1 into 1 4.069 * [backup-simplify]: Simplify (/ 1 1) into 1 4.069 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.070 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.070 * [backup-simplify]: Simplify (- 1) into -1 4.070 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.071 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.071 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 4.072 * [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))))) 4.073 * [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))))) 4.073 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.074 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.075 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.075 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.075 * [backup-simplify]: Simplify (- 0) into 0 4.075 * [backup-simplify]: Simplify (+ 0 0) into 0 4.076 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.076 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.077 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.078 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.078 * [taylor]: Taking taylor expansion of 0 in k 4.078 * [backup-simplify]: Simplify 0 into 0 4.078 * [backup-simplify]: Simplify 0 into 0 4.078 * [backup-simplify]: Simplify 0 into 0 4.079 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.080 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.081 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.081 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.082 * [backup-simplify]: Simplify (- 0) into 0 4.082 * [backup-simplify]: Simplify (+ 0 0) into 0 4.082 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.083 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.084 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.085 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.085 * [taylor]: Taking taylor expansion of 0 in k 4.085 * [backup-simplify]: Simplify 0 into 0 4.085 * [backup-simplify]: Simplify 0 into 0 4.085 * [backup-simplify]: Simplify 0 into 0 4.086 * [backup-simplify]: Simplify 0 into 0 4.086 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.087 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.090 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 4.090 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.090 * [backup-simplify]: Simplify (- 0) into 0 4.090 * [backup-simplify]: Simplify (+ 0 0) into 0 4.091 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.092 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.099 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.101 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.101 * [taylor]: Taking taylor expansion of 0 in k 4.101 * [backup-simplify]: Simplify 0 into 0 4.101 * [backup-simplify]: Simplify 0 into 0 4.102 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.102 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 4.102 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 4.102 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 4.102 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.102 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.102 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 4.102 * [taylor]: Taking taylor expansion of 0.25 in k 4.102 * [backup-simplify]: Simplify 0.25 into 0.25 4.102 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.102 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.102 * [taylor]: Taking taylor expansion of k in k 4.102 * [backup-simplify]: Simplify 0 into 0 4.102 * [backup-simplify]: Simplify 1 into 1 4.103 * [backup-simplify]: Simplify (/ 1 1) into 1 4.103 * [taylor]: Taking taylor expansion of 1.0 in k 4.103 * [backup-simplify]: Simplify 1.0 into 1.0 4.103 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.103 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.103 * [taylor]: Taking taylor expansion of -2.0 in k 4.103 * [backup-simplify]: Simplify -2.0 into -2.0 4.103 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.103 * [taylor]: Taking taylor expansion of PI in k 4.103 * [backup-simplify]: Simplify PI into PI 4.103 * [taylor]: Taking taylor expansion of n in k 4.103 * [backup-simplify]: Simplify n into n 4.103 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.103 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.103 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.103 * [backup-simplify]: Simplify (+ 1 0) into 1 4.104 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 4.104 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 4.104 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.104 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.104 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.104 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.104 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.104 * [taylor]: Taking taylor expansion of 0.25 in n 4.104 * [backup-simplify]: Simplify 0.25 into 0.25 4.104 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.104 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.104 * [taylor]: Taking taylor expansion of k in n 4.104 * [backup-simplify]: Simplify k into k 4.104 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.104 * [taylor]: Taking taylor expansion of 1.0 in n 4.104 * [backup-simplify]: Simplify 1.0 into 1.0 4.104 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.104 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.104 * [taylor]: Taking taylor expansion of -2.0 in n 4.104 * [backup-simplify]: Simplify -2.0 into -2.0 4.104 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.104 * [taylor]: Taking taylor expansion of PI in n 4.104 * [backup-simplify]: Simplify PI into PI 4.104 * [taylor]: Taking taylor expansion of n in n 4.104 * [backup-simplify]: Simplify 0 into 0 4.104 * [backup-simplify]: Simplify 1 into 1 4.104 * [backup-simplify]: Simplify (/ PI 1) into PI 4.105 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.105 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.105 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.105 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.106 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.107 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.108 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.108 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.108 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.108 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.108 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.108 * [taylor]: Taking taylor expansion of 0.25 in n 4.108 * [backup-simplify]: Simplify 0.25 into 0.25 4.108 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.108 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.108 * [taylor]: Taking taylor expansion of k in n 4.108 * [backup-simplify]: Simplify k into k 4.108 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.108 * [taylor]: Taking taylor expansion of 1.0 in n 4.108 * [backup-simplify]: Simplify 1.0 into 1.0 4.108 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.108 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.108 * [taylor]: Taking taylor expansion of -2.0 in n 4.108 * [backup-simplify]: Simplify -2.0 into -2.0 4.108 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.108 * [taylor]: Taking taylor expansion of PI in n 4.108 * [backup-simplify]: Simplify PI into PI 4.108 * [taylor]: Taking taylor expansion of n in n 4.108 * [backup-simplify]: Simplify 0 into 0 4.108 * [backup-simplify]: Simplify 1 into 1 4.108 * [backup-simplify]: Simplify (/ PI 1) into PI 4.109 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.109 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.109 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.109 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.110 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.111 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.112 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.112 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.112 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.112 * [taylor]: Taking taylor expansion of 0.25 in k 4.112 * [backup-simplify]: Simplify 0.25 into 0.25 4.112 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.112 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.112 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.112 * [taylor]: Taking taylor expansion of k in k 4.112 * [backup-simplify]: Simplify 0 into 0 4.112 * [backup-simplify]: Simplify 1 into 1 4.112 * [backup-simplify]: Simplify (/ 1 1) into 1 4.112 * [taylor]: Taking taylor expansion of 1.0 in k 4.112 * [backup-simplify]: Simplify 1.0 into 1.0 4.112 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.112 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.112 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.112 * [taylor]: Taking taylor expansion of -2.0 in k 4.112 * [backup-simplify]: Simplify -2.0 into -2.0 4.112 * [taylor]: Taking taylor expansion of PI in k 4.112 * [backup-simplify]: Simplify PI into PI 4.113 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.113 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.113 * [taylor]: Taking taylor expansion of (log n) in k 4.113 * [taylor]: Taking taylor expansion of n in k 4.113 * [backup-simplify]: Simplify n into n 4.113 * [backup-simplify]: Simplify (log n) into (log n) 4.114 * [backup-simplify]: Simplify (+ 1 0) into 1 4.114 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.114 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.115 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.115 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 4.116 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.117 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.117 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.118 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.119 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.119 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.119 * [backup-simplify]: Simplify (+ 0 0) into 0 4.119 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.120 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.121 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.122 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.122 * [taylor]: Taking taylor expansion of 0 in k 4.122 * [backup-simplify]: Simplify 0 into 0 4.122 * [backup-simplify]: Simplify 0 into 0 4.122 * [backup-simplify]: Simplify 0 into 0 4.123 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.123 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.125 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 4.125 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.125 * [backup-simplify]: Simplify (+ 0 0) into 0 4.126 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.127 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.128 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.129 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.129 * [taylor]: Taking taylor expansion of 0 in k 4.129 * [backup-simplify]: Simplify 0 into 0 4.129 * [backup-simplify]: Simplify 0 into 0 4.129 * [backup-simplify]: Simplify 0 into 0 4.129 * [backup-simplify]: Simplify 0 into 0 4.130 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.131 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.134 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 4.134 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.134 * [backup-simplify]: Simplify (+ 0 0) into 0 4.135 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.135 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.136 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.138 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.138 * [taylor]: Taking taylor expansion of 0 in k 4.138 * [backup-simplify]: Simplify 0 into 0 4.138 * [backup-simplify]: Simplify 0 into 0 4.139 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.139 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 2) 4.139 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) into (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 4.139 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in (n k) around 0 4.139 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in k 4.139 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.139 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.139 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in k 4.139 * [taylor]: Taking taylor expansion of 0.125 in k 4.140 * [backup-simplify]: Simplify 0.125 into 0.125 4.140 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.140 * [taylor]: Taking taylor expansion of 1.0 in k 4.140 * [backup-simplify]: Simplify 1.0 into 1.0 4.140 * [taylor]: Taking taylor expansion of k in k 4.140 * [backup-simplify]: Simplify 0 into 0 4.140 * [backup-simplify]: Simplify 1 into 1 4.140 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.140 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.140 * [taylor]: Taking taylor expansion of 2.0 in k 4.140 * [backup-simplify]: Simplify 2.0 into 2.0 4.140 * [taylor]: Taking taylor expansion of (* n PI) in k 4.140 * [taylor]: Taking taylor expansion of n in k 4.140 * [backup-simplify]: Simplify n into n 4.140 * [taylor]: Taking taylor expansion of PI in k 4.140 * [backup-simplify]: Simplify PI into PI 4.140 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.140 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.140 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.140 * [backup-simplify]: Simplify (- 0) into 0 4.140 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.141 * [backup-simplify]: Simplify (* 0.125 1.0) into 0.125 4.141 * [backup-simplify]: Simplify (* 0.125 (log (* 2.0 (* n PI)))) into (* 0.125 (log (* 2.0 (* n PI)))) 4.141 * [backup-simplify]: Simplify (exp (* 0.125 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.125) 4.141 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.141 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.141 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.141 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.141 * [taylor]: Taking taylor expansion of 0.125 in n 4.141 * [backup-simplify]: Simplify 0.125 into 0.125 4.141 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.141 * [taylor]: Taking taylor expansion of 1.0 in n 4.141 * [backup-simplify]: Simplify 1.0 into 1.0 4.141 * [taylor]: Taking taylor expansion of k in n 4.141 * [backup-simplify]: Simplify k into k 4.141 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.141 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.141 * [taylor]: Taking taylor expansion of 2.0 in n 4.141 * [backup-simplify]: Simplify 2.0 into 2.0 4.141 * [taylor]: Taking taylor expansion of (* n PI) in n 4.141 * [taylor]: Taking taylor expansion of n in n 4.141 * [backup-simplify]: Simplify 0 into 0 4.141 * [backup-simplify]: Simplify 1 into 1 4.141 * [taylor]: Taking taylor expansion of PI in n 4.141 * [backup-simplify]: Simplify PI into PI 4.141 * [backup-simplify]: Simplify (* 0 PI) into 0 4.142 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.142 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.143 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.144 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.144 * [backup-simplify]: Simplify (- k) into (- k) 4.144 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.144 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.145 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.145 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.146 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.146 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.146 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.146 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.146 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.146 * [taylor]: Taking taylor expansion of 0.125 in n 4.146 * [backup-simplify]: Simplify 0.125 into 0.125 4.146 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.146 * [taylor]: Taking taylor expansion of 1.0 in n 4.146 * [backup-simplify]: Simplify 1.0 into 1.0 4.146 * [taylor]: Taking taylor expansion of k in n 4.146 * [backup-simplify]: Simplify k into k 4.146 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.146 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.146 * [taylor]: Taking taylor expansion of 2.0 in n 4.146 * [backup-simplify]: Simplify 2.0 into 2.0 4.146 * [taylor]: Taking taylor expansion of (* n PI) in n 4.146 * [taylor]: Taking taylor expansion of n in n 4.146 * [backup-simplify]: Simplify 0 into 0 4.146 * [backup-simplify]: Simplify 1 into 1 4.146 * [taylor]: Taking taylor expansion of PI in n 4.146 * [backup-simplify]: Simplify PI into PI 4.147 * [backup-simplify]: Simplify (* 0 PI) into 0 4.147 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.148 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.149 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.149 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.149 * [backup-simplify]: Simplify (- k) into (- k) 4.149 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.149 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.150 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.151 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.151 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.152 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.152 * [taylor]: Taking taylor expansion of (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.152 * [taylor]: Taking taylor expansion of 0.125 in k 4.152 * [backup-simplify]: Simplify 0.125 into 0.125 4.152 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.152 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.152 * [taylor]: Taking taylor expansion of 1.0 in k 4.152 * [backup-simplify]: Simplify 1.0 into 1.0 4.152 * [taylor]: Taking taylor expansion of k in k 4.152 * [backup-simplify]: Simplify 0 into 0 4.152 * [backup-simplify]: Simplify 1 into 1 4.152 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.152 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.152 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.152 * [taylor]: Taking taylor expansion of 2.0 in k 4.152 * [backup-simplify]: Simplify 2.0 into 2.0 4.152 * [taylor]: Taking taylor expansion of PI in k 4.152 * [backup-simplify]: Simplify PI into PI 4.152 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.153 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.153 * [taylor]: Taking taylor expansion of (log n) in k 4.153 * [taylor]: Taking taylor expansion of n in k 4.153 * [backup-simplify]: Simplify n into n 4.153 * [backup-simplify]: Simplify (log n) into (log n) 4.153 * [backup-simplify]: Simplify (- 0) into 0 4.153 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.154 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.155 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.155 * [backup-simplify]: Simplify (* 0.125 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.125 (+ (log (* 2.0 PI)) (log n))) 4.156 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.156 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.157 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.158 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.158 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.159 * [backup-simplify]: Simplify (- 0) into 0 4.159 * [backup-simplify]: Simplify (+ 0 0) into 0 4.159 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 k))) into 0 4.160 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.161 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.162 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.162 * [taylor]: Taking taylor expansion of 0 in k 4.162 * [backup-simplify]: Simplify 0 into 0 4.162 * [backup-simplify]: Simplify 0 into 0 4.162 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.163 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.164 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.164 * [backup-simplify]: Simplify (+ 0 0) into 0 4.164 * [backup-simplify]: Simplify (- 1) into -1 4.164 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.165 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.166 * [backup-simplify]: Simplify (+ (* 0.125 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 4.168 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 1) 1)))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.170 * [backup-simplify]: Simplify (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.171 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.171 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.173 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.173 * [backup-simplify]: Simplify (- 0) into 0 4.173 * [backup-simplify]: Simplify (+ 0 0) into 0 4.174 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.175 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.176 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.177 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.177 * [taylor]: Taking taylor expansion of 0 in k 4.177 * [backup-simplify]: Simplify 0 into 0 4.177 * [backup-simplify]: Simplify 0 into 0 4.177 * [backup-simplify]: Simplify 0 into 0 4.178 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.181 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.182 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.182 * [backup-simplify]: Simplify (+ 0 0) into 0 4.182 * [backup-simplify]: Simplify (- 0) into 0 4.182 * [backup-simplify]: Simplify (+ 0 0) into 0 4.183 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.185 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.187 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.197 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.203 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) (* k 1)) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.0078125 (* (pow k 2) (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (* 0.015625 (* (pow k 2) (* (log (* 2.0 PI)) (* (log n) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))))))) (+ (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log (* 2.0 PI))))))) 4.203 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (/ (- 1.0 (/ 1 k)) 2.0) 2) 2)) into (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 4.203 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in (n k) around 0 4.203 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in k 4.203 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.203 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.203 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in k 4.203 * [taylor]: Taking taylor expansion of 0.125 in k 4.203 * [backup-simplify]: Simplify 0.125 into 0.125 4.203 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.203 * [taylor]: Taking taylor expansion of 1.0 in k 4.203 * [backup-simplify]: Simplify 1.0 into 1.0 4.203 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.203 * [taylor]: Taking taylor expansion of k in k 4.203 * [backup-simplify]: Simplify 0 into 0 4.203 * [backup-simplify]: Simplify 1 into 1 4.204 * [backup-simplify]: Simplify (/ 1 1) into 1 4.204 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.204 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.204 * [taylor]: Taking taylor expansion of 2.0 in k 4.204 * [backup-simplify]: Simplify 2.0 into 2.0 4.204 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.204 * [taylor]: Taking taylor expansion of PI in k 4.204 * [backup-simplify]: Simplify PI into PI 4.204 * [taylor]: Taking taylor expansion of n in k 4.204 * [backup-simplify]: Simplify n into n 4.204 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.204 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.204 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.204 * [backup-simplify]: Simplify (- 1) into -1 4.204 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.205 * [backup-simplify]: Simplify (* 0.125 -1) into -0.125 4.205 * [backup-simplify]: Simplify (* -0.125 (log (* 2.0 (/ PI n)))) into (* -0.125 (log (* 2.0 (/ PI n)))) 4.205 * [backup-simplify]: Simplify (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.125 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.205 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.205 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.205 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.205 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.205 * [taylor]: Taking taylor expansion of 0.125 in n 4.205 * [backup-simplify]: Simplify 0.125 into 0.125 4.205 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.205 * [taylor]: Taking taylor expansion of 1.0 in n 4.205 * [backup-simplify]: Simplify 1.0 into 1.0 4.205 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.205 * [taylor]: Taking taylor expansion of k in n 4.205 * [backup-simplify]: Simplify k into k 4.205 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.205 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.205 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.205 * [taylor]: Taking taylor expansion of 2.0 in n 4.205 * [backup-simplify]: Simplify 2.0 into 2.0 4.205 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.205 * [taylor]: Taking taylor expansion of PI in n 4.205 * [backup-simplify]: Simplify PI into PI 4.205 * [taylor]: Taking taylor expansion of n in n 4.205 * [backup-simplify]: Simplify 0 into 0 4.205 * [backup-simplify]: Simplify 1 into 1 4.206 * [backup-simplify]: Simplify (/ PI 1) into PI 4.206 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.206 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.207 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.207 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.207 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.207 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.208 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.209 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.209 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.209 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.209 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.209 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.209 * [taylor]: Taking taylor expansion of 0.125 in n 4.209 * [backup-simplify]: Simplify 0.125 into 0.125 4.209 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.209 * [taylor]: Taking taylor expansion of 1.0 in n 4.209 * [backup-simplify]: Simplify 1.0 into 1.0 4.209 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.209 * [taylor]: Taking taylor expansion of k in n 4.209 * [backup-simplify]: Simplify k into k 4.209 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.209 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.209 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.209 * [taylor]: Taking taylor expansion of 2.0 in n 4.209 * [backup-simplify]: Simplify 2.0 into 2.0 4.209 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.209 * [taylor]: Taking taylor expansion of PI in n 4.209 * [backup-simplify]: Simplify PI into PI 4.209 * [taylor]: Taking taylor expansion of n in n 4.209 * [backup-simplify]: Simplify 0 into 0 4.209 * [backup-simplify]: Simplify 1 into 1 4.210 * [backup-simplify]: Simplify (/ PI 1) into PI 4.210 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.210 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.210 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.211 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.211 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.211 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.212 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.213 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.213 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.213 * [taylor]: Taking taylor expansion of (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.213 * [taylor]: Taking taylor expansion of 0.125 in k 4.213 * [backup-simplify]: Simplify 0.125 into 0.125 4.213 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.213 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.213 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.213 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.213 * [taylor]: Taking taylor expansion of 2.0 in k 4.213 * [backup-simplify]: Simplify 2.0 into 2.0 4.213 * [taylor]: Taking taylor expansion of PI in k 4.213 * [backup-simplify]: Simplify PI into PI 4.213 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.214 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.214 * [taylor]: Taking taylor expansion of (log n) in k 4.214 * [taylor]: Taking taylor expansion of n in k 4.214 * [backup-simplify]: Simplify n into n 4.214 * [backup-simplify]: Simplify (log n) into (log n) 4.214 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.214 * [taylor]: Taking taylor expansion of 1.0 in k 4.214 * [backup-simplify]: Simplify 1.0 into 1.0 4.214 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.214 * [taylor]: Taking taylor expansion of k in k 4.214 * [backup-simplify]: Simplify 0 into 0 4.214 * [backup-simplify]: Simplify 1 into 1 4.214 * [backup-simplify]: Simplify (/ 1 1) into 1 4.214 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.215 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.215 * [backup-simplify]: Simplify (- 1) into -1 4.216 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.216 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.217 * [backup-simplify]: Simplify (* 0.125 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.125 (- (log (* 2.0 PI)) (log n))) 4.217 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.218 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.219 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.219 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.220 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.220 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.220 * [backup-simplify]: Simplify (- 0) into 0 4.221 * [backup-simplify]: Simplify (+ 0 0) into 0 4.221 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.222 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.223 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.224 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.224 * [taylor]: Taking taylor expansion of 0 in k 4.224 * [backup-simplify]: Simplify 0 into 0 4.224 * [backup-simplify]: Simplify 0 into 0 4.224 * [backup-simplify]: Simplify 0 into 0 4.225 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.225 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.227 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.227 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.227 * [backup-simplify]: Simplify (- 0) into 0 4.228 * [backup-simplify]: Simplify (+ 0 0) into 0 4.228 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.229 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.230 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.231 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.231 * [taylor]: Taking taylor expansion of 0 in k 4.231 * [backup-simplify]: Simplify 0 into 0 4.231 * [backup-simplify]: Simplify 0 into 0 4.232 * [backup-simplify]: Simplify 0 into 0 4.232 * [backup-simplify]: Simplify 0 into 0 4.232 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.233 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.235 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 4.236 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.236 * [backup-simplify]: Simplify (- 0) into 0 4.236 * [backup-simplify]: Simplify (+ 0 0) into 0 4.237 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.238 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.239 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.240 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.240 * [taylor]: Taking taylor expansion of 0 in k 4.240 * [backup-simplify]: Simplify 0 into 0 4.240 * [backup-simplify]: Simplify 0 into 0 4.241 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.242 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2) 2)) into (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 4.242 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in (n k) around 0 4.242 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in k 4.242 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.242 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.242 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in k 4.242 * [taylor]: Taking taylor expansion of 0.125 in k 4.242 * [backup-simplify]: Simplify 0.125 into 0.125 4.242 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.242 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.242 * [taylor]: Taking taylor expansion of k in k 4.242 * [backup-simplify]: Simplify 0 into 0 4.242 * [backup-simplify]: Simplify 1 into 1 4.242 * [backup-simplify]: Simplify (/ 1 1) into 1 4.242 * [taylor]: Taking taylor expansion of 1.0 in k 4.242 * [backup-simplify]: Simplify 1.0 into 1.0 4.242 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.242 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.242 * [taylor]: Taking taylor expansion of -2.0 in k 4.242 * [backup-simplify]: Simplify -2.0 into -2.0 4.242 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.242 * [taylor]: Taking taylor expansion of PI in k 4.242 * [backup-simplify]: Simplify PI into PI 4.242 * [taylor]: Taking taylor expansion of n in k 4.242 * [backup-simplify]: Simplify n into n 4.242 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.242 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.242 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.243 * [backup-simplify]: Simplify (+ 1 0) into 1 4.243 * [backup-simplify]: Simplify (* 0.125 1) into 0.125 4.243 * [backup-simplify]: Simplify (* 0.125 (log (* -2.0 (/ PI n)))) into (* 0.125 (log (* -2.0 (/ PI n)))) 4.243 * [backup-simplify]: Simplify (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.243 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.243 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.243 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.243 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.243 * [taylor]: Taking taylor expansion of 0.125 in n 4.243 * [backup-simplify]: Simplify 0.125 into 0.125 4.243 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.243 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.243 * [taylor]: Taking taylor expansion of k in n 4.243 * [backup-simplify]: Simplify k into k 4.243 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.243 * [taylor]: Taking taylor expansion of 1.0 in n 4.243 * [backup-simplify]: Simplify 1.0 into 1.0 4.243 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.243 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.243 * [taylor]: Taking taylor expansion of -2.0 in n 4.243 * [backup-simplify]: Simplify -2.0 into -2.0 4.243 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.243 * [taylor]: Taking taylor expansion of PI in n 4.243 * [backup-simplify]: Simplify PI into PI 4.243 * [taylor]: Taking taylor expansion of n in n 4.243 * [backup-simplify]: Simplify 0 into 0 4.243 * [backup-simplify]: Simplify 1 into 1 4.244 * [backup-simplify]: Simplify (/ PI 1) into PI 4.244 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.245 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.245 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.245 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.246 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.246 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.247 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.247 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.247 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.247 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.247 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.247 * [taylor]: Taking taylor expansion of 0.125 in n 4.247 * [backup-simplify]: Simplify 0.125 into 0.125 4.247 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.247 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.247 * [taylor]: Taking taylor expansion of k in n 4.247 * [backup-simplify]: Simplify k into k 4.247 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.247 * [taylor]: Taking taylor expansion of 1.0 in n 4.247 * [backup-simplify]: Simplify 1.0 into 1.0 4.247 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.247 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.247 * [taylor]: Taking taylor expansion of -2.0 in n 4.247 * [backup-simplify]: Simplify -2.0 into -2.0 4.247 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.247 * [taylor]: Taking taylor expansion of PI in n 4.247 * [backup-simplify]: Simplify PI into PI 4.247 * [taylor]: Taking taylor expansion of n in n 4.247 * [backup-simplify]: Simplify 0 into 0 4.247 * [backup-simplify]: Simplify 1 into 1 4.248 * [backup-simplify]: Simplify (/ PI 1) into PI 4.248 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.249 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.249 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.249 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.249 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.250 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.251 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.251 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.251 * [taylor]: Taking taylor expansion of (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.251 * [taylor]: Taking taylor expansion of 0.125 in k 4.251 * [backup-simplify]: Simplify 0.125 into 0.125 4.251 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.251 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.251 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.251 * [taylor]: Taking taylor expansion of k in k 4.251 * [backup-simplify]: Simplify 0 into 0 4.251 * [backup-simplify]: Simplify 1 into 1 4.251 * [backup-simplify]: Simplify (/ 1 1) into 1 4.251 * [taylor]: Taking taylor expansion of 1.0 in k 4.251 * [backup-simplify]: Simplify 1.0 into 1.0 4.251 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.251 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.251 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.251 * [taylor]: Taking taylor expansion of -2.0 in k 4.251 * [backup-simplify]: Simplify -2.0 into -2.0 4.251 * [taylor]: Taking taylor expansion of PI in k 4.251 * [backup-simplify]: Simplify PI into PI 4.252 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.252 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.252 * [taylor]: Taking taylor expansion of (log n) in k 4.252 * [taylor]: Taking taylor expansion of n in k 4.252 * [backup-simplify]: Simplify n into n 4.252 * [backup-simplify]: Simplify (log n) into (log n) 4.253 * [backup-simplify]: Simplify (+ 1 0) into 1 4.253 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.253 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.254 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.255 * [backup-simplify]: Simplify (* 0.125 (- (log (* -2.0 PI)) (log n))) into (* 0.125 (- (log (* -2.0 PI)) (log n))) 4.255 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.256 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.257 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.257 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.258 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.258 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.258 * [backup-simplify]: Simplify (+ 0 0) into 0 4.259 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.259 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.260 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.261 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.261 * [taylor]: Taking taylor expansion of 0 in k 4.261 * [backup-simplify]: Simplify 0 into 0 4.261 * [backup-simplify]: Simplify 0 into 0 4.261 * [backup-simplify]: Simplify 0 into 0 4.262 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.262 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.264 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 4.264 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.264 * [backup-simplify]: Simplify (+ 0 0) into 0 4.265 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.266 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.266 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.268 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.268 * [taylor]: Taking taylor expansion of 0 in k 4.268 * [backup-simplify]: Simplify 0 into 0 4.268 * [backup-simplify]: Simplify 0 into 0 4.268 * [backup-simplify]: Simplify 0 into 0 4.268 * [backup-simplify]: Simplify 0 into 0 4.269 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.269 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.272 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 4.272 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.272 * [backup-simplify]: Simplify (+ 0 0) into 0 4.273 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.274 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.275 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.276 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.276 * [taylor]: Taking taylor expansion of 0 in k 4.277 * [backup-simplify]: Simplify 0 into 0 4.277 * [backup-simplify]: Simplify 0 into 0 4.277 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.125 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.277 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2 1) 4.278 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) into (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 4.278 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in (n k) around 0 4.278 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in k 4.278 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.278 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.278 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in k 4.278 * [taylor]: Taking taylor expansion of 0.125 in k 4.278 * [backup-simplify]: Simplify 0.125 into 0.125 4.278 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.278 * [taylor]: Taking taylor expansion of 1.0 in k 4.278 * [backup-simplify]: Simplify 1.0 into 1.0 4.278 * [taylor]: Taking taylor expansion of k in k 4.278 * [backup-simplify]: Simplify 0 into 0 4.278 * [backup-simplify]: Simplify 1 into 1 4.278 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.278 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.278 * [taylor]: Taking taylor expansion of 2.0 in k 4.278 * [backup-simplify]: Simplify 2.0 into 2.0 4.278 * [taylor]: Taking taylor expansion of (* n PI) in k 4.278 * [taylor]: Taking taylor expansion of n in k 4.278 * [backup-simplify]: Simplify n into n 4.278 * [taylor]: Taking taylor expansion of PI in k 4.278 * [backup-simplify]: Simplify PI into PI 4.278 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.278 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.278 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.279 * [backup-simplify]: Simplify (- 0) into 0 4.279 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.279 * [backup-simplify]: Simplify (* 0.125 1.0) into 0.125 4.279 * [backup-simplify]: Simplify (* 0.125 (log (* 2.0 (* n PI)))) into (* 0.125 (log (* 2.0 (* n PI)))) 4.279 * [backup-simplify]: Simplify (exp (* 0.125 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.125) 4.279 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.279 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.279 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.279 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.279 * [taylor]: Taking taylor expansion of 0.125 in n 4.279 * [backup-simplify]: Simplify 0.125 into 0.125 4.279 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.279 * [taylor]: Taking taylor expansion of 1.0 in n 4.279 * [backup-simplify]: Simplify 1.0 into 1.0 4.280 * [taylor]: Taking taylor expansion of k in n 4.280 * [backup-simplify]: Simplify k into k 4.280 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.280 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.280 * [taylor]: Taking taylor expansion of 2.0 in n 4.280 * [backup-simplify]: Simplify 2.0 into 2.0 4.280 * [taylor]: Taking taylor expansion of (* n PI) in n 4.280 * [taylor]: Taking taylor expansion of n in n 4.280 * [backup-simplify]: Simplify 0 into 0 4.280 * [backup-simplify]: Simplify 1 into 1 4.280 * [taylor]: Taking taylor expansion of PI in n 4.280 * [backup-simplify]: Simplify PI into PI 4.280 * [backup-simplify]: Simplify (* 0 PI) into 0 4.280 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.281 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.282 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.283 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.283 * [backup-simplify]: Simplify (- k) into (- k) 4.283 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.283 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.290 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.291 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.291 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.292 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.292 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.292 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.292 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.292 * [taylor]: Taking taylor expansion of 0.125 in n 4.292 * [backup-simplify]: Simplify 0.125 into 0.125 4.292 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.292 * [taylor]: Taking taylor expansion of 1.0 in n 4.292 * [backup-simplify]: Simplify 1.0 into 1.0 4.292 * [taylor]: Taking taylor expansion of k in n 4.292 * [backup-simplify]: Simplify k into k 4.292 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.292 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.292 * [taylor]: Taking taylor expansion of 2.0 in n 4.292 * [backup-simplify]: Simplify 2.0 into 2.0 4.292 * [taylor]: Taking taylor expansion of (* n PI) in n 4.292 * [taylor]: Taking taylor expansion of n in n 4.292 * [backup-simplify]: Simplify 0 into 0 4.292 * [backup-simplify]: Simplify 1 into 1 4.292 * [taylor]: Taking taylor expansion of PI in n 4.292 * [backup-simplify]: Simplify PI into PI 4.292 * [backup-simplify]: Simplify (* 0 PI) into 0 4.292 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.293 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.294 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.295 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.295 * [backup-simplify]: Simplify (- k) into (- k) 4.295 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.295 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.296 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.296 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.297 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.297 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.297 * [taylor]: Taking taylor expansion of (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.297 * [taylor]: Taking taylor expansion of 0.125 in k 4.297 * [backup-simplify]: Simplify 0.125 into 0.125 4.297 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.297 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.297 * [taylor]: Taking taylor expansion of 1.0 in k 4.297 * [backup-simplify]: Simplify 1.0 into 1.0 4.297 * [taylor]: Taking taylor expansion of k in k 4.297 * [backup-simplify]: Simplify 0 into 0 4.297 * [backup-simplify]: Simplify 1 into 1 4.297 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.297 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.297 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.297 * [taylor]: Taking taylor expansion of 2.0 in k 4.297 * [backup-simplify]: Simplify 2.0 into 2.0 4.297 * [taylor]: Taking taylor expansion of PI in k 4.297 * [backup-simplify]: Simplify PI into PI 4.298 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.298 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.298 * [taylor]: Taking taylor expansion of (log n) in k 4.298 * [taylor]: Taking taylor expansion of n in k 4.298 * [backup-simplify]: Simplify n into n 4.298 * [backup-simplify]: Simplify (log n) into (log n) 4.298 * [backup-simplify]: Simplify (- 0) into 0 4.299 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.299 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.300 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.301 * [backup-simplify]: Simplify (* 0.125 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.125 (+ (log (* 2.0 PI)) (log n))) 4.301 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.302 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.302 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.303 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.304 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.304 * [backup-simplify]: Simplify (- 0) into 0 4.304 * [backup-simplify]: Simplify (+ 0 0) into 0 4.305 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 k))) into 0 4.305 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.306 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.307 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.307 * [taylor]: Taking taylor expansion of 0 in k 4.307 * [backup-simplify]: Simplify 0 into 0 4.307 * [backup-simplify]: Simplify 0 into 0 4.308 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.309 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.309 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.309 * [backup-simplify]: Simplify (+ 0 0) into 0 4.310 * [backup-simplify]: Simplify (- 1) into -1 4.310 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.311 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.312 * [backup-simplify]: Simplify (+ (* 0.125 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 4.314 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 1) 1)))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.315 * [backup-simplify]: Simplify (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.316 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.317 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.318 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.319 * [backup-simplify]: Simplify (- 0) into 0 4.319 * [backup-simplify]: Simplify (+ 0 0) into 0 4.319 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.320 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.321 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.322 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.322 * [taylor]: Taking taylor expansion of 0 in k 4.322 * [backup-simplify]: Simplify 0 into 0 4.322 * [backup-simplify]: Simplify 0 into 0 4.323 * [backup-simplify]: Simplify 0 into 0 4.323 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.325 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.326 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.326 * [backup-simplify]: Simplify (+ 0 0) into 0 4.326 * [backup-simplify]: Simplify (- 0) into 0 4.326 * [backup-simplify]: Simplify (+ 0 0) into 0 4.327 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.329 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.331 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.334 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.340 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) (* k 1)) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.0078125 (* (pow k 2) (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (* 0.015625 (* (pow k 2) (* (log (* 2.0 PI)) (* (log n) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))))))) (+ (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log (* 2.0 PI))))))) 4.341 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (/ (- 1.0 (/ 1 k)) 2.0) 2) 2)) into (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 4.341 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in (n k) around 0 4.341 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in k 4.341 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.341 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.341 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in k 4.341 * [taylor]: Taking taylor expansion of 0.125 in k 4.341 * [backup-simplify]: Simplify 0.125 into 0.125 4.341 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.341 * [taylor]: Taking taylor expansion of 1.0 in k 4.341 * [backup-simplify]: Simplify 1.0 into 1.0 4.341 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.341 * [taylor]: Taking taylor expansion of k in k 4.341 * [backup-simplify]: Simplify 0 into 0 4.341 * [backup-simplify]: Simplify 1 into 1 4.341 * [backup-simplify]: Simplify (/ 1 1) into 1 4.341 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.341 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.341 * [taylor]: Taking taylor expansion of 2.0 in k 4.341 * [backup-simplify]: Simplify 2.0 into 2.0 4.341 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.341 * [taylor]: Taking taylor expansion of PI in k 4.341 * [backup-simplify]: Simplify PI into PI 4.341 * [taylor]: Taking taylor expansion of n in k 4.341 * [backup-simplify]: Simplify n into n 4.341 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.341 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.342 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.342 * [backup-simplify]: Simplify (- 1) into -1 4.342 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.342 * [backup-simplify]: Simplify (* 0.125 -1) into -0.125 4.342 * [backup-simplify]: Simplify (* -0.125 (log (* 2.0 (/ PI n)))) into (* -0.125 (log (* 2.0 (/ PI n)))) 4.343 * [backup-simplify]: Simplify (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.125 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.343 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.343 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.343 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.343 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.343 * [taylor]: Taking taylor expansion of 0.125 in n 4.343 * [backup-simplify]: Simplify 0.125 into 0.125 4.343 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.343 * [taylor]: Taking taylor expansion of 1.0 in n 4.343 * [backup-simplify]: Simplify 1.0 into 1.0 4.343 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.343 * [taylor]: Taking taylor expansion of k in n 4.343 * [backup-simplify]: Simplify k into k 4.343 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.343 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.343 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.343 * [taylor]: Taking taylor expansion of 2.0 in n 4.343 * [backup-simplify]: Simplify 2.0 into 2.0 4.343 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.343 * [taylor]: Taking taylor expansion of PI in n 4.343 * [backup-simplify]: Simplify PI into PI 4.343 * [taylor]: Taking taylor expansion of n in n 4.343 * [backup-simplify]: Simplify 0 into 0 4.343 * [backup-simplify]: Simplify 1 into 1 4.343 * [backup-simplify]: Simplify (/ PI 1) into PI 4.344 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.344 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.344 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.344 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.344 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.345 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.346 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.347 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.347 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.347 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.347 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.347 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.347 * [taylor]: Taking taylor expansion of 0.125 in n 4.347 * [backup-simplify]: Simplify 0.125 into 0.125 4.347 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.347 * [taylor]: Taking taylor expansion of 1.0 in n 4.347 * [backup-simplify]: Simplify 1.0 into 1.0 4.347 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.347 * [taylor]: Taking taylor expansion of k in n 4.347 * [backup-simplify]: Simplify k into k 4.347 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.347 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.347 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.347 * [taylor]: Taking taylor expansion of 2.0 in n 4.347 * [backup-simplify]: Simplify 2.0 into 2.0 4.347 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.347 * [taylor]: Taking taylor expansion of PI in n 4.347 * [backup-simplify]: Simplify PI into PI 4.347 * [taylor]: Taking taylor expansion of n in n 4.347 * [backup-simplify]: Simplify 0 into 0 4.347 * [backup-simplify]: Simplify 1 into 1 4.347 * [backup-simplify]: Simplify (/ PI 1) into PI 4.348 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.348 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.348 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.348 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.348 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.349 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.350 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.351 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.351 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.351 * [taylor]: Taking taylor expansion of (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.351 * [taylor]: Taking taylor expansion of 0.125 in k 4.351 * [backup-simplify]: Simplify 0.125 into 0.125 4.351 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.351 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.351 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.351 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.351 * [taylor]: Taking taylor expansion of 2.0 in k 4.351 * [backup-simplify]: Simplify 2.0 into 2.0 4.351 * [taylor]: Taking taylor expansion of PI in k 4.351 * [backup-simplify]: Simplify PI into PI 4.351 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.352 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.352 * [taylor]: Taking taylor expansion of (log n) in k 4.352 * [taylor]: Taking taylor expansion of n in k 4.352 * [backup-simplify]: Simplify n into n 4.352 * [backup-simplify]: Simplify (log n) into (log n) 4.352 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.352 * [taylor]: Taking taylor expansion of 1.0 in k 4.352 * [backup-simplify]: Simplify 1.0 into 1.0 4.352 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.352 * [taylor]: Taking taylor expansion of k in k 4.352 * [backup-simplify]: Simplify 0 into 0 4.352 * [backup-simplify]: Simplify 1 into 1 4.352 * [backup-simplify]: Simplify (/ 1 1) into 1 4.352 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.353 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.353 * [backup-simplify]: Simplify (- 1) into -1 4.353 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.354 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.355 * [backup-simplify]: Simplify (* 0.125 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.125 (- (log (* 2.0 PI)) (log n))) 4.355 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.356 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.356 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.357 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.358 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.358 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.358 * [backup-simplify]: Simplify (- 0) into 0 4.358 * [backup-simplify]: Simplify (+ 0 0) into 0 4.359 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.359 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.360 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.361 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.361 * [taylor]: Taking taylor expansion of 0 in k 4.361 * [backup-simplify]: Simplify 0 into 0 4.361 * [backup-simplify]: Simplify 0 into 0 4.361 * [backup-simplify]: Simplify 0 into 0 4.362 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.362 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.364 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.364 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.364 * [backup-simplify]: Simplify (- 0) into 0 4.365 * [backup-simplify]: Simplify (+ 0 0) into 0 4.365 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.366 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.367 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.368 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.368 * [taylor]: Taking taylor expansion of 0 in k 4.368 * [backup-simplify]: Simplify 0 into 0 4.368 * [backup-simplify]: Simplify 0 into 0 4.368 * [backup-simplify]: Simplify 0 into 0 4.368 * [backup-simplify]: Simplify 0 into 0 4.369 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.370 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.372 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 4.373 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.373 * [backup-simplify]: Simplify (- 0) into 0 4.373 * [backup-simplify]: Simplify (+ 0 0) into 0 4.374 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.375 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.376 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.384 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.384 * [taylor]: Taking taylor expansion of 0 in k 4.384 * [backup-simplify]: Simplify 0 into 0 4.384 * [backup-simplify]: Simplify 0 into 0 4.385 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.385 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2) 2)) into (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 4.386 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in (n k) around 0 4.386 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in k 4.386 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.386 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.386 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in k 4.386 * [taylor]: Taking taylor expansion of 0.125 in k 4.386 * [backup-simplify]: Simplify 0.125 into 0.125 4.386 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.386 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.386 * [taylor]: Taking taylor expansion of k in k 4.386 * [backup-simplify]: Simplify 0 into 0 4.386 * [backup-simplify]: Simplify 1 into 1 4.386 * [backup-simplify]: Simplify (/ 1 1) into 1 4.386 * [taylor]: Taking taylor expansion of 1.0 in k 4.386 * [backup-simplify]: Simplify 1.0 into 1.0 4.386 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.386 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.386 * [taylor]: Taking taylor expansion of -2.0 in k 4.386 * [backup-simplify]: Simplify -2.0 into -2.0 4.386 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.386 * [taylor]: Taking taylor expansion of PI in k 4.386 * [backup-simplify]: Simplify PI into PI 4.386 * [taylor]: Taking taylor expansion of n in k 4.386 * [backup-simplify]: Simplify n into n 4.386 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.386 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.386 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.387 * [backup-simplify]: Simplify (+ 1 0) into 1 4.387 * [backup-simplify]: Simplify (* 0.125 1) into 0.125 4.387 * [backup-simplify]: Simplify (* 0.125 (log (* -2.0 (/ PI n)))) into (* 0.125 (log (* -2.0 (/ PI n)))) 4.387 * [backup-simplify]: Simplify (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.387 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.387 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.387 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.387 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.387 * [taylor]: Taking taylor expansion of 0.125 in n 4.387 * [backup-simplify]: Simplify 0.125 into 0.125 4.387 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.387 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.387 * [taylor]: Taking taylor expansion of k in n 4.387 * [backup-simplify]: Simplify k into k 4.387 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.387 * [taylor]: Taking taylor expansion of 1.0 in n 4.387 * [backup-simplify]: Simplify 1.0 into 1.0 4.387 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.387 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.387 * [taylor]: Taking taylor expansion of -2.0 in n 4.387 * [backup-simplify]: Simplify -2.0 into -2.0 4.387 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.387 * [taylor]: Taking taylor expansion of PI in n 4.387 * [backup-simplify]: Simplify PI into PI 4.387 * [taylor]: Taking taylor expansion of n in n 4.387 * [backup-simplify]: Simplify 0 into 0 4.387 * [backup-simplify]: Simplify 1 into 1 4.388 * [backup-simplify]: Simplify (/ PI 1) into PI 4.388 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.389 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.389 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.389 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.390 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.390 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.391 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.391 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.391 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.391 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.391 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.391 * [taylor]: Taking taylor expansion of 0.125 in n 4.391 * [backup-simplify]: Simplify 0.125 into 0.125 4.391 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.391 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.391 * [taylor]: Taking taylor expansion of k in n 4.391 * [backup-simplify]: Simplify k into k 4.391 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.391 * [taylor]: Taking taylor expansion of 1.0 in n 4.391 * [backup-simplify]: Simplify 1.0 into 1.0 4.391 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.391 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.391 * [taylor]: Taking taylor expansion of -2.0 in n 4.391 * [backup-simplify]: Simplify -2.0 into -2.0 4.391 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.391 * [taylor]: Taking taylor expansion of PI in n 4.391 * [backup-simplify]: Simplify PI into PI 4.391 * [taylor]: Taking taylor expansion of n in n 4.391 * [backup-simplify]: Simplify 0 into 0 4.391 * [backup-simplify]: Simplify 1 into 1 4.392 * [backup-simplify]: Simplify (/ PI 1) into PI 4.392 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.393 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.393 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.393 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.393 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.394 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.395 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.395 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.395 * [taylor]: Taking taylor expansion of (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.395 * [taylor]: Taking taylor expansion of 0.125 in k 4.395 * [backup-simplify]: Simplify 0.125 into 0.125 4.395 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.395 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.395 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.395 * [taylor]: Taking taylor expansion of k in k 4.395 * [backup-simplify]: Simplify 0 into 0 4.395 * [backup-simplify]: Simplify 1 into 1 4.395 * [backup-simplify]: Simplify (/ 1 1) into 1 4.395 * [taylor]: Taking taylor expansion of 1.0 in k 4.395 * [backup-simplify]: Simplify 1.0 into 1.0 4.395 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.395 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.395 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.395 * [taylor]: Taking taylor expansion of -2.0 in k 4.395 * [backup-simplify]: Simplify -2.0 into -2.0 4.395 * [taylor]: Taking taylor expansion of PI in k 4.396 * [backup-simplify]: Simplify PI into PI 4.396 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.396 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.396 * [taylor]: Taking taylor expansion of (log n) in k 4.396 * [taylor]: Taking taylor expansion of n in k 4.396 * [backup-simplify]: Simplify n into n 4.396 * [backup-simplify]: Simplify (log n) into (log n) 4.397 * [backup-simplify]: Simplify (+ 1 0) into 1 4.397 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.397 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.398 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.399 * [backup-simplify]: Simplify (* 0.125 (- (log (* -2.0 PI)) (log n))) into (* 0.125 (- (log (* -2.0 PI)) (log n))) 4.399 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.400 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.401 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.402 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.402 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.402 * [backup-simplify]: Simplify (+ 0 0) into 0 4.403 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.404 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.404 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.406 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.406 * [taylor]: Taking taylor expansion of 0 in k 4.406 * [backup-simplify]: Simplify 0 into 0 4.406 * [backup-simplify]: Simplify 0 into 0 4.406 * [backup-simplify]: Simplify 0 into 0 4.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.407 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.408 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 4.409 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.409 * [backup-simplify]: Simplify (+ 0 0) into 0 4.409 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.410 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.411 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.412 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.412 * [taylor]: Taking taylor expansion of 0 in k 4.412 * [backup-simplify]: Simplify 0 into 0 4.413 * [backup-simplify]: Simplify 0 into 0 4.413 * [backup-simplify]: Simplify 0 into 0 4.413 * [backup-simplify]: Simplify 0 into 0 4.413 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.414 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.417 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 4.417 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.417 * [backup-simplify]: Simplify (+ 0 0) into 0 4.418 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.419 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.420 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.421 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.421 * [taylor]: Taking taylor expansion of 0 in k 4.421 * [backup-simplify]: Simplify 0 into 0 4.421 * [backup-simplify]: Simplify 0 into 0 4.422 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.125 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.422 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 4.422 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.422 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.422 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.422 * [taylor]: Taking taylor expansion of 1.0 in k 4.422 * [backup-simplify]: Simplify 1.0 into 1.0 4.422 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.422 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.422 * [taylor]: Taking taylor expansion of k in k 4.422 * [backup-simplify]: Simplify 0 into 0 4.422 * [backup-simplify]: Simplify 1 into 1 4.423 * [backup-simplify]: Simplify (/ 1 1) into 1 4.423 * [backup-simplify]: Simplify (sqrt 0) into 0 4.424 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.424 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.424 * [taylor]: Taking taylor expansion of 1.0 in k 4.424 * [backup-simplify]: Simplify 1.0 into 1.0 4.424 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.424 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.424 * [taylor]: Taking taylor expansion of k in k 4.424 * [backup-simplify]: Simplify 0 into 0 4.424 * [backup-simplify]: Simplify 1 into 1 4.424 * [backup-simplify]: Simplify (/ 1 1) into 1 4.424 * [backup-simplify]: Simplify (sqrt 0) into 0 4.425 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.425 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.425 * [backup-simplify]: Simplify 0 into 0 4.426 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.426 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.427 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.428 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.429 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.429 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.430 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.432 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.433 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.433 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.434 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.434 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.434 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.434 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.434 * [taylor]: Taking taylor expansion of 1.0 in k 4.434 * [backup-simplify]: Simplify 1.0 into 1.0 4.434 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.434 * [taylor]: Taking taylor expansion of k in k 4.434 * [backup-simplify]: Simplify 0 into 0 4.434 * [backup-simplify]: Simplify 1 into 1 4.435 * [backup-simplify]: Simplify (sqrt 0) into 0 4.435 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.435 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.435 * [taylor]: Taking taylor expansion of 1.0 in k 4.435 * [backup-simplify]: Simplify 1.0 into 1.0 4.435 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.435 * [taylor]: Taking taylor expansion of k in k 4.436 * [backup-simplify]: Simplify 0 into 0 4.436 * [backup-simplify]: Simplify 1 into 1 4.436 * [backup-simplify]: Simplify (sqrt 0) into 0 4.436 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.437 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.437 * [backup-simplify]: Simplify 0 into 0 4.438 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.438 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.439 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.441 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.441 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.443 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.444 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.445 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.446 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 4.446 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.446 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.446 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.446 * [taylor]: Taking taylor expansion of 1.0 in k 4.446 * [backup-simplify]: Simplify 1.0 into 1.0 4.446 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.446 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.446 * [taylor]: Taking taylor expansion of -1 in k 4.446 * [backup-simplify]: Simplify -1 into -1 4.446 * [taylor]: Taking taylor expansion of k in k 4.446 * [backup-simplify]: Simplify 0 into 0 4.446 * [backup-simplify]: Simplify 1 into 1 4.446 * [backup-simplify]: Simplify (/ -1 1) into -1 4.446 * [backup-simplify]: Simplify (sqrt 0) into 0 4.447 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.447 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.448 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.448 * [taylor]: Taking taylor expansion of 1.0 in k 4.448 * [backup-simplify]: Simplify 1.0 into 1.0 4.448 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.448 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.448 * [taylor]: Taking taylor expansion of -1 in k 4.448 * [backup-simplify]: Simplify -1 into -1 4.448 * [taylor]: Taking taylor expansion of k in k 4.448 * [backup-simplify]: Simplify 0 into 0 4.448 * [backup-simplify]: Simplify 1 into 1 4.448 * [backup-simplify]: Simplify (/ -1 1) into -1 4.448 * [backup-simplify]: Simplify (sqrt 0) into 0 4.449 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.449 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.449 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.450 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.451 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.453 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.453 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.454 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.456 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.458 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.458 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.459 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 4.459 * * * [progress]: simplifying candidates 4.477 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (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) (/ 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h4)) (* (log h3) (exp (* h9 (+ (log (* h0 h4)) (log h3))))))))))) (+ (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log h3)))) (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log (* h0 h4))))))) (exp (* h9 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h9 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (+ (* h11 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h9 (+ (log (* h0 h4)) (log h3))))))) (+ (* h11 (* (pow h1 2) (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (* h10 (* (pow h1 2) (* (log (* h0 h4)) (* (log h3) (exp (* h9 (+ (log (* h0 h4)) (log h3))))))))))) (+ (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log h3)))) (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log (* h0 h4))))))) (exp (* h9 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h9 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h12 h1) (- (+ (* h12 (pow h1 2)) (- h12))))) (- (+ (* h12 (/ 1 (pow h1 2))) (- (+ (* h12 (/ 1 h1)) (- (* h12 (/ 1 (pow h1 3)))))))) (- (+ (* h12 (/ 1 (pow h1 2))) (- (+ (* h12 (/ 1 h1)) (- h12))))) 4.501 * * [simplify]: iteration 0 : 1959 enodes (cost 5547 ) 4.522 * * [simplify]: iteration 1 : 5001 enodes (cost 5350 ) 4.547 * * * [progress]: adding candidates to table 6.828 * [progress]: [Phase 3 of 3] Extracting. 6.828 * * [regime]: Finding splitpoints for: (# # # # # # # #) 6.831 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 6.831 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 6.865 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 6.902 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 6.941 * * * [regime]: Found split indices: #