10.502 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.076 * * * [progress]: [2/2] Setting up program. 0.079 * [progress]: [Phase 2 of 3] Improving. 0.079 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.079 * [simplify]: Sending expressions to egg_math: (* (/ h0 (sqrt h1)) (pow (* (* h2 PI) h3) (/ (- h0 h1) h2))) 0.081 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.083 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.084 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.087 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.093 * * [simplify]: iteration 4 : 1044 enodes (cost 8 ) 0.115 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.115 * * [progress]: iteration 1 / 4 0.115 * * * [progress]: picking best candidate 0.118 * * * * [pick]: Picked # 0.118 * * * [progress]: localizing error 0.135 * * * [progress]: generating rewritten candidates 0.135 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.156 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.174 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.180 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.228 * * * [progress]: generating series expansions 0.228 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.228 * [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 0.229 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.229 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.229 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.229 * [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)))) 0.230 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.230 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.230 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.230 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.230 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.230 * [taylor]: Taking taylor expansion of 0.5 in n 0.230 * [backup-simplify]: Simplify 0.5 into 0.5 0.230 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.230 * [taylor]: Taking taylor expansion of 1.0 in n 0.230 * [backup-simplify]: Simplify 1.0 into 1.0 0.230 * [taylor]: Taking taylor expansion of k in n 0.230 * [backup-simplify]: Simplify k into k 0.230 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.230 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.230 * [taylor]: Taking taylor expansion of 2.0 in n 0.230 * [backup-simplify]: Simplify 2.0 into 2.0 0.230 * [taylor]: Taking taylor expansion of (* n PI) in n 0.230 * [taylor]: Taking taylor expansion of n in n 0.230 * [backup-simplify]: Simplify 0 into 0 0.230 * [backup-simplify]: Simplify 1 into 1 0.230 * [taylor]: Taking taylor expansion of PI in n 0.230 * [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) 0.233 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.233 * [backup-simplify]: Simplify (- k) into (- k) 0.233 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.233 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.234 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.235 * [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)))) 0.236 * [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))))) 0.236 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.236 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.236 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.236 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.236 * [taylor]: Taking taylor expansion of 0.5 in n 0.236 * [backup-simplify]: Simplify 0.5 into 0.5 0.236 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.236 * [taylor]: Taking taylor expansion of 1.0 in n 0.236 * [backup-simplify]: Simplify 1.0 into 1.0 0.236 * [taylor]: Taking taylor expansion of k in n 0.236 * [backup-simplify]: Simplify k into k 0.236 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.236 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.236 * [taylor]: Taking taylor expansion of 2.0 in n 0.236 * [backup-simplify]: Simplify 2.0 into 2.0 0.236 * [taylor]: Taking taylor expansion of (* n PI) in n 0.236 * [taylor]: Taking taylor expansion of n in n 0.236 * [backup-simplify]: Simplify 0 into 0 0.236 * [backup-simplify]: Simplify 1 into 1 0.236 * [taylor]: Taking taylor expansion of PI in n 0.236 * [backup-simplify]: Simplify PI into PI 0.236 * [backup-simplify]: Simplify (* 0 PI) into 0 0.236 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.237 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.238 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.239 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.239 * [backup-simplify]: Simplify (- k) into (- k) 0.239 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.239 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.240 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.240 * [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)))) 0.241 * [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))))) 0.241 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.241 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.241 * [taylor]: Taking taylor expansion of 0.5 in k 0.241 * [backup-simplify]: Simplify 0.5 into 0.5 0.241 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.241 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.241 * [taylor]: Taking taylor expansion of 1.0 in k 0.241 * [backup-simplify]: Simplify 1.0 into 1.0 0.241 * [taylor]: Taking taylor expansion of k in k 0.241 * [backup-simplify]: Simplify 0 into 0 0.241 * [backup-simplify]: Simplify 1 into 1 0.241 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.241 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.241 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.241 * [taylor]: Taking taylor expansion of 2.0 in k 0.241 * [backup-simplify]: Simplify 2.0 into 2.0 0.241 * [taylor]: Taking taylor expansion of PI in k 0.241 * [backup-simplify]: Simplify PI into PI 0.242 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.242 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.242 * [taylor]: Taking taylor expansion of (log n) in k 0.242 * [taylor]: Taking taylor expansion of n in k 0.242 * [backup-simplify]: Simplify n into n 0.242 * [backup-simplify]: Simplify (log n) into (log n) 0.243 * [backup-simplify]: Simplify (- 0) into 0 0.243 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.244 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.244 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.245 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.246 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.246 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.247 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.247 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.248 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.249 * [backup-simplify]: Simplify (- 0) into 0 0.249 * [backup-simplify]: Simplify (+ 0 0) into 0 0.249 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 0.250 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.251 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.252 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.252 * [taylor]: Taking taylor expansion of 0 in k 0.252 * [backup-simplify]: Simplify 0 into 0 0.252 * [backup-simplify]: Simplify 0 into 0 0.252 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.253 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.254 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.254 * [backup-simplify]: Simplify (+ 0 0) into 0 0.254 * [backup-simplify]: Simplify (- 1) into -1 0.254 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.255 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.257 * [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)))) 0.258 * [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)))))) 0.264 * [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)))))) 0.265 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.266 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.267 * [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 0.268 * [backup-simplify]: Simplify (- 0) into 0 0.268 * [backup-simplify]: Simplify (+ 0 0) into 0 0.268 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 0.269 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.270 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.271 * [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 0.271 * [taylor]: Taking taylor expansion of 0 in k 0.271 * [backup-simplify]: Simplify 0 into 0 0.272 * [backup-simplify]: Simplify 0 into 0 0.272 * [backup-simplify]: Simplify 0 into 0 0.272 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.274 * [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 0.275 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 0.275 * [backup-simplify]: Simplify (+ 0 0) into 0 0.275 * [backup-simplify]: Simplify (- 0) into 0 0.276 * [backup-simplify]: Simplify (+ 0 0) into 0 0.277 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.279 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 0.281 * [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)))))) 0.284 * [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)))))) 0.290 * [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)))))) 0.291 * [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)))) 0.291 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.291 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.291 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.291 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.291 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.291 * [taylor]: Taking taylor expansion of 0.5 in k 0.291 * [backup-simplify]: Simplify 0.5 into 0.5 0.291 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.291 * [taylor]: Taking taylor expansion of 1.0 in k 0.291 * [backup-simplify]: Simplify 1.0 into 1.0 0.291 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.291 * [taylor]: Taking taylor expansion of k in k 0.291 * [backup-simplify]: Simplify 0 into 0 0.291 * [backup-simplify]: Simplify 1 into 1 0.291 * [backup-simplify]: Simplify (/ 1 1) into 1 0.291 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.291 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.291 * [taylor]: Taking taylor expansion of 2.0 in k 0.291 * [backup-simplify]: Simplify 2.0 into 2.0 0.291 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.291 * [taylor]: Taking taylor expansion of PI in k 0.291 * [backup-simplify]: Simplify PI into PI 0.291 * [taylor]: Taking taylor expansion of n in k 0.291 * [backup-simplify]: Simplify n into n 0.291 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.291 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.291 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.292 * [backup-simplify]: Simplify (- 1) into -1 0.292 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.292 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.292 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.292 * [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))))) 0.292 * [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)))) 0.297 * [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 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.297 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.297 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.297 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.297 * [taylor]: Taking taylor expansion of 0.5 in n 0.297 * [backup-simplify]: Simplify 0.5 into 0.5 0.297 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.297 * [taylor]: Taking taylor expansion of 1.0 in n 0.297 * [backup-simplify]: Simplify 1.0 into 1.0 0.297 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.297 * [taylor]: Taking taylor expansion of k in n 0.297 * [backup-simplify]: Simplify k into k 0.297 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.297 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.297 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.297 * [taylor]: Taking taylor expansion of 2.0 in n 0.297 * [backup-simplify]: Simplify 2.0 into 2.0 0.297 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.297 * [taylor]: Taking taylor expansion of PI in n 0.297 * [backup-simplify]: Simplify PI into PI 0.297 * [taylor]: Taking taylor expansion of n in n 0.297 * [backup-simplify]: Simplify 0 into 0 0.297 * [backup-simplify]: Simplify 1 into 1 0.297 * [backup-simplify]: Simplify (/ PI 1) into PI 0.298 * [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 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.298 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.298 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.299 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.300 * [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)))) 0.301 * [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))))) 0.301 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.301 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.301 * [taylor]: Taking taylor expansion of 0.5 in k 0.301 * [backup-simplify]: Simplify 0.5 into 0.5 0.301 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.301 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.301 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.301 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.301 * [taylor]: Taking taylor expansion of 2.0 in k 0.301 * [backup-simplify]: Simplify 2.0 into 2.0 0.301 * [taylor]: Taking taylor expansion of PI in k 0.301 * [backup-simplify]: Simplify PI into PI 0.301 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.302 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.302 * [taylor]: Taking taylor expansion of (log n) in k 0.302 * [taylor]: Taking taylor expansion of n in k 0.302 * [backup-simplify]: Simplify n into n 0.302 * [backup-simplify]: Simplify (log n) into (log n) 0.302 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.302 * [taylor]: Taking taylor expansion of 1.0 in k 0.302 * [backup-simplify]: Simplify 1.0 into 1.0 0.302 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.302 * [taylor]: Taking taylor expansion of k in k 0.302 * [backup-simplify]: Simplify 0 into 0 0.302 * [backup-simplify]: Simplify 1 into 1 0.302 * [backup-simplify]: Simplify (/ 1 1) into 1 0.302 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.303 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.303 * [backup-simplify]: Simplify (- 1) into -1 0.303 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.304 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.305 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 0.305 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.306 * [backup-simplify]: Simplify (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))))) 0.307 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.307 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.308 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.308 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.308 * [backup-simplify]: Simplify (- 0) into 0 0.309 * [backup-simplify]: Simplify (+ 0 0) into 0 0.309 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.310 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.310 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.312 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.312 * [taylor]: Taking taylor expansion of 0 in k 0.312 * [backup-simplify]: Simplify 0 into 0 0.312 * [backup-simplify]: Simplify 0 into 0 0.312 * [backup-simplify]: Simplify 0 into 0 0.312 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.313 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.315 * [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 0.315 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.315 * [backup-simplify]: Simplify (- 0) into 0 0.315 * [backup-simplify]: Simplify (+ 0 0) into 0 0.316 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 0.317 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.317 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 0.319 * [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 0.319 * [taylor]: Taking taylor expansion of 0 in k 0.319 * [backup-simplify]: Simplify 0 into 0 0.319 * [backup-simplify]: Simplify 0 into 0 0.319 * [backup-simplify]: Simplify 0 into 0 0.319 * [backup-simplify]: Simplify 0 into 0 0.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.320 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.323 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 0.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.324 * [backup-simplify]: Simplify (- 0) into 0 0.324 * [backup-simplify]: Simplify (+ 0 0) into 0 0.325 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 0.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.328 * [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)))) 0.331 * [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))) 0.331 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.331 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.331 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.331 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.331 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.331 * [taylor]: Taking taylor expansion of 0.5 in k 0.331 * [backup-simplify]: Simplify 0.5 into 0.5 0.331 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.331 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.331 * [taylor]: Taking taylor expansion of k in k 0.331 * [backup-simplify]: Simplify 0 into 0 0.331 * [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))) 0.332 * [backup-simplify]: Simplify (+ 1 0) into 1 0.332 * [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 0.333 * [backup-simplify]: Simplify PI into PI 0.333 * [taylor]: Taking taylor expansion of n in n 0.333 * [backup-simplify]: Simplify 0 into 0 0.333 * [backup-simplify]: Simplify 1 into 1 0.333 * [backup-simplify]: Simplify (/ PI 1) into PI 0.333 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.334 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.334 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.334 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.335 * [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 0.337 * [taylor]: Taking taylor expansion of -2.0 in n 0.337 * [backup-simplify]: Simplify -2.0 into -2.0 0.337 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.337 * [taylor]: Taking taylor expansion of PI in n 0.337 * [backup-simplify]: Simplify PI into PI 0.337 * [taylor]: Taking taylor expansion of n in n 0.337 * [backup-simplify]: Simplify 0 into 0 0.337 * [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) 0.338 * [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)) 0.339 * [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))))) 0.345 * [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 (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.346 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.347 * [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 0.351 * [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 0.356 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.362 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 0.364 * [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 0.364 * [taylor]: Taking taylor expansion of 0 in k 0.364 * [backup-simplify]: Simplify 0 into 0 0.364 * [backup-simplify]: Simplify 0 into 0 0.364 * [backup-simplify]: Simplify 0 into 0 0.364 * [backup-simplify]: Simplify 0 into 0 0.364 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.365 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.368 * [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 0.368 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.368 * [backup-simplify]: Simplify (+ 0 0) into 0 0.369 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.370 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.371 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 0.373 * [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 0.373 * [taylor]: Taking taylor expansion of 0 in k 0.373 * [backup-simplify]: Simplify 0 into 0 0.373 * [backup-simplify]: Simplify 0 into 0 0.373 * [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)))))) 0.374 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.374 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.374 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.374 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.374 * [taylor]: Taking taylor expansion of 2.0 in n 0.374 * [backup-simplify]: Simplify 2.0 into 2.0 0.374 * [taylor]: Taking taylor expansion of (* n PI) in n 0.374 * [taylor]: Taking taylor expansion of n in n 0.374 * [backup-simplify]: Simplify 0 into 0 0.374 * [backup-simplify]: Simplify 1 into 1 0.374 * [taylor]: Taking taylor expansion of PI in n 0.374 * [backup-simplify]: Simplify PI into PI 0.374 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.374 * [taylor]: Taking taylor expansion of 2.0 in n 0.374 * [backup-simplify]: Simplify 2.0 into 2.0 0.374 * [taylor]: Taking taylor expansion of (* n PI) in n 0.374 * [taylor]: Taking taylor expansion of n in n 0.374 * [backup-simplify]: Simplify 0 into 0 0.374 * [backup-simplify]: Simplify 1 into 1 0.374 * [taylor]: Taking taylor expansion of PI in n 0.374 * [backup-simplify]: Simplify PI into PI 0.374 * [backup-simplify]: Simplify (* 0 PI) into 0 0.375 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.375 * [backup-simplify]: Simplify 0 into 0 0.376 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.377 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.377 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.378 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.378 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.378 * [backup-simplify]: Simplify 0 into 0 0.379 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.379 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.380 * [backup-simplify]: Simplify 0 into 0 0.380 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.381 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.381 * [backup-simplify]: Simplify 0 into 0 0.382 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.383 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 0.383 * [backup-simplify]: Simplify 0 into 0 0.383 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.384 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.384 * [backup-simplify]: Simplify 0 into 0 0.385 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.386 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.386 * [backup-simplify]: Simplify 0 into 0 0.387 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.387 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 0.387 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.387 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.387 * [taylor]: Taking taylor expansion of 2.0 in n 0.387 * [backup-simplify]: Simplify 2.0 into 2.0 0.387 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.387 * [taylor]: Taking taylor expansion of PI in n 0.387 * [backup-simplify]: Simplify PI into PI 0.387 * [taylor]: Taking taylor expansion of n in n 0.387 * [backup-simplify]: Simplify 0 into 0 0.387 * [backup-simplify]: Simplify 1 into 1 0.387 * [backup-simplify]: Simplify (/ PI 1) into PI 0.388 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.388 * [taylor]: Taking taylor expansion of 2.0 in n 0.388 * [backup-simplify]: Simplify 2.0 into 2.0 0.388 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.388 * [taylor]: Taking taylor expansion of PI in n 0.388 * [backup-simplify]: Simplify PI into PI 0.388 * [taylor]: Taking taylor expansion of n in n 0.388 * [backup-simplify]: Simplify 0 into 0 0.388 * [backup-simplify]: Simplify 1 into 1 0.388 * [backup-simplify]: Simplify (/ PI 1) into PI 0.388 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.389 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.389 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.389 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.390 * [backup-simplify]: Simplify 0 into 0 0.390 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.391 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.391 * [backup-simplify]: Simplify 0 into 0 0.391 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.392 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.392 * [backup-simplify]: Simplify 0 into 0 0.392 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.393 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 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)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.395 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 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)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.396 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 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 (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.397 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.397 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.397 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.397 * [taylor]: Taking taylor expansion of -2.0 in n 0.397 * [backup-simplify]: Simplify -2.0 into -2.0 0.397 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.397 * [taylor]: Taking taylor expansion of PI in n 0.397 * [backup-simplify]: Simplify PI into PI 0.397 * [taylor]: Taking taylor expansion of n in n 0.397 * [backup-simplify]: Simplify 0 into 0 0.397 * [backup-simplify]: Simplify 1 into 1 0.397 * [backup-simplify]: Simplify (/ PI 1) into PI 0.397 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.397 * [taylor]: Taking taylor expansion of -2.0 in n 0.397 * [backup-simplify]: Simplify -2.0 into -2.0 0.397 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.397 * [taylor]: Taking taylor expansion of PI in n 0.397 * [backup-simplify]: Simplify PI into PI 0.397 * [taylor]: Taking taylor expansion of n in n 0.397 * [backup-simplify]: Simplify 0 into 0 0.397 * [backup-simplify]: Simplify 1 into 1 0.398 * [backup-simplify]: Simplify (/ PI 1) into PI 0.398 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.398 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.399 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.399 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.399 * [backup-simplify]: Simplify 0 into 0 0.400 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.400 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.401 * [backup-simplify]: Simplify 0 into 0 0.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.402 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.402 * [backup-simplify]: Simplify 0 into 0 0.402 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.403 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.403 * [backup-simplify]: Simplify 0 into 0 0.404 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.404 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.404 * [backup-simplify]: Simplify 0 into 0 0.405 * [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 0.406 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.406 * [backup-simplify]: Simplify 0 into 0 0.406 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.406 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.406 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.406 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.406 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.407 * [taylor]: Taking taylor expansion of 1.0 in k 0.407 * [backup-simplify]: Simplify 1.0 into 1.0 0.407 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.407 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.407 * [taylor]: Taking taylor expansion of k in k 0.407 * [backup-simplify]: Simplify 0 into 0 0.407 * [backup-simplify]: Simplify 1 into 1 0.407 * [backup-simplify]: Simplify (/ 1 1) into 1 0.407 * [backup-simplify]: Simplify (sqrt 0) into 0 0.408 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.408 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.408 * [taylor]: Taking taylor expansion of 1.0 in k 0.408 * [backup-simplify]: Simplify 1.0 into 1.0 0.408 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.408 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.408 * [taylor]: Taking taylor expansion of k in k 0.408 * [backup-simplify]: Simplify 0 into 0 0.408 * [backup-simplify]: Simplify 1 into 1 0.408 * [backup-simplify]: Simplify (/ 1 1) into 1 0.409 * [backup-simplify]: Simplify (sqrt 0) into 0 0.409 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.410 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.410 * [backup-simplify]: Simplify 0 into 0 0.410 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.411 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.411 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.413 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.414 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.415 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.415 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.417 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.418 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.419 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.420 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 0.420 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 0.420 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.420 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.420 * [taylor]: Taking taylor expansion of 1.0 in k 0.420 * [backup-simplify]: Simplify 1.0 into 1.0 0.420 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.420 * [taylor]: Taking taylor expansion of k in k 0.420 * [backup-simplify]: Simplify 0 into 0 0.420 * [backup-simplify]: Simplify 1 into 1 0.420 * [backup-simplify]: Simplify (sqrt 0) into 0 0.421 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.421 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.421 * [taylor]: Taking taylor expansion of 1.0 in k 0.421 * [backup-simplify]: Simplify 1.0 into 1.0 0.421 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.421 * [taylor]: Taking taylor expansion of k in k 0.421 * [backup-simplify]: Simplify 0 into 0 0.421 * [backup-simplify]: Simplify 1 into 1 0.421 * [backup-simplify]: Simplify (sqrt 0) into 0 0.422 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.422 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.422 * [backup-simplify]: Simplify 0 into 0 0.423 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.423 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.425 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.426 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.427 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.429 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.430 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.430 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.431 * [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)))))))) 0.432 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.432 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.432 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.432 * [taylor]: Taking taylor expansion of 1.0 in k 0.432 * [backup-simplify]: Simplify 1.0 into 1.0 0.432 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.432 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.432 * [taylor]: Taking taylor expansion of -1 in k 0.432 * [backup-simplify]: Simplify -1 into -1 0.432 * [taylor]: Taking taylor expansion of k in k 0.432 * [backup-simplify]: Simplify 0 into 0 0.432 * [backup-simplify]: Simplify 1 into 1 0.432 * [backup-simplify]: Simplify (/ -1 1) into -1 0.432 * [backup-simplify]: Simplify (sqrt 0) into 0 0.433 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.433 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.433 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.433 * [taylor]: Taking taylor expansion of 1.0 in k 0.433 * [backup-simplify]: Simplify 1.0 into 1.0 0.433 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.433 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.433 * [taylor]: Taking taylor expansion of -1 in k 0.433 * [backup-simplify]: Simplify -1 into -1 0.433 * [taylor]: Taking taylor expansion of k in k 0.433 * [backup-simplify]: Simplify 0 into 0 0.433 * [backup-simplify]: Simplify 1 into 1 0.434 * [backup-simplify]: Simplify (/ -1 1) into -1 0.434 * [backup-simplify]: Simplify (sqrt 0) into 0 0.435 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.435 * [backup-simplify]: Simplify (/ 1.0 +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)))) into 0 0.437 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.438 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 0.439 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.439 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.441 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.444 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 0.444 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.445 * [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))))) 0.445 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.445 * [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))))) 0.445 * [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 0.445 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.445 * [taylor]: Taking taylor expansion of 1.0 in n 0.445 * [backup-simplify]: Simplify 1.0 into 1.0 0.445 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.445 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.445 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.445 * [taylor]: Taking taylor expansion of k in n 0.445 * [backup-simplify]: Simplify k into k 0.445 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.445 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 0.445 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.445 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 0.445 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.446 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.446 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.446 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.446 * [taylor]: Taking taylor expansion of 0.5 in n 0.446 * [backup-simplify]: Simplify 0.5 into 0.5 0.446 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.446 * [taylor]: Taking taylor expansion of 1.0 in n 0.446 * [backup-simplify]: Simplify 1.0 into 1.0 0.446 * [taylor]: Taking taylor expansion of k in n 0.446 * [backup-simplify]: Simplify k into k 0.446 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.446 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.446 * [taylor]: Taking taylor expansion of 2.0 in n 0.446 * [backup-simplify]: Simplify 2.0 into 2.0 0.446 * [taylor]: Taking taylor expansion of (* n PI) in n 0.446 * [taylor]: Taking taylor expansion of n in n 0.446 * [backup-simplify]: Simplify 0 into 0 0.446 * [backup-simplify]: Simplify 1 into 1 0.446 * [taylor]: Taking taylor expansion of PI in n 0.446 * [backup-simplify]: Simplify PI into PI 0.446 * [backup-simplify]: Simplify (* 0 PI) into 0 0.446 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.447 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.448 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.449 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.449 * [backup-simplify]: Simplify (- k) into (- k) 0.449 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.449 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.450 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.456 * [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)))) 0.457 * [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))))) 0.457 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.457 * [taylor]: Taking taylor expansion of 1.0 in k 0.457 * [backup-simplify]: Simplify 1.0 into 1.0 0.457 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.457 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.457 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.457 * [taylor]: Taking taylor expansion of k in k 0.457 * [backup-simplify]: Simplify 0 into 0 0.457 * [backup-simplify]: Simplify 1 into 1 0.458 * [backup-simplify]: Simplify (/ 1 1) into 1 0.458 * [backup-simplify]: Simplify (sqrt 0) into 0 0.459 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.459 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.459 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.459 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.459 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.459 * [taylor]: Taking taylor expansion of 0.5 in k 0.459 * [backup-simplify]: Simplify 0.5 into 0.5 0.459 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.459 * [taylor]: Taking taylor expansion of 1.0 in k 0.459 * [backup-simplify]: Simplify 1.0 into 1.0 0.459 * [taylor]: Taking taylor expansion of k in k 0.459 * [backup-simplify]: Simplify 0 into 0 0.459 * [backup-simplify]: Simplify 1 into 1 0.459 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.459 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.459 * [taylor]: Taking taylor expansion of 2.0 in k 0.459 * [backup-simplify]: Simplify 2.0 into 2.0 0.459 * [taylor]: Taking taylor expansion of (* n PI) in k 0.459 * [taylor]: Taking taylor expansion of n in k 0.459 * [backup-simplify]: Simplify n into n 0.459 * [taylor]: Taking taylor expansion of PI in k 0.459 * [backup-simplify]: Simplify PI into PI 0.459 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.459 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.459 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.459 * [backup-simplify]: Simplify (- 0) into 0 0.460 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.460 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.460 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.460 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.460 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.460 * [taylor]: Taking taylor expansion of 1.0 in k 0.460 * [backup-simplify]: Simplify 1.0 into 1.0 0.460 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.460 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.460 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.460 * [taylor]: Taking taylor expansion of k in k 0.460 * [backup-simplify]: Simplify 0 into 0 0.460 * [backup-simplify]: Simplify 1 into 1 0.461 * [backup-simplify]: Simplify (/ 1 1) into 1 0.461 * [backup-simplify]: Simplify (sqrt 0) into 0 0.461 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.461 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.462 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.462 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.462 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.462 * [taylor]: Taking taylor expansion of 0.5 in k 0.462 * [backup-simplify]: Simplify 0.5 into 0.5 0.462 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.462 * [taylor]: Taking taylor expansion of 1.0 in k 0.462 * [backup-simplify]: Simplify 1.0 into 1.0 0.462 * [taylor]: Taking taylor expansion of k in k 0.462 * [backup-simplify]: Simplify 0 into 0 0.462 * [backup-simplify]: Simplify 1 into 1 0.462 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.462 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.462 * [taylor]: Taking taylor expansion of 2.0 in k 0.462 * [backup-simplify]: Simplify 2.0 into 2.0 0.462 * [taylor]: Taking taylor expansion of (* n PI) in k 0.462 * [taylor]: Taking taylor expansion of n in k 0.462 * [backup-simplify]: Simplify n into n 0.462 * [taylor]: Taking taylor expansion of PI in k 0.462 * [backup-simplify]: Simplify PI into PI 0.462 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.462 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.462 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.462 * [backup-simplify]: Simplify (- 0) into 0 0.462 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.463 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.463 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.463 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.463 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 0.463 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.463 * [taylor]: Taking taylor expansion of 0 in n 0.463 * [backup-simplify]: Simplify 0 into 0 0.463 * [backup-simplify]: Simplify 0 into 0 0.464 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 0.464 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 0.465 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 0.465 * [backup-simplify]: Simplify (- 1) into -1 0.465 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.466 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 0.466 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 0.467 * [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))) 0.468 * [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))) 0.469 * [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))) 0.469 * [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 0.469 * [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 0.469 * [taylor]: Taking taylor expansion of +nan.0 in n 0.469 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.469 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.469 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.469 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.469 * [taylor]: Taking taylor expansion of 0.5 in n 0.469 * [backup-simplify]: Simplify 0.5 into 0.5 0.469 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.469 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.469 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.469 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.469 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.469 * [taylor]: Taking taylor expansion of 1.0 in n 0.469 * [backup-simplify]: Simplify 1.0 into 1.0 0.469 * [taylor]: Taking taylor expansion of (log PI) in n 0.469 * [taylor]: Taking taylor expansion of PI in n 0.469 * [backup-simplify]: Simplify PI into PI 0.469 * [backup-simplify]: Simplify (log PI) into (log PI) 0.470 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.471 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.471 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.471 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.471 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.471 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.471 * [taylor]: Taking taylor expansion of 1.0 in n 0.471 * [backup-simplify]: Simplify 1.0 into 1.0 0.471 * [taylor]: Taking taylor expansion of (log n) in n 0.471 * [taylor]: Taking taylor expansion of n in n 0.471 * [backup-simplify]: Simplify 0 into 0 0.471 * [backup-simplify]: Simplify 1 into 1 0.471 * [backup-simplify]: Simplify (log 1) into 0 0.472 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.472 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.472 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.472 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.472 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.472 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.472 * [taylor]: Taking taylor expansion of 1.0 in n 0.472 * [backup-simplify]: Simplify 1.0 into 1.0 0.472 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.472 * [taylor]: Taking taylor expansion of 2.0 in n 0.472 * [backup-simplify]: Simplify 2.0 into 2.0 0.472 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.473 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.473 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.474 * [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) 0.475 * [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) 0.475 * [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)) 0.476 * [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))) 0.477 * [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) 0.478 * [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)) 0.479 * [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))) 0.480 * [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))) 0.480 * [backup-simplify]: Simplify 0 into 0 0.480 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 0.481 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 0.482 * [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 0.482 * [backup-simplify]: Simplify (- 0) into 0 0.482 * [backup-simplify]: Simplify (+ 0 0) into 0 0.483 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.483 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 0.484 * [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))) 0.485 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.486 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.488 * [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)))))))) 0.491 * [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)))))))) 0.491 * [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 0.491 * [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 0.491 * [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 0.491 * [taylor]: Taking taylor expansion of +nan.0 in n 0.491 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.491 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.491 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.491 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.492 * [taylor]: Taking taylor expansion of 0.5 in n 0.492 * [backup-simplify]: Simplify 0.5 into 0.5 0.492 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.492 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.492 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.492 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.492 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.492 * [taylor]: Taking taylor expansion of 1.0 in n 0.492 * [backup-simplify]: Simplify 1.0 into 1.0 0.492 * [taylor]: Taking taylor expansion of (log 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) 0.493 * [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) (pow 2.0 1.0)) in n 0.493 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.494 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.494 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.494 * [taylor]: Taking taylor expansion of 1.0 in n 0.494 * [backup-simplify]: Simplify 1.0 into 1.0 0.494 * [taylor]: Taking taylor expansion of (log n) in n 0.494 * [taylor]: Taking taylor expansion of n in n 0.494 * [backup-simplify]: Simplify 0 into 0 0.494 * [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 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.494 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.494 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.494 * [taylor]: Taking taylor expansion of 1.0 in n 0.494 * [backup-simplify]: Simplify 1.0 into 1.0 0.494 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.494 * [taylor]: Taking taylor expansion of 2.0 in n 0.494 * [backup-simplify]: Simplify 2.0 into 2.0 0.495 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.495 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.496 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.496 * [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) 0.497 * [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) 0.498 * [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)) 0.499 * [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))) 0.500 * [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) 0.500 * [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 0.500 * [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 0.500 * [taylor]: Taking taylor expansion of +nan.0 in n 0.500 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.500 * [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 0.500 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.500 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.500 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.500 * [taylor]: Taking taylor expansion of 0.5 in n 0.500 * [backup-simplify]: Simplify 0.5 into 0.5 0.500 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.500 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.500 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.500 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.500 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.500 * [taylor]: Taking taylor expansion of 1.0 in n 0.500 * [backup-simplify]: Simplify 1.0 into 1.0 0.500 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.500 * [taylor]: Taking taylor expansion of 2.0 in n 0.500 * [backup-simplify]: Simplify 2.0 into 2.0 0.500 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.501 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.502 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.502 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.502 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.502 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.502 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.502 * [taylor]: Taking taylor expansion of 1.0 in n 0.502 * [backup-simplify]: Simplify 1.0 into 1.0 0.502 * [taylor]: Taking taylor expansion of (log PI) in n 0.502 * [taylor]: Taking taylor expansion of PI in n 0.502 * [backup-simplify]: Simplify PI into PI 0.502 * [backup-simplify]: Simplify (log PI) into (log PI) 0.503 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.503 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.503 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.504 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.504 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.504 * [taylor]: Taking taylor expansion of 1.0 in n 0.504 * [backup-simplify]: Simplify 1.0 into 1.0 0.504 * [taylor]: Taking taylor expansion of (log n) in n 0.504 * [taylor]: Taking taylor expansion of n in n 0.504 * [backup-simplify]: Simplify 0 into 0 0.504 * [backup-simplify]: Simplify 1 into 1 0.504 * [backup-simplify]: Simplify (log 1) into 0 0.504 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.504 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.504 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.505 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.505 * [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) 0.506 * [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)) 0.507 * [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))) 0.508 * [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) 0.508 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.508 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.508 * [taylor]: Taking taylor expansion of 2.0 in n 0.508 * [backup-simplify]: Simplify 2.0 into 2.0 0.508 * [taylor]: Taking taylor expansion of (* n PI) in n 0.508 * [taylor]: Taking taylor expansion of n in n 0.508 * [backup-simplify]: Simplify 0 into 0 0.508 * [backup-simplify]: Simplify 1 into 1 0.508 * [taylor]: Taking taylor expansion of PI in n 0.508 * [backup-simplify]: Simplify PI into PI 0.508 * [backup-simplify]: Simplify (* 0 PI) into 0 0.508 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.509 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.510 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.511 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.512 * [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)) 0.513 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.514 * [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)) 0.516 * [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))) 0.517 * [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)))))) 0.521 * [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)))))))) 0.524 * [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)))))))) 0.528 * [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)))))))) 0.529 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 0.530 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 0.531 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 0.531 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 0.532 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.532 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.533 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 0.533 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 0.534 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 0.534 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 0.535 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 0.536 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 0.537 * [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 0.538 * [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 0.540 * [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 0.541 * [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 0.541 * [backup-simplify]: Simplify (- 0) into 0 0.541 * [backup-simplify]: Simplify 0 into 0 0.541 * [backup-simplify]: Simplify 0 into 0 0.542 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.542 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 0.544 * [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 0.544 * [backup-simplify]: Simplify (- 0) into 0 0.544 * [backup-simplify]: Simplify (+ 0 0) into 0 0.545 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 0.546 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 0.547 * [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))) 0.548 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.550 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.559 * [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)))))))) 0.565 * [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)))))))) 0.565 * [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 0.565 * [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 0.565 * [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 0.565 * [taylor]: Taking taylor expansion of +nan.0 in n 0.565 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.565 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.565 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.565 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.565 * [taylor]: Taking taylor expansion of 0.5 in n 0.565 * [backup-simplify]: Simplify 0.5 into 0.5 0.565 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.565 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.565 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.565 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.565 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) 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 2.0) in n 0.565 * [taylor]: Taking taylor expansion of 2.0 in n 0.565 * [backup-simplify]: Simplify 2.0 into 2.0 0.566 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.566 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.567 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.567 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.567 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.567 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.567 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.567 * [taylor]: Taking taylor expansion of 1.0 in n 0.567 * [backup-simplify]: Simplify 1.0 into 1.0 0.567 * [taylor]: Taking taylor expansion of (log n) in n 0.567 * [taylor]: Taking taylor expansion of n in n 0.567 * [backup-simplify]: Simplify 0 into 0 0.567 * [backup-simplify]: Simplify 1 into 1 0.567 * [backup-simplify]: Simplify (log 1) into 0 0.568 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.568 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.568 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.568 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.568 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.568 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.568 * [taylor]: Taking taylor expansion of 1.0 in n 0.568 * [backup-simplify]: Simplify 1.0 into 1.0 0.568 * [taylor]: Taking taylor expansion of (log PI) in n 0.568 * [taylor]: Taking taylor expansion of PI in n 0.568 * [backup-simplify]: Simplify PI into PI 0.568 * [backup-simplify]: Simplify (log PI) into (log PI) 0.569 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.570 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.570 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.571 * [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) 0.572 * [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)) 0.572 * [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))) 0.573 * [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) 0.573 * [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 0.573 * [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 0.573 * [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 0.573 * [taylor]: Taking taylor expansion of +nan.0 in n 0.573 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.573 * [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 0.573 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.573 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.573 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.573 * [taylor]: Taking taylor expansion of 0.5 in n 0.574 * [backup-simplify]: Simplify 0.5 into 0.5 0.574 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.574 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.574 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.574 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.574 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) 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 2.0) in n 0.574 * [taylor]: Taking taylor expansion of 2.0 in n 0.574 * [backup-simplify]: Simplify 2.0 into 2.0 0.574 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.574 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.575 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.575 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.575 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.575 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.575 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.575 * [taylor]: Taking taylor expansion of 1.0 in n 0.575 * [backup-simplify]: Simplify 1.0 into 1.0 0.575 * [taylor]: Taking taylor expansion of (log PI) in n 0.575 * [taylor]: Taking taylor expansion of PI in n 0.576 * [backup-simplify]: Simplify PI into PI 0.576 * [backup-simplify]: Simplify (log PI) into (log PI) 0.576 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.577 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.577 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.577 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.577 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.577 * [taylor]: Taking taylor expansion of 1.0 in n 0.577 * [backup-simplify]: Simplify 1.0 into 1.0 0.577 * [taylor]: Taking taylor expansion of (log n) in n 0.577 * [taylor]: Taking taylor expansion of n in n 0.577 * [backup-simplify]: Simplify 0 into 0 0.577 * [backup-simplify]: Simplify 1 into 1 0.578 * [backup-simplify]: Simplify (log 1) into 0 0.578 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.578 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.578 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.579 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.579 * [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) 0.580 * [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)) 0.581 * [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))) 0.582 * [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) 0.582 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.582 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.582 * [taylor]: Taking taylor expansion of 2.0 in n 0.582 * [backup-simplify]: Simplify 2.0 into 2.0 0.582 * [taylor]: Taking taylor expansion of (* n PI) in n 0.582 * [taylor]: Taking taylor expansion of n in n 0.582 * [backup-simplify]: Simplify 0 into 0 0.582 * [backup-simplify]: Simplify 1 into 1 0.582 * [taylor]: Taking taylor expansion of PI in n 0.582 * [backup-simplify]: Simplify PI into PI 0.582 * [backup-simplify]: Simplify (* 0 PI) into 0 0.583 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.583 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.584 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.585 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.585 * [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 0.585 * [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 0.585 * [taylor]: Taking taylor expansion of +nan.0 in n 0.585 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.585 * [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 0.585 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.585 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.585 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.585 * [taylor]: Taking taylor expansion of 0.5 in n 0.585 * [backup-simplify]: Simplify 0.5 into 0.5 0.585 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.585 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.585 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.585 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.585 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.585 * [taylor]: Taking taylor expansion of 1.0 in n 0.585 * [backup-simplify]: Simplify 1.0 into 1.0 0.585 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.585 * [taylor]: Taking taylor expansion of 2.0 in n 0.585 * [backup-simplify]: Simplify 2.0 into 2.0 0.586 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.586 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.587 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.587 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.587 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.587 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.587 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.587 * [taylor]: Taking taylor expansion of 1.0 in n 0.587 * [backup-simplify]: Simplify 1.0 into 1.0 0.587 * [taylor]: Taking taylor expansion of (log PI) in n 0.587 * [taylor]: Taking taylor expansion of PI in n 0.587 * [backup-simplify]: Simplify PI into PI 0.587 * [backup-simplify]: Simplify (log PI) into (log PI) 0.588 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.589 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.589 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.589 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.589 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.589 * [taylor]: Taking taylor expansion of 1.0 in n 0.589 * [backup-simplify]: Simplify 1.0 into 1.0 0.589 * [taylor]: Taking taylor expansion of (log n) in n 0.589 * [taylor]: Taking taylor expansion of n in n 0.589 * [backup-simplify]: Simplify 0 into 0 0.589 * [backup-simplify]: Simplify 1 into 1 0.589 * [backup-simplify]: Simplify (log 1) into 0 0.589 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.590 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.590 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.590 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.591 * [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) 0.592 * [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)) 0.592 * [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))) 0.593 * [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) 0.593 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.593 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.593 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.593 * [taylor]: Taking taylor expansion of 2.0 in n 0.593 * [backup-simplify]: Simplify 2.0 into 2.0 0.593 * [taylor]: Taking taylor expansion of (* n PI) in n 0.593 * [taylor]: Taking taylor expansion of n in n 0.593 * [backup-simplify]: Simplify 0 into 0 0.593 * [backup-simplify]: Simplify 1 into 1 0.593 * [taylor]: Taking taylor expansion of PI in n 0.593 * [backup-simplify]: Simplify PI into PI 0.594 * [backup-simplify]: Simplify (* 0 PI) into 0 0.594 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.595 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.596 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.596 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.597 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.598 * [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)) 0.599 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.600 * [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)) 0.602 * [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))) 0.603 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.604 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.605 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 0.606 * [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)) 0.608 * [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))) 0.610 * [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)))))))) 0.616 * [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)))))))))))) 0.625 * [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)))))))))))) 0.634 * [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)))))))))))))) 0.643 * [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)))))))))))))) 0.657 * [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)))))))))))))) 0.672 * [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)))))))))))))))))))))) 0.673 * [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)))))) 0.673 * [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 0.673 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.673 * [taylor]: Taking taylor expansion of 1.0 in n 0.673 * [backup-simplify]: Simplify 1.0 into 1.0 0.673 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.673 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.673 * [taylor]: Taking taylor expansion of k in n 0.673 * [backup-simplify]: Simplify k into k 0.673 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 0.673 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 0.673 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.673 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.673 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.673 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.673 * [taylor]: Taking taylor expansion of 0.5 in n 0.673 * [backup-simplify]: Simplify 0.5 into 0.5 0.673 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.673 * [taylor]: Taking taylor expansion of 1.0 in n 0.673 * [backup-simplify]: Simplify 1.0 into 1.0 0.673 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.673 * [taylor]: Taking taylor expansion of k in n 0.673 * [backup-simplify]: Simplify k into k 0.673 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.673 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.673 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.673 * [taylor]: Taking taylor expansion of 2.0 in n 0.673 * [backup-simplify]: Simplify 2.0 into 2.0 0.673 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.673 * [taylor]: Taking taylor expansion of PI in n 0.673 * [backup-simplify]: Simplify PI into PI 0.673 * [taylor]: Taking taylor expansion of n in n 0.673 * [backup-simplify]: Simplify 0 into 0 0.673 * [backup-simplify]: Simplify 1 into 1 0.674 * [backup-simplify]: Simplify (/ PI 1) into PI 0.674 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.675 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.675 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.675 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.675 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.676 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.676 * [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)))) 0.677 * [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))))) 0.677 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.677 * [taylor]: Taking taylor expansion of 1.0 in k 0.677 * [backup-simplify]: Simplify 1.0 into 1.0 0.677 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.677 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.677 * [taylor]: Taking taylor expansion of k in k 0.677 * [backup-simplify]: Simplify 0 into 0 0.677 * [backup-simplify]: Simplify 1 into 1 0.677 * [backup-simplify]: Simplify (sqrt 0) into 0 0.678 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.678 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.678 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.679 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.679 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.679 * [taylor]: Taking taylor expansion of 0.5 in k 0.679 * [backup-simplify]: Simplify 0.5 into 0.5 0.679 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.679 * [taylor]: Taking taylor expansion of 1.0 in k 0.679 * [backup-simplify]: Simplify 1.0 into 1.0 0.679 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.679 * [taylor]: Taking taylor expansion of k in k 0.679 * [backup-simplify]: Simplify 0 into 0 0.679 * [backup-simplify]: Simplify 1 into 1 0.679 * [backup-simplify]: Simplify (/ 1 1) into 1 0.679 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.679 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.679 * [taylor]: Taking taylor expansion of 2.0 in k 0.679 * [backup-simplify]: Simplify 2.0 into 2.0 0.679 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.679 * [taylor]: Taking taylor expansion of PI in k 0.679 * [backup-simplify]: Simplify PI into PI 0.679 * [taylor]: Taking taylor expansion of n in k 0.679 * [backup-simplify]: Simplify n into n 0.679 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.679 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.679 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.679 * [backup-simplify]: Simplify (- 1) into -1 0.680 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.680 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.680 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.680 * [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))))) 0.680 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.680 * [taylor]: Taking taylor expansion of 1.0 in k 0.680 * [backup-simplify]: Simplify 1.0 into 1.0 0.680 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.680 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.680 * [taylor]: Taking taylor expansion of k in k 0.680 * [backup-simplify]: Simplify 0 into 0 0.680 * [backup-simplify]: Simplify 1 into 1 0.681 * [backup-simplify]: Simplify (sqrt 0) into 0 0.681 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.681 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.681 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.681 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.681 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.681 * [taylor]: Taking taylor expansion of 0.5 in k 0.681 * [backup-simplify]: Simplify 0.5 into 0.5 0.682 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.682 * [taylor]: Taking taylor expansion of 1.0 in k 0.682 * [backup-simplify]: Simplify 1.0 into 1.0 0.682 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.682 * [taylor]: Taking taylor expansion of k in k 0.682 * [backup-simplify]: Simplify 0 into 0 0.682 * [backup-simplify]: Simplify 1 into 1 0.682 * [backup-simplify]: Simplify (/ 1 1) into 1 0.682 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.682 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.682 * [taylor]: Taking taylor expansion of 2.0 in k 0.682 * [backup-simplify]: Simplify 2.0 into 2.0 0.682 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.682 * [taylor]: Taking taylor expansion of PI in k 0.682 * [backup-simplify]: Simplify PI into PI 0.682 * [taylor]: Taking taylor expansion of n in k 0.682 * [backup-simplify]: Simplify n into n 0.682 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.682 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.682 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.682 * [backup-simplify]: Simplify (- 1) into -1 0.683 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.683 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.683 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.683 * [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))))) 0.683 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 0.684 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.684 * [taylor]: Taking taylor expansion of 0 in n 0.684 * [backup-simplify]: Simplify 0 into 0 0.684 * [backup-simplify]: Simplify 0 into 0 0.684 * [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))))))) 0.684 * [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))))))) 0.684 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.684 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.684 * [taylor]: Taking taylor expansion of +nan.0 in n 0.685 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.685 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.685 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.685 * [taylor]: Taking taylor expansion of 0.5 in n 0.685 * [backup-simplify]: Simplify 0.5 into 0.5 0.685 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.685 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.685 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.685 * [taylor]: Taking taylor expansion of 2.0 in n 0.685 * [backup-simplify]: Simplify 2.0 into 2.0 0.685 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.685 * [taylor]: Taking taylor expansion of PI in n 0.685 * [backup-simplify]: Simplify PI into PI 0.685 * [taylor]: Taking taylor expansion of n in n 0.685 * [backup-simplify]: Simplify 0 into 0 0.685 * [backup-simplify]: Simplify 1 into 1 0.685 * [backup-simplify]: Simplify (/ PI 1) into PI 0.685 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.686 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.686 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.686 * [taylor]: Taking taylor expansion of 1.0 in n 0.686 * [backup-simplify]: Simplify 1.0 into 1.0 0.686 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.686 * [taylor]: Taking taylor expansion of k in n 0.686 * [backup-simplify]: Simplify k into k 0.686 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.687 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.687 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.687 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.688 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.688 * [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)))) 0.689 * [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))))) 0.690 * [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)))))) 0.691 * [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))))))) 0.691 * [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))))))) 0.691 * [backup-simplify]: Simplify 0 into 0 0.693 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.694 * [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))))))) 0.694 * [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))))))) 0.694 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.694 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.694 * [taylor]: Taking taylor expansion of +nan.0 in n 0.694 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.694 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.695 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.695 * [taylor]: Taking taylor expansion of 0.5 in n 0.695 * [backup-simplify]: Simplify 0.5 into 0.5 0.695 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.695 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.695 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.695 * [taylor]: Taking taylor expansion of 2.0 in n 0.695 * [backup-simplify]: Simplify 2.0 into 2.0 0.695 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.695 * [taylor]: Taking taylor expansion of PI in n 0.695 * [backup-simplify]: Simplify PI into PI 0.695 * [taylor]: Taking taylor expansion of n in n 0.695 * [backup-simplify]: Simplify 0 into 0 0.695 * [backup-simplify]: Simplify 1 into 1 0.695 * [backup-simplify]: Simplify (/ PI 1) into PI 0.695 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.696 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.696 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.696 * [taylor]: Taking taylor expansion of 1.0 in n 0.696 * [backup-simplify]: Simplify 1.0 into 1.0 0.696 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.696 * [taylor]: Taking taylor expansion of k in n 0.696 * [backup-simplify]: Simplify k into k 0.696 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.697 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.697 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.697 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.698 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.698 * [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)))) 0.699 * [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))))) 0.700 * [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)))))) 0.701 * [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))))))) 0.701 * [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))))))) 0.702 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.702 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.703 * [backup-simplify]: Simplify (- 0) into 0 0.703 * [backup-simplify]: Simplify (+ 0 0) into 0 0.703 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.704 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.705 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.705 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.706 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 0.708 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.709 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 0.709 * [backup-simplify]: Simplify (- 0) into 0 0.709 * [backup-simplify]: Simplify 0 into 0 0.709 * [backup-simplify]: Simplify 0 into 0 0.711 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.712 * [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))))))) 0.713 * [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))))))) 0.713 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.713 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.713 * [taylor]: Taking taylor expansion of +nan.0 in n 0.713 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.713 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.713 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.713 * [taylor]: Taking taylor expansion of 0.5 in n 0.713 * [backup-simplify]: Simplify 0.5 into 0.5 0.713 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.713 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.713 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.713 * [taylor]: Taking taylor expansion of 2.0 in n 0.713 * [backup-simplify]: Simplify 2.0 into 2.0 0.713 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.713 * [taylor]: Taking taylor expansion of PI in n 0.713 * [backup-simplify]: Simplify PI into PI 0.713 * [taylor]: Taking taylor expansion of n in n 0.713 * [backup-simplify]: Simplify 0 into 0 0.713 * [backup-simplify]: Simplify 1 into 1 0.714 * [backup-simplify]: Simplify (/ PI 1) into PI 0.714 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.714 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.714 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.715 * [taylor]: Taking taylor expansion of 1.0 in n 0.715 * [backup-simplify]: Simplify 1.0 into 1.0 0.715 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.715 * [taylor]: Taking taylor expansion of k in n 0.715 * [backup-simplify]: Simplify k into k 0.715 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.715 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.716 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.716 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.716 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.717 * [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)))) 0.718 * [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))))) 0.719 * [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)))))) 0.719 * [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))))))) 0.720 * [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))))))) 0.723 * [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)))))))) 0.723 * [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)))) 0.724 * [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 0.724 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.724 * [taylor]: Taking taylor expansion of 1.0 in n 0.724 * [backup-simplify]: Simplify 1.0 into 1.0 0.724 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.724 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.724 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.724 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.724 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.724 * [taylor]: Taking taylor expansion of 0.5 in n 0.724 * [backup-simplify]: Simplify 0.5 into 0.5 0.724 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.724 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.724 * [taylor]: Taking taylor expansion of k in n 0.724 * [backup-simplify]: Simplify k into k 0.724 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.724 * [taylor]: Taking taylor expansion of 1.0 in n 0.724 * [backup-simplify]: Simplify 1.0 into 1.0 0.724 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.724 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.724 * [taylor]: Taking taylor expansion of -2.0 in n 0.724 * [backup-simplify]: Simplify -2.0 into -2.0 0.724 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.724 * [taylor]: Taking taylor expansion of PI in n 0.724 * [backup-simplify]: Simplify PI into PI 0.724 * [taylor]: Taking taylor expansion of n in n 0.724 * [backup-simplify]: Simplify 0 into 0 0.724 * [backup-simplify]: Simplify 1 into 1 0.724 * [backup-simplify]: Simplify (/ PI 1) into PI 0.725 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.725 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.725 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.725 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.726 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.727 * [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)))) 0.728 * [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))))) 0.728 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.728 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.728 * [taylor]: Taking taylor expansion of -1 in n 0.728 * [backup-simplify]: Simplify -1 into -1 0.728 * [taylor]: Taking taylor expansion of k in n 0.728 * [backup-simplify]: Simplify k into k 0.728 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 0.728 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 0.728 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 0.728 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 0.729 * [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))) 0.729 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.729 * [taylor]: Taking taylor expansion of 1.0 in k 0.729 * [backup-simplify]: Simplify 1.0 into 1.0 0.729 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.729 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.729 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.729 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.729 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.729 * [taylor]: Taking taylor expansion of 0.5 in k 0.729 * [backup-simplify]: Simplify 0.5 into 0.5 0.729 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.729 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.729 * [taylor]: Taking taylor expansion of k in k 0.729 * [backup-simplify]: Simplify 0 into 0 0.729 * [backup-simplify]: Simplify 1 into 1 0.729 * [backup-simplify]: Simplify (/ 1 1) into 1 0.729 * [taylor]: Taking taylor expansion of 1.0 in k 0.729 * [backup-simplify]: Simplify 1.0 into 1.0 0.729 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.729 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.730 * [taylor]: Taking taylor expansion of -2.0 in k 0.730 * [backup-simplify]: Simplify -2.0 into -2.0 0.730 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.730 * [taylor]: Taking taylor expansion of PI in k 0.730 * [backup-simplify]: Simplify PI into PI 0.730 * [taylor]: Taking taylor expansion of n in k 0.730 * [backup-simplify]: Simplify n into n 0.730 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.730 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.730 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.730 * [backup-simplify]: Simplify (+ 1 0) into 1 0.730 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.730 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.730 * [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)))))) 0.730 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.731 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.731 * [taylor]: Taking taylor expansion of -1 in k 0.731 * [backup-simplify]: Simplify -1 into -1 0.731 * [taylor]: Taking taylor expansion of k in k 0.731 * [backup-simplify]: Simplify 0 into 0 0.731 * [backup-simplify]: Simplify 1 into 1 0.731 * [backup-simplify]: Simplify (/ -1 1) into -1 0.731 * [backup-simplify]: Simplify (sqrt 0) into 0 0.732 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.732 * [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))))))) 0.732 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.732 * [taylor]: Taking taylor expansion of 1.0 in k 0.732 * [backup-simplify]: Simplify 1.0 into 1.0 0.732 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.732 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.732 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.732 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.732 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.732 * [taylor]: Taking taylor expansion of 0.5 in k 0.732 * [backup-simplify]: Simplify 0.5 into 0.5 0.732 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.732 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.732 * [taylor]: Taking taylor expansion of k in k 0.732 * [backup-simplify]: Simplify 0 into 0 0.732 * [backup-simplify]: Simplify 1 into 1 0.733 * [backup-simplify]: Simplify (/ 1 1) into 1 0.733 * [taylor]: Taking taylor expansion of 1.0 in k 0.733 * [backup-simplify]: Simplify 1.0 into 1.0 0.733 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.733 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.733 * [taylor]: Taking taylor expansion of -2.0 in k 0.733 * [backup-simplify]: Simplify -2.0 into -2.0 0.733 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.733 * [taylor]: Taking taylor expansion of PI in k 0.733 * [backup-simplify]: Simplify PI into PI 0.733 * [taylor]: Taking taylor expansion of n in k 0.733 * [backup-simplify]: Simplify n into n 0.733 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.733 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.733 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.733 * [backup-simplify]: Simplify (+ 1 0) into 1 0.733 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.733 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.734 * [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)))))) 0.734 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.734 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.734 * [taylor]: Taking taylor expansion of -1 in k 0.734 * [backup-simplify]: Simplify -1 into -1 0.734 * [taylor]: Taking taylor expansion of k in k 0.734 * [backup-simplify]: Simplify 0 into 0 0.734 * [backup-simplify]: Simplify 1 into 1 0.734 * [backup-simplify]: Simplify (/ -1 1) into -1 0.734 * [backup-simplify]: Simplify (sqrt 0) into 0 0.735 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.735 * [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))))))) 0.735 * [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))))))) 0.735 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.735 * [taylor]: Taking taylor expansion of +nan.0 in n 0.735 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.735 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.735 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.735 * [taylor]: Taking taylor expansion of 0.5 in n 0.735 * [backup-simplify]: Simplify 0.5 into 0.5 0.736 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.736 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.736 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.736 * [taylor]: Taking taylor expansion of k in n 0.736 * [backup-simplify]: Simplify k into k 0.736 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.736 * [taylor]: Taking taylor expansion of 1.0 in n 0.736 * [backup-simplify]: Simplify 1.0 into 1.0 0.736 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.736 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.736 * [taylor]: Taking taylor expansion of -2.0 in n 0.736 * [backup-simplify]: Simplify -2.0 into -2.0 0.736 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.736 * [taylor]: Taking taylor expansion of PI in n 0.736 * [backup-simplify]: Simplify PI into PI 0.736 * [taylor]: Taking taylor expansion of n in n 0.736 * [backup-simplify]: Simplify 0 into 0 0.736 * [backup-simplify]: Simplify 1 into 1 0.736 * [backup-simplify]: Simplify (/ PI 1) into PI 0.736 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.737 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.737 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.738 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.739 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.739 * [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)))) 0.740 * [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))))) 0.741 * [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 (* +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) (+ (* -1 (/ 0 1)))) into 0 0.744 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.744 * [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)))))))) 0.745 * [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)))))))) 0.745 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.745 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.745 * [taylor]: Taking taylor expansion of +nan.0 in n 0.745 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.745 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.745 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.745 * [taylor]: Taking taylor expansion of 0.5 in n 0.745 * [backup-simplify]: Simplify 0.5 into 0.5 0.745 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.745 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.745 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.745 * [taylor]: Taking taylor expansion of k in n 0.745 * [backup-simplify]: Simplify k into k 0.745 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.745 * [taylor]: Taking taylor expansion of 1.0 in n 0.745 * [backup-simplify]: Simplify 1.0 into 1.0 0.745 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.745 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.745 * [taylor]: Taking taylor expansion of -2.0 in n 0.745 * [backup-simplify]: Simplify -2.0 into -2.0 0.745 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.745 * [taylor]: Taking taylor expansion of PI in n 0.745 * [backup-simplify]: Simplify PI into PI 0.745 * [taylor]: Taking taylor expansion of n in n 0.745 * [backup-simplify]: Simplify 0 into 0 0.745 * [backup-simplify]: Simplify 1 into 1 0.745 * [backup-simplify]: Simplify (/ PI 1) into PI 0.746 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.746 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.746 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.753 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.753 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.754 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.755 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.756 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.756 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 0.757 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 0.758 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.758 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.759 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.759 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.760 * [backup-simplify]: Simplify (+ 0 0) into 0 0.760 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.761 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.762 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 0.763 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.764 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 0.764 * [backup-simplify]: Simplify 0 into 0 0.765 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.767 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.768 * [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)))))))) 0.768 * [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)))))))) 0.768 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.768 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.768 * [taylor]: Taking taylor expansion of +nan.0 in n 0.768 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.768 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.768 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.768 * [taylor]: Taking taylor expansion of 0.5 in n 0.768 * [backup-simplify]: Simplify 0.5 into 0.5 0.768 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.769 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.769 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.769 * [taylor]: Taking taylor expansion of k in n 0.769 * [backup-simplify]: Simplify k into k 0.769 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.769 * [taylor]: Taking taylor expansion of 1.0 in n 0.769 * [backup-simplify]: Simplify 1.0 into 1.0 0.769 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.769 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.769 * [taylor]: Taking taylor expansion of -2.0 in n 0.769 * [backup-simplify]: Simplify -2.0 into -2.0 0.769 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.769 * [taylor]: Taking taylor expansion of PI in n 0.769 * [backup-simplify]: Simplify PI into PI 0.769 * [taylor]: Taking taylor expansion of n in n 0.769 * [backup-simplify]: Simplify 0 into 0 0.769 * [backup-simplify]: Simplify 1 into 1 0.769 * [backup-simplify]: Simplify (/ PI 1) into PI 0.769 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.770 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.770 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.771 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.772 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.772 * [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)))) 0.773 * [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))))) 0.774 * [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)))))) 0.775 * [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))))))) 0.775 * [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))))))) 0.778 * [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)))))))))))) 0.778 * * * [progress]: simplifying candidates 0.781 * [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))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) 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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))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 0.782 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ h2 h0)) (pow (* (* h0 PI) h1) (/ h3 h0)) (pow (* (* h0 PI) h1) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* h0 PI) h1) (sqrt (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) 1) (pow (* (* h0 PI) h1) (- h2 h3)) (pow (* h0 PI) (/ (- h2 h3) h0)) (pow h1 (/ (- h2 h3) h0)) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (exp (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (expm1 (* (* h0 PI) h1)) (log1p (* (* h0 PI) h1)) (* (* h0 PI) h1) (* (* h0 PI) h1) (+ (+ (log h0) (log PI)) (log h1)) (+ (log (* h0 PI)) (log h1)) (log (* (* h0 PI) h1)) (exp (* (* h0 PI) h1)) (* (* (* (* h0 h0) h0) (* (* PI PI) PI)) (* (* h1 h1) h1)) (* (* (* (* h0 PI) (* h0 PI)) (* h0 PI)) (* (* h1 h1) h1)) (* (cbrt (* (* h0 PI) h1)) (cbrt (* (* h0 PI) h1))) (cbrt (* (* h0 PI) h1)) (* (* (* (* h0 PI) h1) (* (* h0 PI) h1)) (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (* (* h0 PI) (sqrt h1)) (* (* h0 PI) 1) (* PI h1) (expm1 (/ h2 (sqrt h3))) (log1p (/ h2 (sqrt h3))) (- (log h2) (log (sqrt h3))) (log (/ h2 (sqrt h3))) (exp (/ h2 (sqrt h3))) (/ (* (* h2 h2) h2) (* (* (sqrt h3) (sqrt h3)) (sqrt h3))) (* (cbrt (/ h2 (sqrt h3))) (cbrt (/ h2 (sqrt 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(sqrt h3)) (cbrt (sqrt h3)))) (/ h2 (cbrt (sqrt h3))) (/ 1 (sqrt (* (cbrt h3) (cbrt h3)))) (/ h2 (sqrt (cbrt h3))) (/ 1 (sqrt (sqrt h3))) (/ h2 (sqrt (sqrt h3))) (/ 1 (sqrt 1)) (/ h2 (sqrt h3)) (/ 1 (sqrt (sqrt h3))) (/ h2 (sqrt (sqrt h3))) (/ 1 1) (/ h2 (sqrt h3)) (/ 1 (sqrt h3)) (/ (sqrt h3) h2) (/ h2 (* (cbrt (sqrt h3)) (cbrt (sqrt h3)))) (/ h2 (sqrt (* (cbrt h3) (cbrt h3)))) (/ h2 (sqrt (sqrt h3))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h3))) (/ h2 1) (/ (sqrt h3) (cbrt h2)) (/ (sqrt h3) (sqrt h2)) (/ (sqrt h3) h2) (expm1 (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (log1p (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (+ (- (log h2) (log (sqrt h3))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0))) (+ (- (log h2) (log (sqrt h3))) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0))) (+ (- (log h2) (log (sqrt h3))) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0))) (+ (- (log h2) (log (sqrt h3))) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0))) (+ (- (log h2) (log (sqrt h3))) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (+ (log (/ h2 (sqrt h3))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0))) (+ (log (/ h2 (sqrt h3))) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0))) (+ (log (/ h2 (sqrt h3))) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0))) (+ (log (/ h2 (sqrt h3))) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0))) (+ (log (/ h2 (sqrt h3))) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (log (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (exp (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ (* (* h2 h2) h2) (* (* (sqrt h3) (sqrt h3)) (sqrt h3))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (* (* (/ h2 (sqrt h3)) (/ h2 (sqrt h3))) (/ h2 (sqrt h3))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (cbrt (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))))) (cbrt (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (* (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (sqrt (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (sqrt (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* h2 (pow (* (* h0 PI) h1) (/ h2 h0))) (* (sqrt h3) (pow (* (* h0 PI) h1) (/ h3 h0))) (* (sqrt (/ h2 (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (sqrt (/ h2 (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (sqrt (/ h2 (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (sqrt (/ h2 (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (/ h2 (sqrt h3)) (pow (* h0 PI) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))))) (* (/ h2 (sqrt h3)) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ h2 (sqrt h3)) 1) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (cbrt (/ h2 (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (sqrt (/ h2 (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (cbrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (sqrt (cbrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (cbrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (sqrt (cbrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (cbrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt (cbrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ 1 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ h2 h0))) (* h2 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (- (+ (* h8 h3) (- (+ (* h8 (pow h3 2)) (- h8))))) (- (+ (* h8 (/ 1 (pow h3 2))) (- (+ (* h8 (/ 1 h3)) (- (* h8 (/ 1 (pow h3 3)))))))) (- (+ (* h8 (/ 1 (pow h3 2))) (- (+ (* h8 (/ 1 h3)) (- h8))))) (- (+ (* h8 (* (* (pow h3 2) (pow (log (* h0 PI)) 2)) (pow (* (pow h0 h2) (* (pow h1 h2) (pow PI h2))) h5))) (- (+ (* h8 (* (* (pow h3 2) (log (* h0 PI))) (pow (* (pow PI h2) (* (pow h1 h2) (pow h0 h2))) h5))) (- (+ (* h8 (* (* (pow h3 2) (* (log (* h0 PI)) (log h1))) (pow (* (pow PI h2) (* (pow h0 h2) (pow h1 h2))) h5))) (- (+ (* h8 (* (* (pow h3 2) (log h1)) (pow (* (pow h0 h2) (* (pow PI h2) (pow h1 h2))) h5))) (- (+ (* h8 (* (* h3 (log (* h0 PI))) (pow (* (pow h0 h2) (* (pow h1 h2) (pow PI h2))) h5))) (- (+ (* h8 (* (* (pow h3 2) (pow (log h1) 2)) (pow (* (pow h0 h2) (* (pow PI h2) (pow h1 h2))) h5))) (- (+ (* h8 (* (* h3 (log h1)) (pow (* (pow h0 h2) (* (pow PI h2) (pow h1 h2))) h5))) (- (+ (* h8 (pow (* (pow h0 h2) (* (pow h1 h2) (pow PI h2))) h5)) (- (+ (* h8 (* (pow h3 2) (pow (* (pow PI h2) (* (pow h1 h2) (pow h0 h2))) h5))) (- (* h8 (* h3 (pow (* (pow h0 h2) (* (pow h1 h2) (pow PI h2))) h5)))))))))))))))))))))) (- (+ (* h8 (/ (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (pow h3 3))) (- (+ (* h8 (/ (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) h3)) (- (* h8 (/ (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (pow h3 2)))))))) (- (+ (* h8 (/ (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) h3)) (- (+ (* h8 (/ (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (pow h3 2))) (- (* h8 (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))))))))) 0.791 * * [simplify]: iteration 0 : 981 enodes (cost 1502 ) 0.809 * * [simplify]: iteration 1 : 4021 enodes (cost 1398 ) 0.875 * * [simplify]: iteration 2 : 5003 enodes (cost 1383 ) 0.882 * * * [progress]: adding candidates to table 1.319 * * [progress]: iteration 2 / 4 1.319 * * * [progress]: picking best candidate 1.336 * * * * [pick]: Picked # 1.336 * * * [progress]: localizing error 1.352 * * * [progress]: generating rewritten candidates 1.352 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 1.378 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 1.400 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 1) 1.418 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1) 1.441 * * * [progress]: generating series expansions 1.441 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 1.442 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.442 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.442 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.442 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.442 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.442 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.442 * [taylor]: Taking taylor expansion of 0.5 in k 1.442 * [backup-simplify]: Simplify 0.5 into 0.5 1.442 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.442 * [taylor]: Taking taylor expansion of 1.0 in k 1.442 * [backup-simplify]: Simplify 1.0 into 1.0 1.442 * [taylor]: Taking taylor expansion of k in k 1.442 * [backup-simplify]: Simplify 0 into 0 1.442 * [backup-simplify]: Simplify 1 into 1 1.442 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.442 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.442 * [taylor]: Taking taylor expansion of 2.0 in k 1.442 * [backup-simplify]: Simplify 2.0 into 2.0 1.442 * [taylor]: Taking taylor expansion of (* n PI) in k 1.442 * [taylor]: Taking taylor expansion of n in k 1.442 * [backup-simplify]: Simplify n into n 1.442 * [taylor]: Taking taylor expansion of PI in k 1.443 * [backup-simplify]: Simplify PI into PI 1.443 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.443 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.443 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.443 * [backup-simplify]: Simplify (- 0) into 0 1.443 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.444 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.444 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.444 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.444 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.444 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.444 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.444 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.444 * [taylor]: Taking taylor expansion of 0.5 in n 1.444 * [backup-simplify]: Simplify 0.5 into 0.5 1.444 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.444 * [taylor]: Taking taylor expansion of 1.0 in n 1.444 * [backup-simplify]: Simplify 1.0 into 1.0 1.444 * [taylor]: Taking taylor expansion of k in n 1.444 * [backup-simplify]: Simplify k into k 1.444 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.444 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.444 * [taylor]: Taking taylor expansion of 2.0 in n 1.444 * [backup-simplify]: Simplify 2.0 into 2.0 1.444 * [taylor]: Taking taylor expansion of (* n PI) in n 1.444 * [taylor]: Taking taylor expansion of n in n 1.444 * [backup-simplify]: Simplify 0 into 0 1.444 * [backup-simplify]: Simplify 1 into 1 1.444 * [taylor]: Taking taylor expansion of PI in n 1.444 * [backup-simplify]: Simplify PI into PI 1.444 * [backup-simplify]: Simplify (* 0 PI) into 0 1.445 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.446 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.447 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.447 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.447 * [backup-simplify]: Simplify (- k) into (- k) 1.447 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.447 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.448 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.449 * [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)))) 1.450 * [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))))) 1.450 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.450 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.450 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.450 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.450 * [taylor]: Taking taylor expansion of 0.5 in n 1.450 * [backup-simplify]: Simplify 0.5 into 0.5 1.450 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.450 * [taylor]: Taking taylor expansion of 1.0 in n 1.450 * [backup-simplify]: Simplify 1.0 into 1.0 1.450 * [taylor]: Taking taylor expansion of k in n 1.450 * [backup-simplify]: Simplify k into k 1.450 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.450 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.450 * [taylor]: Taking taylor expansion of 2.0 in n 1.450 * [backup-simplify]: Simplify 2.0 into 2.0 1.450 * [taylor]: Taking taylor expansion of (* n PI) in n 1.450 * [taylor]: Taking taylor expansion of n in n 1.450 * [backup-simplify]: Simplify 0 into 0 1.450 * [backup-simplify]: Simplify 1 into 1 1.450 * [taylor]: Taking taylor expansion of PI in n 1.450 * [backup-simplify]: Simplify PI into PI 1.450 * [backup-simplify]: Simplify (* 0 PI) into 0 1.450 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.451 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.452 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.453 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.453 * [backup-simplify]: Simplify (- k) into (- k) 1.453 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.453 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.454 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.454 * [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)))) 1.455 * [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))))) 1.455 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.455 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.455 * [taylor]: Taking taylor expansion of 0.5 in k 1.455 * [backup-simplify]: Simplify 0.5 into 0.5 1.455 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.455 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.455 * [taylor]: Taking taylor expansion of 1.0 in k 1.455 * [backup-simplify]: Simplify 1.0 into 1.0 1.455 * [taylor]: Taking taylor expansion of k in k 1.455 * [backup-simplify]: Simplify 0 into 0 1.455 * [backup-simplify]: Simplify 1 into 1 1.455 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.455 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.455 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.456 * [taylor]: Taking taylor expansion of 2.0 in k 1.456 * [backup-simplify]: Simplify 2.0 into 2.0 1.456 * [taylor]: Taking taylor expansion of PI in k 1.456 * [backup-simplify]: Simplify PI into PI 1.456 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.457 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.457 * [taylor]: Taking taylor expansion of (log n) in k 1.457 * [taylor]: Taking taylor expansion of n in k 1.457 * [backup-simplify]: Simplify n into n 1.457 * [backup-simplify]: Simplify (log n) into (log n) 1.457 * [backup-simplify]: Simplify (- 0) into 0 1.457 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.458 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.459 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.459 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.460 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.461 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.461 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.462 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.463 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.463 * [backup-simplify]: Simplify (- 0) into 0 1.463 * [backup-simplify]: Simplify (+ 0 0) into 0 1.464 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.464 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.465 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.466 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.466 * [taylor]: Taking taylor expansion of 0 in k 1.466 * [backup-simplify]: Simplify 0 into 0 1.466 * [backup-simplify]: Simplify 0 into 0 1.467 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.468 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.468 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.469 * [backup-simplify]: Simplify (+ 0 0) into 0 1.469 * [backup-simplify]: Simplify (- 1) into -1 1.469 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.470 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.471 * [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)))) 1.473 * [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)))))) 1.475 * [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)))))) 1.476 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.476 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.478 * [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 1.478 * [backup-simplify]: Simplify (- 0) into 0 1.478 * [backup-simplify]: Simplify (+ 0 0) into 0 1.479 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.480 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.481 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.483 * [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 1.483 * [taylor]: Taking taylor expansion of 0 in k 1.483 * [backup-simplify]: Simplify 0 into 0 1.483 * [backup-simplify]: Simplify 0 into 0 1.483 * [backup-simplify]: Simplify 0 into 0 1.483 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.485 * [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 1.486 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.487 * [backup-simplify]: Simplify (+ 0 0) into 0 1.487 * [backup-simplify]: Simplify (- 0) into 0 1.487 * [backup-simplify]: Simplify (+ 0 0) into 0 1.488 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.490 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.492 * [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)))))) 1.495 * [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)))))) 1.501 * [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)))))) 1.501 * [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)))) 1.501 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.501 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.501 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.501 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.501 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.501 * [taylor]: Taking taylor expansion of 0.5 in k 1.501 * [backup-simplify]: Simplify 0.5 into 0.5 1.501 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.501 * [taylor]: Taking taylor expansion of 1.0 in k 1.501 * [backup-simplify]: Simplify 1.0 into 1.0 1.502 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.502 * [taylor]: Taking taylor expansion of k in k 1.502 * [backup-simplify]: Simplify 0 into 0 1.502 * [backup-simplify]: Simplify 1 into 1 1.502 * [backup-simplify]: Simplify (/ 1 1) into 1 1.502 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.502 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.502 * [taylor]: Taking taylor expansion of 2.0 in k 1.502 * [backup-simplify]: Simplify 2.0 into 2.0 1.502 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.502 * [taylor]: Taking taylor expansion of PI in k 1.502 * [backup-simplify]: Simplify PI into PI 1.502 * [taylor]: Taking taylor expansion of n in k 1.502 * [backup-simplify]: Simplify n into n 1.502 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.502 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.502 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.502 * [backup-simplify]: Simplify (- 1) into -1 1.503 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.503 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.503 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.503 * [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))))) 1.503 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.503 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.503 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.503 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.503 * [taylor]: Taking taylor expansion of 0.5 in n 1.503 * [backup-simplify]: Simplify 0.5 into 0.5 1.503 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.503 * [taylor]: Taking taylor expansion of 1.0 in n 1.503 * [backup-simplify]: Simplify 1.0 into 1.0 1.503 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.503 * [taylor]: Taking taylor expansion of k in n 1.503 * [backup-simplify]: Simplify k into k 1.503 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.503 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.503 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.503 * [taylor]: Taking taylor expansion of 2.0 in n 1.503 * [backup-simplify]: Simplify 2.0 into 2.0 1.503 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.503 * [taylor]: Taking taylor expansion of PI in n 1.503 * [backup-simplify]: Simplify PI into PI 1.503 * [taylor]: Taking taylor expansion of n in n 1.503 * [backup-simplify]: Simplify 0 into 0 1.503 * [backup-simplify]: Simplify 1 into 1 1.504 * [backup-simplify]: Simplify (/ PI 1) into PI 1.504 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.505 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.505 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.505 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.505 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.506 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.506 * [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)))) 1.507 * [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))))) 1.507 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.507 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.507 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.507 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.507 * [taylor]: Taking taylor expansion of 0.5 in n 1.507 * [backup-simplify]: Simplify 0.5 into 0.5 1.507 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.507 * [taylor]: Taking taylor expansion of 1.0 in n 1.507 * [backup-simplify]: Simplify 1.0 into 1.0 1.507 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.507 * [taylor]: Taking taylor expansion of k in n 1.507 * [backup-simplify]: Simplify k into k 1.507 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.507 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.507 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.507 * [taylor]: Taking taylor expansion of 2.0 in n 1.507 * [backup-simplify]: Simplify 2.0 into 2.0 1.507 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.507 * [taylor]: Taking taylor expansion of PI in n 1.507 * [backup-simplify]: Simplify PI into PI 1.507 * [taylor]: Taking taylor expansion of n in n 1.507 * [backup-simplify]: Simplify 0 into 0 1.507 * [backup-simplify]: Simplify 1 into 1 1.508 * [backup-simplify]: Simplify (/ PI 1) into PI 1.508 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.509 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.509 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.509 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.509 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.510 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.510 * [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)))) 1.511 * [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))))) 1.511 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.511 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.511 * [taylor]: Taking taylor expansion of 0.5 in k 1.511 * [backup-simplify]: Simplify 0.5 into 0.5 1.511 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.511 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.511 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.511 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.511 * [taylor]: Taking taylor expansion of 2.0 in k 1.511 * [backup-simplify]: Simplify 2.0 into 2.0 1.511 * [taylor]: Taking taylor expansion of PI in k 1.511 * [backup-simplify]: Simplify PI into PI 1.512 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.512 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.512 * [taylor]: Taking taylor expansion of (log n) in k 1.512 * [taylor]: Taking taylor expansion of n in k 1.512 * [backup-simplify]: Simplify n into n 1.512 * [backup-simplify]: Simplify (log n) into (log n) 1.512 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.512 * [taylor]: Taking taylor expansion of 1.0 in k 1.512 * [backup-simplify]: Simplify 1.0 into 1.0 1.512 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.512 * [taylor]: Taking taylor expansion of k in k 1.512 * [backup-simplify]: Simplify 0 into 0 1.512 * [backup-simplify]: Simplify 1 into 1 1.513 * [backup-simplify]: Simplify (/ 1 1) into 1 1.513 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.513 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.514 * [backup-simplify]: Simplify (- 1) into -1 1.514 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.515 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.515 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.516 * [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))))) 1.517 * [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))))) 1.517 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.518 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.519 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.519 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.519 * [backup-simplify]: Simplify (- 0) into 0 1.519 * [backup-simplify]: Simplify (+ 0 0) into 0 1.519 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.520 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.521 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.522 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.522 * [taylor]: Taking taylor expansion of 0 in k 1.522 * [backup-simplify]: Simplify 0 into 0 1.522 * [backup-simplify]: Simplify 0 into 0 1.522 * [backup-simplify]: Simplify 0 into 0 1.523 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.523 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.531 * [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 1.531 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.531 * [backup-simplify]: Simplify (- 0) into 0 1.532 * [backup-simplify]: Simplify (+ 0 0) into 0 1.532 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.533 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.534 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.535 * [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 1.535 * [taylor]: Taking taylor expansion of 0 in k 1.535 * [backup-simplify]: Simplify 0 into 0 1.535 * [backup-simplify]: Simplify 0 into 0 1.536 * [backup-simplify]: Simplify 0 into 0 1.536 * [backup-simplify]: Simplify 0 into 0 1.536 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.537 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.540 * [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 1.540 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.540 * [backup-simplify]: Simplify (- 0) into 0 1.540 * [backup-simplify]: Simplify (+ 0 0) into 0 1.541 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.542 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.543 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.545 * [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 1.545 * [taylor]: Taking taylor expansion of 0 in k 1.545 * [backup-simplify]: Simplify 0 into 0 1.545 * [backup-simplify]: Simplify 0 into 0 1.545 * [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)))) 1.546 * [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))) 1.546 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.546 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.546 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.546 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.546 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.546 * [taylor]: Taking taylor expansion of 0.5 in k 1.546 * [backup-simplify]: Simplify 0.5 into 0.5 1.546 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.546 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.546 * [taylor]: Taking taylor expansion of k in k 1.546 * [backup-simplify]: Simplify 0 into 0 1.546 * [backup-simplify]: Simplify 1 into 1 1.546 * [backup-simplify]: Simplify (/ 1 1) into 1 1.546 * [taylor]: Taking taylor expansion of 1.0 in k 1.546 * [backup-simplify]: Simplify 1.0 into 1.0 1.546 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.546 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.546 * [taylor]: Taking taylor expansion of -2.0 in k 1.546 * [backup-simplify]: Simplify -2.0 into -2.0 1.546 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.546 * [taylor]: Taking taylor expansion of PI in k 1.546 * [backup-simplify]: Simplify PI into PI 1.546 * [taylor]: Taking taylor expansion of n in k 1.546 * [backup-simplify]: Simplify n into n 1.547 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.547 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.547 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.547 * [backup-simplify]: Simplify (+ 1 0) into 1 1.547 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.547 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.547 * [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)))))) 1.547 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.547 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.547 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.547 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.547 * [taylor]: Taking taylor expansion of 0.5 in n 1.547 * [backup-simplify]: Simplify 0.5 into 0.5 1.548 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.548 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.548 * [taylor]: Taking taylor expansion of k in n 1.548 * [backup-simplify]: Simplify k into k 1.548 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.548 * [taylor]: Taking taylor expansion of 1.0 in n 1.548 * [backup-simplify]: Simplify 1.0 into 1.0 1.548 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.548 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.548 * [taylor]: Taking taylor expansion of -2.0 in n 1.548 * [backup-simplify]: Simplify -2.0 into -2.0 1.548 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.548 * [taylor]: Taking taylor expansion of PI in n 1.548 * [backup-simplify]: Simplify PI into PI 1.548 * [taylor]: Taking taylor expansion of n in n 1.548 * [backup-simplify]: Simplify 0 into 0 1.548 * [backup-simplify]: Simplify 1 into 1 1.548 * [backup-simplify]: Simplify (/ PI 1) into PI 1.548 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.549 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.549 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.549 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.550 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.551 * [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)))) 1.551 * [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))))) 1.551 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.551 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.551 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.551 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.551 * [taylor]: Taking taylor expansion of 0.5 in n 1.551 * [backup-simplify]: Simplify 0.5 into 0.5 1.552 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.552 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.552 * [taylor]: Taking taylor expansion of k in n 1.552 * [backup-simplify]: Simplify k into k 1.552 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.552 * [taylor]: Taking taylor expansion of 1.0 in n 1.552 * [backup-simplify]: Simplify 1.0 into 1.0 1.552 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.552 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.552 * [taylor]: Taking taylor expansion of -2.0 in n 1.552 * [backup-simplify]: Simplify -2.0 into -2.0 1.552 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.552 * [taylor]: Taking taylor expansion of PI in n 1.552 * [backup-simplify]: Simplify PI into PI 1.552 * [taylor]: Taking taylor expansion of n in n 1.552 * [backup-simplify]: Simplify 0 into 0 1.552 * [backup-simplify]: Simplify 1 into 1 1.552 * [backup-simplify]: Simplify (/ PI 1) into PI 1.552 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.553 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.553 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.553 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.554 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.555 * [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)))) 1.555 * [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))))) 1.556 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.556 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.556 * [taylor]: Taking taylor expansion of 0.5 in k 1.556 * [backup-simplify]: Simplify 0.5 into 0.5 1.556 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.556 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.556 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.556 * [taylor]: Taking taylor expansion of k in k 1.556 * [backup-simplify]: Simplify 0 into 0 1.556 * [backup-simplify]: Simplify 1 into 1 1.556 * [backup-simplify]: Simplify (/ 1 1) into 1 1.556 * [taylor]: Taking taylor expansion of 1.0 in k 1.556 * [backup-simplify]: Simplify 1.0 into 1.0 1.556 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.556 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.556 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.556 * [taylor]: Taking taylor expansion of -2.0 in k 1.556 * [backup-simplify]: Simplify -2.0 into -2.0 1.556 * [taylor]: Taking taylor expansion of PI in k 1.556 * [backup-simplify]: Simplify PI into PI 1.557 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.557 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.557 * [taylor]: Taking taylor expansion of (log n) in k 1.557 * [taylor]: Taking taylor expansion of n in k 1.557 * [backup-simplify]: Simplify n into n 1.557 * [backup-simplify]: Simplify (log n) into (log n) 1.558 * [backup-simplify]: Simplify (+ 1 0) into 1 1.558 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.558 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.559 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.560 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.560 * [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))))) 1.561 * [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))))) 1.562 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.562 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.563 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.563 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.563 * [backup-simplify]: Simplify (+ 0 0) into 0 1.564 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.564 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.565 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.566 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.566 * [taylor]: Taking taylor expansion of 0 in k 1.566 * [backup-simplify]: Simplify 0 into 0 1.566 * [backup-simplify]: Simplify 0 into 0 1.566 * [backup-simplify]: Simplify 0 into 0 1.567 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.568 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.569 * [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 1.569 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.570 * [backup-simplify]: Simplify (+ 0 0) into 0 1.570 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.571 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.572 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.573 * [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 1.573 * [taylor]: Taking taylor expansion of 0 in k 1.573 * [backup-simplify]: Simplify 0 into 0 1.573 * [backup-simplify]: Simplify 0 into 0 1.573 * [backup-simplify]: Simplify 0 into 0 1.573 * [backup-simplify]: Simplify 0 into 0 1.574 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.575 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.577 * [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 1.578 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.580 * [backup-simplify]: Simplify (+ 0 0) into 0 1.580 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.581 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.582 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.584 * [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 1.584 * [taylor]: Taking taylor expansion of 0 in k 1.584 * [backup-simplify]: Simplify 0 into 0 1.584 * [backup-simplify]: Simplify 0 into 0 1.585 * [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)))))) 1.585 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 1.586 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.586 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.586 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.586 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.586 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.586 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.586 * [taylor]: Taking taylor expansion of 0.5 in k 1.586 * [backup-simplify]: Simplify 0.5 into 0.5 1.586 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.586 * [taylor]: Taking taylor expansion of 1.0 in k 1.586 * [backup-simplify]: Simplify 1.0 into 1.0 1.586 * [taylor]: Taking taylor expansion of k in k 1.586 * [backup-simplify]: Simplify 0 into 0 1.586 * [backup-simplify]: Simplify 1 into 1 1.586 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.586 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.586 * [taylor]: Taking taylor expansion of 2.0 in k 1.586 * [backup-simplify]: Simplify 2.0 into 2.0 1.586 * [taylor]: Taking taylor expansion of (* n PI) in k 1.586 * [taylor]: Taking taylor expansion of n in k 1.586 * [backup-simplify]: Simplify n into n 1.586 * [taylor]: Taking taylor expansion of PI in k 1.586 * [backup-simplify]: Simplify PI into PI 1.586 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.586 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.586 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.587 * [backup-simplify]: Simplify (- 0) into 0 1.587 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.587 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.587 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.587 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.587 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.587 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.587 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.587 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.587 * [taylor]: Taking taylor expansion of 0.5 in n 1.587 * [backup-simplify]: Simplify 0.5 into 0.5 1.587 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.587 * [taylor]: Taking taylor expansion of 1.0 in n 1.587 * [backup-simplify]: Simplify 1.0 into 1.0 1.587 * [taylor]: Taking taylor expansion of k in n 1.587 * [backup-simplify]: Simplify k into k 1.587 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.587 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.587 * [taylor]: Taking taylor expansion of 2.0 in n 1.587 * [backup-simplify]: Simplify 2.0 into 2.0 1.588 * [taylor]: Taking taylor expansion of (* n PI) in n 1.588 * [taylor]: Taking taylor expansion of n in n 1.588 * [backup-simplify]: Simplify 0 into 0 1.588 * [backup-simplify]: Simplify 1 into 1 1.588 * [taylor]: Taking taylor expansion of PI in n 1.588 * [backup-simplify]: Simplify PI into PI 1.588 * [backup-simplify]: Simplify (* 0 PI) into 0 1.588 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.589 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.590 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.591 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.591 * [backup-simplify]: Simplify (- k) into (- k) 1.591 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.591 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.592 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.592 * [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)))) 1.593 * [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))))) 1.593 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.593 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.593 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.593 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.593 * [taylor]: Taking taylor expansion of 0.5 in n 1.593 * [backup-simplify]: Simplify 0.5 into 0.5 1.593 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.593 * [taylor]: Taking taylor expansion of 1.0 in n 1.593 * [backup-simplify]: Simplify 1.0 into 1.0 1.593 * [taylor]: Taking taylor expansion of k in n 1.593 * [backup-simplify]: Simplify k into k 1.593 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.593 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.593 * [taylor]: Taking taylor expansion of 2.0 in n 1.593 * [backup-simplify]: Simplify 2.0 into 2.0 1.593 * [taylor]: Taking taylor expansion of (* n PI) in n 1.593 * [taylor]: Taking taylor expansion of n in n 1.593 * [backup-simplify]: Simplify 0 into 0 1.593 * [backup-simplify]: Simplify 1 into 1 1.593 * [taylor]: Taking taylor expansion of PI in n 1.593 * [backup-simplify]: Simplify PI into PI 1.594 * [backup-simplify]: Simplify (* 0 PI) into 0 1.594 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.595 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.596 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.596 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.596 * [backup-simplify]: Simplify (- k) into (- k) 1.596 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.596 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.597 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.598 * [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)))) 1.599 * [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))))) 1.599 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.599 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.599 * [taylor]: Taking taylor expansion of 0.5 in k 1.599 * [backup-simplify]: Simplify 0.5 into 0.5 1.599 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.599 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.599 * [taylor]: Taking taylor expansion of 1.0 in k 1.599 * [backup-simplify]: Simplify 1.0 into 1.0 1.599 * [taylor]: Taking taylor expansion of k in k 1.599 * [backup-simplify]: Simplify 0 into 0 1.599 * [backup-simplify]: Simplify 1 into 1 1.599 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.599 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.599 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.599 * [taylor]: Taking taylor expansion of 2.0 in k 1.599 * [backup-simplify]: Simplify 2.0 into 2.0 1.599 * [taylor]: Taking taylor expansion of PI in k 1.599 * [backup-simplify]: Simplify PI into PI 1.599 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.600 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.600 * [taylor]: Taking taylor expansion of (log n) in k 1.600 * [taylor]: Taking taylor expansion of n in k 1.600 * [backup-simplify]: Simplify n into n 1.600 * [backup-simplify]: Simplify (log n) into (log n) 1.600 * [backup-simplify]: Simplify (- 0) into 0 1.600 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.601 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.602 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.602 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.603 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.604 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.604 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.605 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.606 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.606 * [backup-simplify]: Simplify (- 0) into 0 1.606 * [backup-simplify]: Simplify (+ 0 0) into 0 1.607 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.608 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.608 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.610 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.610 * [taylor]: Taking taylor expansion of 0 in k 1.610 * [backup-simplify]: Simplify 0 into 0 1.610 * [backup-simplify]: Simplify 0 into 0 1.610 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.611 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.612 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.612 * [backup-simplify]: Simplify (+ 0 0) into 0 1.612 * [backup-simplify]: Simplify (- 1) into -1 1.612 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.613 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.614 * [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)))) 1.616 * [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)))))) 1.618 * [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)))))) 1.619 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.619 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.621 * [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 1.621 * [backup-simplify]: Simplify (- 0) into 0 1.622 * [backup-simplify]: Simplify (+ 0 0) into 0 1.629 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.630 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.630 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.632 * [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 1.632 * [taylor]: Taking taylor expansion of 0 in k 1.632 * [backup-simplify]: Simplify 0 into 0 1.632 * [backup-simplify]: Simplify 0 into 0 1.632 * [backup-simplify]: Simplify 0 into 0 1.633 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.634 * [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 1.635 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.636 * [backup-simplify]: Simplify (+ 0 0) into 0 1.636 * [backup-simplify]: Simplify (- 0) into 0 1.636 * [backup-simplify]: Simplify (+ 0 0) into 0 1.637 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.639 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.641 * [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)))))) 1.644 * [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)))))) 1.650 * [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)))))) 1.651 * [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)))) 1.651 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.651 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.651 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.651 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.651 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.651 * [taylor]: Taking taylor expansion of 0.5 in k 1.651 * [backup-simplify]: Simplify 0.5 into 0.5 1.651 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.651 * [taylor]: Taking taylor expansion of 1.0 in k 1.651 * [backup-simplify]: Simplify 1.0 into 1.0 1.651 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.651 * [taylor]: Taking taylor expansion of k in k 1.651 * [backup-simplify]: Simplify 0 into 0 1.651 * [backup-simplify]: Simplify 1 into 1 1.652 * [backup-simplify]: Simplify (/ 1 1) into 1 1.652 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.652 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.652 * [taylor]: Taking taylor expansion of 2.0 in k 1.652 * [backup-simplify]: Simplify 2.0 into 2.0 1.652 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.652 * [taylor]: Taking taylor expansion of PI in k 1.652 * [backup-simplify]: Simplify PI into PI 1.652 * [taylor]: Taking taylor expansion of n in k 1.652 * [backup-simplify]: Simplify n into n 1.652 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.652 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.652 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.652 * [backup-simplify]: Simplify (- 1) into -1 1.652 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.653 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.653 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.653 * [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))))) 1.653 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.653 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.653 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.653 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.653 * [taylor]: Taking taylor expansion of 0.5 in n 1.653 * [backup-simplify]: Simplify 0.5 into 0.5 1.653 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.653 * [taylor]: Taking taylor expansion of 1.0 in n 1.653 * [backup-simplify]: Simplify 1.0 into 1.0 1.653 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.653 * [taylor]: Taking taylor expansion of k in n 1.653 * [backup-simplify]: Simplify k into k 1.653 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.653 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.653 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.653 * [taylor]: Taking taylor expansion of 2.0 in n 1.653 * [backup-simplify]: Simplify 2.0 into 2.0 1.653 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.653 * [taylor]: Taking taylor expansion of PI in n 1.653 * [backup-simplify]: Simplify PI into PI 1.653 * [taylor]: Taking taylor expansion of n in n 1.653 * [backup-simplify]: Simplify 0 into 0 1.653 * [backup-simplify]: Simplify 1 into 1 1.654 * [backup-simplify]: Simplify (/ PI 1) into PI 1.654 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.654 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.654 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.655 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.655 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.655 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.656 * [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)))) 1.657 * [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))))) 1.657 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.657 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.657 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.657 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.657 * [taylor]: Taking taylor expansion of 0.5 in n 1.657 * [backup-simplify]: Simplify 0.5 into 0.5 1.657 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.657 * [taylor]: Taking taylor expansion of 1.0 in n 1.657 * [backup-simplify]: Simplify 1.0 into 1.0 1.657 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.657 * [taylor]: Taking taylor expansion of k in n 1.657 * [backup-simplify]: Simplify k into k 1.657 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.657 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.657 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.657 * [taylor]: Taking taylor expansion of 2.0 in n 1.657 * [backup-simplify]: Simplify 2.0 into 2.0 1.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.657 * [taylor]: Taking taylor expansion of PI in n 1.657 * [backup-simplify]: Simplify PI into PI 1.657 * [taylor]: Taking taylor expansion of n in n 1.657 * [backup-simplify]: Simplify 0 into 0 1.657 * [backup-simplify]: Simplify 1 into 1 1.658 * [backup-simplify]: Simplify (/ PI 1) into PI 1.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.658 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.659 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.659 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.659 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.659 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.660 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.661 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.661 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.661 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.661 * [taylor]: Taking taylor expansion of 0.5 in k 1.661 * [backup-simplify]: Simplify 0.5 into 0.5 1.661 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.661 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.661 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.661 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.661 * [taylor]: Taking taylor expansion of 2.0 in k 1.661 * [backup-simplify]: Simplify 2.0 into 2.0 1.661 * [taylor]: Taking taylor expansion of PI in k 1.661 * [backup-simplify]: Simplify PI into PI 1.661 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.662 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.662 * [taylor]: Taking taylor expansion of (log n) in k 1.662 * [taylor]: Taking taylor expansion of n in k 1.662 * [backup-simplify]: Simplify n into n 1.662 * [backup-simplify]: Simplify (log n) into (log n) 1.662 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.662 * [taylor]: Taking taylor expansion of 1.0 in k 1.662 * [backup-simplify]: Simplify 1.0 into 1.0 1.662 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.662 * [taylor]: Taking taylor expansion of k in k 1.662 * [backup-simplify]: Simplify 0 into 0 1.662 * [backup-simplify]: Simplify 1 into 1 1.663 * [backup-simplify]: Simplify (/ 1 1) into 1 1.663 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.663 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.663 * [backup-simplify]: Simplify (- 1) into -1 1.664 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.664 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.665 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.666 * [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))))) 1.666 * [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))))) 1.667 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.667 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.668 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.668 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.669 * [backup-simplify]: Simplify (- 0) into 0 1.669 * [backup-simplify]: Simplify (+ 0 0) into 0 1.669 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.670 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.671 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.672 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.672 * [taylor]: Taking taylor expansion of 0 in k 1.672 * [backup-simplify]: Simplify 0 into 0 1.672 * [backup-simplify]: Simplify 0 into 0 1.672 * [backup-simplify]: Simplify 0 into 0 1.673 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.673 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.675 * [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 1.675 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.675 * [backup-simplify]: Simplify (- 0) into 0 1.675 * [backup-simplify]: Simplify (+ 0 0) into 0 1.676 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.677 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.678 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.679 * [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 1.679 * [taylor]: Taking taylor expansion of 0 in k 1.679 * [backup-simplify]: Simplify 0 into 0 1.679 * [backup-simplify]: Simplify 0 into 0 1.679 * [backup-simplify]: Simplify 0 into 0 1.679 * [backup-simplify]: Simplify 0 into 0 1.680 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.680 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.683 * [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 1.683 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.684 * [backup-simplify]: Simplify (- 0) into 0 1.684 * [backup-simplify]: Simplify (+ 0 0) into 0 1.685 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.686 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.687 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.688 * [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 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 (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)))) 1.690 * [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))) 1.690 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.690 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.690 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.690 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.690 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.690 * [taylor]: Taking taylor expansion of 0.5 in k 1.690 * [backup-simplify]: Simplify 0.5 into 0.5 1.690 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.690 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.690 * [taylor]: Taking taylor expansion of k in k 1.690 * [backup-simplify]: Simplify 0 into 0 1.690 * [backup-simplify]: Simplify 1 into 1 1.690 * [backup-simplify]: Simplify (/ 1 1) into 1 1.690 * [taylor]: Taking taylor expansion of 1.0 in k 1.690 * [backup-simplify]: Simplify 1.0 into 1.0 1.691 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.691 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.691 * [taylor]: Taking taylor expansion of -2.0 in k 1.691 * [backup-simplify]: Simplify -2.0 into -2.0 1.691 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.691 * [taylor]: Taking taylor expansion of PI in k 1.691 * [backup-simplify]: Simplify PI into PI 1.691 * [taylor]: Taking taylor expansion of n in k 1.691 * [backup-simplify]: Simplify n into n 1.691 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.691 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.691 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.691 * [backup-simplify]: Simplify (+ 1 0) into 1 1.691 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.691 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.692 * [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)))))) 1.692 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.692 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.692 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.692 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.692 * [taylor]: Taking taylor expansion of 0.5 in n 1.692 * [backup-simplify]: Simplify 0.5 into 0.5 1.692 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.692 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.692 * [taylor]: Taking taylor expansion of k in n 1.692 * [backup-simplify]: Simplify k into k 1.692 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.692 * [taylor]: Taking taylor expansion of 1.0 in n 1.692 * [backup-simplify]: Simplify 1.0 into 1.0 1.692 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.692 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.692 * [taylor]: Taking taylor expansion of -2.0 in n 1.692 * [backup-simplify]: Simplify -2.0 into -2.0 1.692 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.692 * [taylor]: Taking taylor expansion of PI in n 1.692 * [backup-simplify]: Simplify PI into PI 1.692 * [taylor]: Taking taylor expansion of n in n 1.692 * [backup-simplify]: Simplify 0 into 0 1.692 * [backup-simplify]: Simplify 1 into 1 1.692 * [backup-simplify]: Simplify (/ PI 1) into PI 1.692 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.693 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.693 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.693 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.694 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.695 * [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)))) 1.695 * [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))))) 1.696 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.696 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.696 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.696 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.696 * [taylor]: Taking taylor expansion of 0.5 in n 1.696 * [backup-simplify]: Simplify 0.5 into 0.5 1.696 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.696 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.696 * [taylor]: Taking taylor expansion of k in n 1.696 * [backup-simplify]: Simplify k into k 1.696 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.696 * [taylor]: Taking taylor expansion of 1.0 in n 1.696 * [backup-simplify]: Simplify 1.0 into 1.0 1.696 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.696 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.696 * [taylor]: Taking taylor expansion of -2.0 in n 1.696 * [backup-simplify]: Simplify -2.0 into -2.0 1.696 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.696 * [taylor]: Taking taylor expansion of PI in n 1.696 * [backup-simplify]: Simplify PI into PI 1.696 * [taylor]: Taking taylor expansion of n in n 1.696 * [backup-simplify]: Simplify 0 into 0 1.696 * [backup-simplify]: Simplify 1 into 1 1.696 * [backup-simplify]: Simplify (/ PI 1) into PI 1.696 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.697 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.697 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.697 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.698 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.699 * [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)))) 1.699 * [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))))) 1.700 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.700 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.700 * [taylor]: Taking taylor expansion of 0.5 in k 1.700 * [backup-simplify]: Simplify 0.5 into 0.5 1.700 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.700 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.700 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.700 * [taylor]: Taking taylor expansion of k in k 1.700 * [backup-simplify]: Simplify 0 into 0 1.700 * [backup-simplify]: Simplify 1 into 1 1.700 * [backup-simplify]: Simplify (/ 1 1) into 1 1.700 * [taylor]: Taking taylor expansion of 1.0 in k 1.700 * [backup-simplify]: Simplify 1.0 into 1.0 1.700 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.700 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.700 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.700 * [taylor]: Taking taylor expansion of -2.0 in k 1.700 * [backup-simplify]: Simplify -2.0 into -2.0 1.700 * [taylor]: Taking taylor expansion of PI in k 1.700 * [backup-simplify]: Simplify PI into PI 1.700 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.701 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.701 * [taylor]: Taking taylor expansion of (log n) in k 1.701 * [taylor]: Taking taylor expansion of n in k 1.701 * [backup-simplify]: Simplify n into n 1.701 * [backup-simplify]: Simplify (log n) into (log n) 1.701 * [backup-simplify]: Simplify (+ 1 0) into 1 1.701 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.702 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.703 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.703 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.704 * [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))))) 1.705 * [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))))) 1.705 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.706 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.707 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.707 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.707 * [backup-simplify]: Simplify (+ 0 0) into 0 1.707 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.708 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.709 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.710 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.710 * [taylor]: Taking taylor expansion of 0 in k 1.710 * [backup-simplify]: Simplify 0 into 0 1.710 * [backup-simplify]: Simplify 0 into 0 1.710 * [backup-simplify]: Simplify 0 into 0 1.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.711 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.713 * [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 1.713 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.713 * [backup-simplify]: Simplify (+ 0 0) into 0 1.714 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.715 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.716 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.717 * [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 1.717 * [taylor]: Taking taylor expansion of 0 in k 1.717 * [backup-simplify]: Simplify 0 into 0 1.717 * [backup-simplify]: Simplify 0 into 0 1.717 * [backup-simplify]: Simplify 0 into 0 1.717 * [backup-simplify]: Simplify 0 into 0 1.718 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.718 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.727 * [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 1.728 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.728 * [backup-simplify]: Simplify (+ 0 0) into 0 1.729 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.730 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.731 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.732 * [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 1.732 * [taylor]: Taking taylor expansion of 0 in k 1.732 * [backup-simplify]: Simplify 0 into 0 1.732 * [backup-simplify]: Simplify 0 into 0 1.733 * [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)))))) 1.733 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 1) 1.734 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.734 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.734 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.734 * [taylor]: Taking taylor expansion of 2.0 in n 1.734 * [backup-simplify]: Simplify 2.0 into 2.0 1.734 * [taylor]: Taking taylor expansion of (* n PI) in n 1.734 * [taylor]: Taking taylor expansion of n in n 1.734 * [backup-simplify]: Simplify 0 into 0 1.734 * [backup-simplify]: Simplify 1 into 1 1.734 * [taylor]: Taking taylor expansion of PI in n 1.734 * [backup-simplify]: Simplify PI into PI 1.734 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.734 * [taylor]: Taking taylor expansion of 2.0 in n 1.734 * [backup-simplify]: Simplify 2.0 into 2.0 1.734 * [taylor]: Taking taylor expansion of (* n PI) in n 1.734 * [taylor]: Taking taylor expansion of n in n 1.734 * [backup-simplify]: Simplify 0 into 0 1.734 * [backup-simplify]: Simplify 1 into 1 1.734 * [taylor]: Taking taylor expansion of PI in n 1.734 * [backup-simplify]: Simplify PI into PI 1.734 * [backup-simplify]: Simplify (* 0 PI) into 0 1.735 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.735 * [backup-simplify]: Simplify 0 into 0 1.735 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.736 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.737 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.737 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.738 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.738 * [backup-simplify]: Simplify 0 into 0 1.738 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.739 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.739 * [backup-simplify]: Simplify 0 into 0 1.740 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.741 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 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 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.742 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.742 * [backup-simplify]: Simplify 0 into 0 1.743 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 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 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.746 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 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 (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.747 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.747 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.747 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.747 * [taylor]: Taking taylor expansion of 2.0 in n 1.747 * [backup-simplify]: Simplify 2.0 into 2.0 1.747 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.747 * [taylor]: Taking taylor expansion of PI in n 1.747 * [backup-simplify]: Simplify PI into PI 1.747 * [taylor]: Taking taylor expansion of n in n 1.747 * [backup-simplify]: Simplify 0 into 0 1.747 * [backup-simplify]: Simplify 1 into 1 1.747 * [backup-simplify]: Simplify (/ PI 1) into PI 1.747 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.748 * [taylor]: Taking taylor expansion of 2.0 in n 1.748 * [backup-simplify]: Simplify 2.0 into 2.0 1.748 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.748 * [taylor]: Taking taylor expansion of PI in n 1.748 * [backup-simplify]: Simplify PI into PI 1.748 * [taylor]: Taking taylor expansion of n in n 1.748 * [backup-simplify]: Simplify 0 into 0 1.748 * [backup-simplify]: Simplify 1 into 1 1.748 * [backup-simplify]: Simplify (/ PI 1) into PI 1.748 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.749 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.750 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.750 * [backup-simplify]: Simplify 0 into 0 1.750 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.751 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.751 * [backup-simplify]: Simplify 0 into 0 1.752 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.752 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 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)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.754 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.754 * [backup-simplify]: Simplify 0 into 0 1.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.755 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.755 * [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)) (* 0 (/ 0 1)))) into 0 1.757 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.757 * [backup-simplify]: Simplify 0 into 0 1.757 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.757 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.757 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.757 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.757 * [taylor]: Taking taylor expansion of -2.0 in n 1.757 * [backup-simplify]: Simplify -2.0 into -2.0 1.758 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.758 * [taylor]: Taking taylor expansion of PI in n 1.758 * [backup-simplify]: Simplify PI into PI 1.758 * [taylor]: Taking taylor expansion of n in n 1.758 * [backup-simplify]: Simplify 0 into 0 1.758 * [backup-simplify]: Simplify 1 into 1 1.758 * [backup-simplify]: Simplify (/ PI 1) into PI 1.758 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.758 * [taylor]: Taking taylor expansion of -2.0 in n 1.758 * [backup-simplify]: Simplify -2.0 into -2.0 1.758 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.758 * [taylor]: Taking taylor expansion of PI in n 1.758 * [backup-simplify]: Simplify PI into PI 1.758 * [taylor]: Taking taylor expansion of n in n 1.758 * [backup-simplify]: Simplify 0 into 0 1.758 * [backup-simplify]: Simplify 1 into 1 1.758 * [backup-simplify]: Simplify (/ PI 1) into PI 1.759 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.759 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.760 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.760 * [backup-simplify]: Simplify 0 into 0 1.760 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.761 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.761 * [backup-simplify]: Simplify 0 into 0 1.762 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.762 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.762 * [backup-simplify]: Simplify 0 into 0 1.763 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.764 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.764 * [backup-simplify]: Simplify 0 into 0 1.764 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 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 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)) (* 0 (/ 0 1)))) into 0 1.767 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 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 (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.767 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1) 1.767 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.767 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.767 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.767 * [taylor]: Taking taylor expansion of 2.0 in n 1.767 * [backup-simplify]: Simplify 2.0 into 2.0 1.767 * [taylor]: Taking taylor expansion of (* n PI) in n 1.767 * [taylor]: Taking taylor expansion of n in n 1.767 * [backup-simplify]: Simplify 0 into 0 1.768 * [backup-simplify]: Simplify 1 into 1 1.768 * [taylor]: Taking taylor expansion of PI in n 1.768 * [backup-simplify]: Simplify PI into PI 1.768 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.768 * [taylor]: Taking taylor expansion of 2.0 in n 1.768 * [backup-simplify]: Simplify 2.0 into 2.0 1.768 * [taylor]: Taking taylor expansion of (* n PI) in n 1.768 * [taylor]: Taking taylor expansion of n in n 1.768 * [backup-simplify]: Simplify 0 into 0 1.768 * [backup-simplify]: Simplify 1 into 1 1.768 * [taylor]: Taking taylor expansion of PI in n 1.768 * [backup-simplify]: Simplify PI into PI 1.768 * [backup-simplify]: Simplify (* 0 PI) into 0 1.768 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.768 * [backup-simplify]: Simplify 0 into 0 1.769 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.770 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.770 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.771 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.772 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.772 * [backup-simplify]: Simplify 0 into 0 1.772 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.773 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.773 * [backup-simplify]: Simplify 0 into 0 1.774 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.774 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.774 * [backup-simplify]: Simplify 0 into 0 1.775 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.776 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.776 * [backup-simplify]: Simplify 0 into 0 1.777 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.778 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.778 * [backup-simplify]: Simplify 0 into 0 1.779 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.780 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.780 * [backup-simplify]: Simplify 0 into 0 1.780 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.780 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.780 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.781 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.781 * [taylor]: Taking taylor expansion of 2.0 in n 1.781 * [backup-simplify]: Simplify 2.0 into 2.0 1.781 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.781 * [taylor]: Taking taylor expansion of PI in n 1.781 * [backup-simplify]: Simplify PI into PI 1.781 * [taylor]: Taking taylor expansion of n in n 1.781 * [backup-simplify]: Simplify 0 into 0 1.781 * [backup-simplify]: Simplify 1 into 1 1.781 * [backup-simplify]: Simplify (/ PI 1) into PI 1.781 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.781 * [taylor]: Taking taylor expansion of 2.0 in n 1.781 * [backup-simplify]: Simplify 2.0 into 2.0 1.781 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.781 * [taylor]: Taking taylor expansion of PI in n 1.781 * [backup-simplify]: Simplify PI into PI 1.781 * [taylor]: Taking taylor expansion of n in n 1.781 * [backup-simplify]: Simplify 0 into 0 1.781 * [backup-simplify]: Simplify 1 into 1 1.781 * [backup-simplify]: Simplify (/ PI 1) into PI 1.782 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.782 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.783 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.783 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.783 * [backup-simplify]: Simplify 0 into 0 1.784 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.784 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.784 * [backup-simplify]: Simplify 0 into 0 1.785 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.786 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.786 * [backup-simplify]: Simplify 0 into 0 1.786 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.787 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.787 * [backup-simplify]: Simplify 0 into 0 1.788 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.789 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.789 * [backup-simplify]: Simplify 0 into 0 1.789 * [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 1.790 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.790 * [backup-simplify]: Simplify 0 into 0 1.790 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.791 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.791 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.791 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.791 * [taylor]: Taking taylor expansion of -2.0 in n 1.791 * [backup-simplify]: Simplify -2.0 into -2.0 1.791 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.791 * [taylor]: Taking taylor expansion of PI in n 1.791 * [backup-simplify]: Simplify PI into PI 1.791 * [taylor]: Taking taylor expansion of n in n 1.791 * [backup-simplify]: Simplify 0 into 0 1.791 * [backup-simplify]: Simplify 1 into 1 1.791 * [backup-simplify]: Simplify (/ PI 1) into PI 1.791 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.791 * [taylor]: Taking taylor expansion of -2.0 in n 1.792 * [backup-simplify]: Simplify -2.0 into -2.0 1.792 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.792 * [taylor]: Taking taylor expansion of PI in n 1.792 * [backup-simplify]: Simplify PI into PI 1.792 * [taylor]: Taking taylor expansion of n in n 1.792 * [backup-simplify]: Simplify 0 into 0 1.792 * [backup-simplify]: Simplify 1 into 1 1.792 * [backup-simplify]: Simplify (/ PI 1) into PI 1.792 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.793 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.793 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.793 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.794 * [backup-simplify]: Simplify 0 into 0 1.794 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.795 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.795 * [backup-simplify]: Simplify 0 into 0 1.795 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.796 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.796 * [backup-simplify]: Simplify 0 into 0 1.797 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.797 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.797 * [backup-simplify]: Simplify 0 into 0 1.798 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.799 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.799 * [backup-simplify]: Simplify 0 into 0 1.799 * [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 1.800 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.800 * [backup-simplify]: Simplify 0 into 0 1.801 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.801 * * * [progress]: simplifying candidates 1.802 * [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 (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 (* (* 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) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.125 (* (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)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 1.803 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ h2 h0)) (pow (* (* h0 PI) h1) (/ h3 h0)) (pow (* (* h0 PI) h1) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* h0 PI) h1) (sqrt (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) 1) (pow (* (* h0 PI) h1) (- h2 h3)) (pow (* h0 PI) (/ (- h2 h3) h0)) (pow h1 (/ (- h2 h3) h0)) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (exp (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ h2 h0)) (pow (* (* h0 PI) h1) (/ h3 h0)) (pow (* (* h0 PI) h1) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* h0 PI) h1) (sqrt (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) 1) (pow (* (* h0 PI) h1) (- h2 h3)) (pow (* h0 PI) (/ (- h2 h3) h0)) (pow h1 (/ (- h2 h3) h0)) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (exp (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (expm1 (* (* h0 PI) h1)) (log1p (* (* h0 PI) h1)) (* (* h0 PI) h1) (* (* h0 PI) h1) (+ (+ (log h0) (log PI)) (log h1)) (+ (log (* h0 PI)) (log h1)) (log (* (* h0 PI) h1)) (exp (* (* h0 PI) h1)) (* (* (* (* h0 h0) h0) (* (* PI PI) PI)) (* (* h1 h1) h1)) (* (* (* (* h0 PI) (* h0 PI)) (* h0 PI)) (* (* h1 h1) h1)) (* (cbrt (* (* h0 PI) h1)) (cbrt (* (* h0 PI) h1))) (cbrt (* (* h0 PI) h1)) (* (* (* (* h0 PI) h1) (* (* h0 PI) h1)) (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (* (* h0 PI) (sqrt h1)) (* (* h0 PI) 1) (* PI h1) (expm1 (* (* h0 PI) h1)) (log1p (* (* h0 PI) h1)) (* (* h0 PI) h1) (* (* h0 PI) h1) (+ (+ (log h0) (log PI)) (log h1)) (+ (log (* h0 PI)) (log h1)) (log (* (* h0 PI) h1)) (exp (* (* h0 PI) h1)) (* (* (* (* h0 h0) h0) (* (* PI PI) PI)) (* (* h1 h1) h1)) (* (* (* (* h0 PI) (* h0 PI)) (* h0 PI)) (* (* h1 h1) h1)) (* (cbrt (* (* h0 PI) h1)) (cbrt (* (* h0 PI) h1))) (cbrt (* (* h0 PI) h1)) (* (* (* (* h0 PI) h1) (* (* h0 PI) h1)) (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (* (* h0 PI) (sqrt h1)) (* (* h0 PI) 1) (* PI h1) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) 1.809 * * [simplify]: iteration 0 : 407 enodes (cost 832 ) 1.816 * * [simplify]: iteration 1 : 1658 enodes (cost 770 ) 1.849 * * [simplify]: iteration 2 : 5001 enodes (cost 732 ) 1.853 * * * [progress]: adding candidates to table 2.253 * * [progress]: iteration 3 / 4 2.253 * * * [progress]: picking best candidate 2.268 * * * * [pick]: Picked # 2.268 * * * [progress]: localizing error 2.299 * * * [progress]: generating rewritten candidates 2.299 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 2.406 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 2.430 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 1 2) 2.430 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1 1 1 2 2) 2.435 * * * [progress]: generating series expansions 2.435 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 2.436 * [backup-simplify]: Simplify (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 2.436 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.436 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.436 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.436 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.436 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.436 * [taylor]: Taking taylor expansion of 0.5 in k 2.436 * [backup-simplify]: Simplify 0.5 into 0.5 2.436 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.436 * [taylor]: Taking taylor expansion of 1.0 in k 2.436 * [backup-simplify]: Simplify 1.0 into 1.0 2.436 * [taylor]: Taking taylor expansion of k in k 2.436 * [backup-simplify]: Simplify 0 into 0 2.436 * [backup-simplify]: Simplify 1 into 1 2.436 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.436 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.436 * [taylor]: Taking taylor expansion of 2.0 in k 2.436 * [backup-simplify]: Simplify 2.0 into 2.0 2.436 * [taylor]: Taking taylor expansion of (* n PI) in k 2.436 * [taylor]: Taking taylor expansion of n in k 2.436 * [backup-simplify]: Simplify n into n 2.436 * [taylor]: Taking taylor expansion of PI in k 2.436 * [backup-simplify]: Simplify PI into PI 2.436 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.436 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.437 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.437 * [backup-simplify]: Simplify (- 0) into 0 2.437 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.437 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.438 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.438 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.438 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.438 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.438 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.438 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.438 * [taylor]: Taking taylor expansion of 0.5 in n 2.438 * [backup-simplify]: Simplify 0.5 into 0.5 2.438 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.438 * [taylor]: Taking taylor expansion of 1.0 in n 2.438 * [backup-simplify]: Simplify 1.0 into 1.0 2.438 * [taylor]: Taking taylor expansion of k in n 2.438 * [backup-simplify]: Simplify k into k 2.438 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.438 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.438 * [taylor]: Taking taylor expansion of 2.0 in n 2.438 * [backup-simplify]: Simplify 2.0 into 2.0 2.438 * [taylor]: Taking taylor expansion of (* n PI) in n 2.438 * [taylor]: Taking taylor expansion of n in n 2.438 * [backup-simplify]: Simplify 0 into 0 2.438 * [backup-simplify]: Simplify 1 into 1 2.438 * [taylor]: Taking taylor expansion of PI in n 2.438 * [backup-simplify]: Simplify PI into PI 2.438 * [backup-simplify]: Simplify (* 0 PI) into 0 2.439 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.440 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.441 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.442 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.442 * [backup-simplify]: Simplify (- k) into (- k) 2.442 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.442 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.443 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.443 * [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)))) 2.444 * [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))))) 2.444 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.444 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.444 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.444 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.444 * [taylor]: Taking taylor expansion of 0.5 in n 2.444 * [backup-simplify]: Simplify 0.5 into 0.5 2.444 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.444 * [taylor]: Taking taylor expansion of 1.0 in n 2.444 * [backup-simplify]: Simplify 1.0 into 1.0 2.444 * [taylor]: Taking taylor expansion of k in n 2.444 * [backup-simplify]: Simplify k into k 2.444 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.444 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.444 * [taylor]: Taking taylor expansion of 2.0 in n 2.444 * [backup-simplify]: Simplify 2.0 into 2.0 2.444 * [taylor]: Taking taylor expansion of (* n PI) in n 2.444 * [taylor]: Taking taylor expansion of n in n 2.444 * [backup-simplify]: Simplify 0 into 0 2.444 * [backup-simplify]: Simplify 1 into 1 2.444 * [taylor]: Taking taylor expansion of PI in n 2.444 * [backup-simplify]: Simplify PI into PI 2.445 * [backup-simplify]: Simplify (* 0 PI) into 0 2.445 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.446 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.447 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.447 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.447 * [backup-simplify]: Simplify (- k) into (- k) 2.447 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.447 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.448 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.449 * [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)))) 2.450 * [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))))) 2.450 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.450 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.450 * [taylor]: Taking taylor expansion of 0.5 in k 2.450 * [backup-simplify]: Simplify 0.5 into 0.5 2.450 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.450 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.450 * [taylor]: Taking taylor expansion of 1.0 in k 2.450 * [backup-simplify]: Simplify 1.0 into 1.0 2.450 * [taylor]: Taking taylor expansion of k in k 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 1 into 1 2.450 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.450 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.450 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.450 * [taylor]: Taking taylor expansion of 2.0 in k 2.450 * [backup-simplify]: Simplify 2.0 into 2.0 2.450 * [taylor]: Taking taylor expansion of PI in k 2.450 * [backup-simplify]: Simplify PI into PI 2.450 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.451 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.451 * [taylor]: Taking taylor expansion of (log n) in k 2.451 * [taylor]: Taking taylor expansion of n in k 2.451 * [backup-simplify]: Simplify n into n 2.451 * [backup-simplify]: Simplify (log n) into (log n) 2.451 * [backup-simplify]: Simplify (- 0) into 0 2.452 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.452 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.453 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.453 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 2.454 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.455 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.455 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.456 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.457 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.457 * [backup-simplify]: Simplify (- 0) into 0 2.457 * [backup-simplify]: Simplify (+ 0 0) into 0 2.458 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 2.459 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.459 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.461 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.461 * [taylor]: Taking taylor expansion of 0 in k 2.461 * [backup-simplify]: Simplify 0 into 0 2.461 * [backup-simplify]: Simplify 0 into 0 2.461 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.462 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.463 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.463 * [backup-simplify]: Simplify (+ 0 0) into 0 2.463 * [backup-simplify]: Simplify (- 1) into -1 2.463 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.464 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.466 * [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)))) 2.468 * [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)))))) 2.469 * [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)))))) 2.470 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.471 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.472 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.473 * [backup-simplify]: Simplify (- 0) into 0 2.473 * [backup-simplify]: Simplify (+ 0 0) into 0 2.473 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.474 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.475 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.477 * [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 2.477 * [taylor]: Taking taylor expansion of 0 in k 2.477 * [backup-simplify]: Simplify 0 into 0 2.477 * [backup-simplify]: Simplify 0 into 0 2.477 * [backup-simplify]: Simplify 0 into 0 2.477 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.479 * [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 2.480 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.480 * [backup-simplify]: Simplify (+ 0 0) into 0 2.480 * [backup-simplify]: Simplify (- 0) into 0 2.481 * [backup-simplify]: Simplify (+ 0 0) into 0 2.482 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.483 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.486 * [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)))))) 2.489 * [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)))))) 2.494 * [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)))))) 2.495 * [backup-simplify]: Simplify (pow (* (* (* 2.0 PI) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 2.495 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.496 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.496 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.496 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.496 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.496 * [taylor]: Taking taylor expansion of 0.5 in k 2.496 * [backup-simplify]: Simplify 0.5 into 0.5 2.496 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.496 * [taylor]: Taking taylor expansion of 1.0 in k 2.496 * [backup-simplify]: Simplify 1.0 into 1.0 2.496 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.496 * [taylor]: Taking taylor expansion of k in k 2.496 * [backup-simplify]: Simplify 0 into 0 2.496 * [backup-simplify]: Simplify 1 into 1 2.496 * [backup-simplify]: Simplify (/ 1 1) into 1 2.496 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.496 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.496 * [taylor]: Taking taylor expansion of 2.0 in k 2.496 * [backup-simplify]: Simplify 2.0 into 2.0 2.496 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.496 * [taylor]: Taking taylor expansion of PI in k 2.496 * [backup-simplify]: Simplify PI into PI 2.496 * [taylor]: Taking taylor expansion of n in k 2.496 * [backup-simplify]: Simplify n into n 2.496 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.496 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.496 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.496 * [backup-simplify]: Simplify (- 1) into -1 2.497 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.497 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.497 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.497 * [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))))) 2.497 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.497 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.497 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.497 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.497 * [taylor]: Taking taylor expansion of 0.5 in n 2.497 * [backup-simplify]: Simplify 0.5 into 0.5 2.497 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.497 * [taylor]: Taking taylor expansion of 1.0 in n 2.497 * [backup-simplify]: Simplify 1.0 into 1.0 2.497 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.497 * [taylor]: Taking taylor expansion of k in n 2.497 * [backup-simplify]: Simplify k into k 2.497 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.497 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.498 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.498 * [taylor]: Taking taylor expansion of 2.0 in n 2.498 * [backup-simplify]: Simplify 2.0 into 2.0 2.498 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.498 * [taylor]: Taking taylor expansion of PI in n 2.498 * [backup-simplify]: Simplify PI into PI 2.498 * [taylor]: Taking taylor expansion of n in n 2.498 * [backup-simplify]: Simplify 0 into 0 2.498 * [backup-simplify]: Simplify 1 into 1 2.498 * [backup-simplify]: Simplify (/ PI 1) into PI 2.498 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.499 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.499 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.499 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.499 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.500 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.506 * [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)))) 2.507 * [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))))) 2.507 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.507 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.507 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.507 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.507 * [taylor]: Taking taylor expansion of 0.5 in n 2.507 * [backup-simplify]: Simplify 0.5 into 0.5 2.507 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.507 * [taylor]: Taking taylor expansion of 1.0 in n 2.507 * [backup-simplify]: Simplify 1.0 into 1.0 2.507 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.507 * [taylor]: Taking taylor expansion of k in n 2.507 * [backup-simplify]: Simplify k into k 2.507 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.507 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.507 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.507 * [taylor]: Taking taylor expansion of 2.0 in n 2.507 * [backup-simplify]: Simplify 2.0 into 2.0 2.507 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.507 * [taylor]: Taking taylor expansion of PI in n 2.507 * [backup-simplify]: Simplify PI into PI 2.507 * [taylor]: Taking taylor expansion of n in n 2.507 * [backup-simplify]: Simplify 0 into 0 2.507 * [backup-simplify]: Simplify 1 into 1 2.508 * [backup-simplify]: Simplify (/ PI 1) into PI 2.508 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.509 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.509 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.509 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.509 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.510 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.510 * [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)))) 2.511 * [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))))) 2.511 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.511 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.511 * [taylor]: Taking taylor expansion of 0.5 in k 2.511 * [backup-simplify]: Simplify 0.5 into 0.5 2.511 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.511 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.511 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.511 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.511 * [taylor]: Taking taylor expansion of 2.0 in k 2.511 * [backup-simplify]: Simplify 2.0 into 2.0 2.511 * [taylor]: Taking taylor expansion of PI in k 2.511 * [backup-simplify]: Simplify PI into PI 2.512 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.512 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.512 * [taylor]: Taking taylor expansion of (log n) in k 2.512 * [taylor]: Taking taylor expansion of n in k 2.512 * [backup-simplify]: Simplify n into n 2.513 * [backup-simplify]: Simplify (log n) into (log n) 2.513 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.513 * [taylor]: Taking taylor expansion of 1.0 in k 2.513 * [backup-simplify]: Simplify 1.0 into 1.0 2.513 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.513 * [taylor]: Taking taylor expansion of k in k 2.513 * [backup-simplify]: Simplify 0 into 0 2.513 * [backup-simplify]: Simplify 1 into 1 2.513 * [backup-simplify]: Simplify (/ 1 1) into 1 2.513 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.514 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.514 * [backup-simplify]: Simplify (- 1) into -1 2.514 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.515 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.515 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.516 * [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))))) 2.517 * [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))))) 2.517 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.518 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.519 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.519 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.519 * [backup-simplify]: Simplify (- 0) into 0 2.519 * [backup-simplify]: Simplify (+ 0 0) into 0 2.520 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.520 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.521 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.522 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.522 * [taylor]: Taking taylor expansion of 0 in k 2.522 * [backup-simplify]: Simplify 0 into 0 2.522 * [backup-simplify]: Simplify 0 into 0 2.522 * [backup-simplify]: Simplify 0 into 0 2.523 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.523 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.525 * [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 2.525 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.526 * [backup-simplify]: Simplify (- 0) into 0 2.526 * [backup-simplify]: Simplify (+ 0 0) into 0 2.526 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.527 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.528 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.530 * [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 2.530 * [taylor]: Taking taylor expansion of 0 in k 2.530 * [backup-simplify]: Simplify 0 into 0 2.530 * [backup-simplify]: Simplify 0 into 0 2.530 * [backup-simplify]: Simplify 0 into 0 2.530 * [backup-simplify]: Simplify 0 into 0 2.530 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.531 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.534 * [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 2.534 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.534 * [backup-simplify]: Simplify (- 0) into 0 2.534 * [backup-simplify]: Simplify (+ 0 0) into 0 2.535 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.536 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.537 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.539 * [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 2.539 * [taylor]: Taking taylor expansion of 0 in k 2.539 * [backup-simplify]: Simplify 0 into 0 2.539 * [backup-simplify]: Simplify 0 into 0 2.540 * [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)))) 2.540 * [backup-simplify]: Simplify (pow (* (* (* 2.0 PI) (* (cbrt (/ 1 (- n))) (cbrt (/ 1 (- n))))) (cbrt (/ 1 (- n)))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) 2.540 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.540 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.540 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in k 2.540 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in k 2.540 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.540 * [taylor]: Taking taylor expansion of 0.5 in k 2.540 * [backup-simplify]: Simplify 0.5 into 0.5 2.541 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.541 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.541 * [taylor]: Taking taylor expansion of k in k 2.541 * [backup-simplify]: Simplify 0 into 0 2.541 * [backup-simplify]: Simplify 1 into 1 2.541 * [backup-simplify]: Simplify (/ 1 1) into 1 2.541 * [taylor]: Taking taylor expansion of 1.0 in k 2.541 * [backup-simplify]: Simplify 1.0 into 1.0 2.541 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in k 2.541 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in k 2.541 * [taylor]: Taking taylor expansion of 2.0 in k 2.541 * [backup-simplify]: Simplify 2.0 into 2.0 2.541 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in k 2.541 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in k 2.541 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in k 2.541 * [taylor]: Taking taylor expansion of (cbrt -1) in k 2.541 * [taylor]: Taking taylor expansion of -1 in k 2.541 * [backup-simplify]: Simplify -1 into -1 2.541 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.542 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.542 * [taylor]: Taking taylor expansion of PI in k 2.542 * [backup-simplify]: Simplify PI into PI 2.542 * [taylor]: Taking taylor expansion of n in k 2.542 * [backup-simplify]: Simplify n into n 2.543 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 2.544 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 2.545 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 2.545 * [backup-simplify]: Simplify (/ (* -1 PI) n) into (* -1 (/ PI n)) 2.545 * [backup-simplify]: Simplify (* 2.0 (* -1 (/ PI n))) into (* -2.0 (/ PI n)) 2.546 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.546 * [backup-simplify]: Simplify (+ 1 0) into 1 2.546 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.546 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.547 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.547 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.547 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 2.547 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 2.547 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.547 * [taylor]: Taking taylor expansion of 0.5 in n 2.547 * [backup-simplify]: Simplify 0.5 into 0.5 2.547 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.547 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.547 * [taylor]: Taking taylor expansion of k in n 2.547 * [backup-simplify]: Simplify k into k 2.548 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.548 * [taylor]: Taking taylor expansion of 1.0 in n 2.548 * [backup-simplify]: Simplify 1.0 into 1.0 2.548 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 2.548 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 2.548 * [taylor]: Taking taylor expansion of 2.0 in n 2.548 * [backup-simplify]: Simplify 2.0 into 2.0 2.548 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 2.548 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 2.548 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 2.548 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.548 * [taylor]: Taking taylor expansion of -1 in n 2.548 * [backup-simplify]: Simplify -1 into -1 2.548 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.548 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.548 * [taylor]: Taking taylor expansion of PI in n 2.548 * [backup-simplify]: Simplify PI into PI 2.548 * [taylor]: Taking taylor expansion of n in n 2.548 * [backup-simplify]: Simplify 0 into 0 2.548 * [backup-simplify]: Simplify 1 into 1 2.549 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 2.550 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 2.552 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 2.552 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 2.553 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 2.553 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.553 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.554 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.554 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.555 * [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)))) 2.556 * [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))))) 2.556 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.556 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 2.556 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 2.556 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.556 * [taylor]: Taking taylor expansion of 0.5 in n 2.556 * [backup-simplify]: Simplify 0.5 into 0.5 2.556 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.556 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.556 * [taylor]: Taking taylor expansion of k in n 2.556 * [backup-simplify]: Simplify k into k 2.556 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.556 * [taylor]: Taking taylor expansion of 1.0 in n 2.556 * [backup-simplify]: Simplify 1.0 into 1.0 2.556 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 2.556 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 2.556 * [taylor]: Taking taylor expansion of 2.0 in n 2.556 * [backup-simplify]: Simplify 2.0 into 2.0 2.556 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 2.556 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 2.556 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 2.556 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.556 * [taylor]: Taking taylor expansion of -1 in n 2.556 * [backup-simplify]: Simplify -1 into -1 2.556 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.557 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.557 * [taylor]: Taking taylor expansion of PI in n 2.557 * [backup-simplify]: Simplify PI into PI 2.557 * [taylor]: Taking taylor expansion of n in n 2.557 * [backup-simplify]: Simplify 0 into 0 2.557 * [backup-simplify]: Simplify 1 into 1 2.558 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 2.559 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 2.560 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 2.561 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 2.561 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 2.562 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.562 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.562 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.563 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.564 * [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)))) 2.565 * [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))))) 2.565 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.565 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.565 * [taylor]: Taking taylor expansion of 0.5 in k 2.565 * [backup-simplify]: Simplify 0.5 into 0.5 2.565 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.565 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.565 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.565 * [taylor]: Taking taylor expansion of k in k 2.565 * [backup-simplify]: Simplify 0 into 0 2.565 * [backup-simplify]: Simplify 1 into 1 2.565 * [backup-simplify]: Simplify (/ 1 1) into 1 2.565 * [taylor]: Taking taylor expansion of 1.0 in k 2.565 * [backup-simplify]: Simplify 1.0 into 1.0 2.565 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.565 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.565 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.565 * [taylor]: Taking taylor expansion of -2.0 in k 2.565 * [backup-simplify]: Simplify -2.0 into -2.0 2.565 * [taylor]: Taking taylor expansion of PI in k 2.565 * [backup-simplify]: Simplify PI into PI 2.565 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.566 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.566 * [taylor]: Taking taylor expansion of (log n) in k 2.566 * [taylor]: Taking taylor expansion of n in k 2.566 * [backup-simplify]: Simplify n into n 2.566 * [backup-simplify]: Simplify (log n) into (log n) 2.566 * [backup-simplify]: Simplify (+ 1 0) into 1 2.567 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.567 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.568 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.568 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.569 * [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))))) 2.570 * [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))))) 2.570 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (cbrt -1))) into 0 2.571 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow (cbrt -1) 2))) into 0 2.572 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (* 0 PI)) into 0 2.572 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)))) into 0 2.573 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* -1 PI))) into 0 2.574 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.574 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.574 * [backup-simplify]: Simplify (+ 0 0) into 0 2.574 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.575 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.576 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.577 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.577 * [taylor]: Taking taylor expansion of 0 in k 2.577 * [backup-simplify]: Simplify 0 into 0 2.577 * [backup-simplify]: Simplify 0 into 0 2.577 * [backup-simplify]: Simplify 0 into 0 2.578 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.579 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (cbrt -1)))) into 0 2.579 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2)))) into 0 2.580 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (* 0 PI))) into 0 2.581 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.581 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* -1 PI)))) into 0 2.583 * [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 2.583 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.583 * [backup-simplify]: Simplify (+ 0 0) into 0 2.584 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.585 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.586 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.587 * [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 2.587 * [taylor]: Taking taylor expansion of 0 in k 2.587 * [backup-simplify]: Simplify 0 into 0 2.587 * [backup-simplify]: Simplify 0 into 0 2.587 * [backup-simplify]: Simplify 0 into 0 2.587 * [backup-simplify]: Simplify 0 into 0 2.588 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.589 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1))))) into 0 2.589 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2))))) into 0 2.590 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.591 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.592 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* -1 PI))))) into 0 2.595 * [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 2.595 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.595 * [backup-simplify]: Simplify (+ 0 0) into 0 2.603 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.604 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.605 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.606 * [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 2.606 * [taylor]: Taking taylor expansion of 0 in k 2.606 * [backup-simplify]: Simplify 0 into 0 2.606 * [backup-simplify]: Simplify 0 into 0 2.607 * [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)))))) 2.607 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 2.608 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 2.608 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.608 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.608 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.608 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.608 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.608 * [taylor]: Taking taylor expansion of 0.5 in k 2.608 * [backup-simplify]: Simplify 0.5 into 0.5 2.608 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.608 * [taylor]: Taking taylor expansion of 1.0 in k 2.608 * [backup-simplify]: Simplify 1.0 into 1.0 2.608 * [taylor]: Taking taylor expansion of k in k 2.608 * [backup-simplify]: Simplify 0 into 0 2.608 * [backup-simplify]: Simplify 1 into 1 2.608 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.608 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.608 * [taylor]: Taking taylor expansion of 2.0 in k 2.608 * [backup-simplify]: Simplify 2.0 into 2.0 2.608 * [taylor]: Taking taylor expansion of (* n PI) in k 2.608 * [taylor]: Taking taylor expansion of n in k 2.608 * [backup-simplify]: Simplify n into n 2.608 * [taylor]: Taking taylor expansion of PI in k 2.608 * [backup-simplify]: Simplify PI into PI 2.608 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.608 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.608 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.608 * [backup-simplify]: Simplify (- 0) into 0 2.609 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.609 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.609 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.609 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.609 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.609 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.609 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.609 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.609 * [taylor]: Taking taylor expansion of 0.5 in n 2.609 * [backup-simplify]: Simplify 0.5 into 0.5 2.609 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.609 * [taylor]: Taking taylor expansion of 1.0 in n 2.609 * [backup-simplify]: Simplify 1.0 into 1.0 2.609 * [taylor]: Taking taylor expansion of k in n 2.609 * [backup-simplify]: Simplify k into k 2.609 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.609 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.609 * [taylor]: Taking taylor expansion of 2.0 in n 2.609 * [backup-simplify]: Simplify 2.0 into 2.0 2.609 * [taylor]: Taking taylor expansion of (* n PI) in n 2.609 * [taylor]: Taking taylor expansion of n in n 2.609 * [backup-simplify]: Simplify 0 into 0 2.609 * [backup-simplify]: Simplify 1 into 1 2.609 * [taylor]: Taking taylor expansion of PI in n 2.609 * [backup-simplify]: Simplify PI into PI 2.610 * [backup-simplify]: Simplify (* 0 PI) into 0 2.610 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.611 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.612 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.612 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.612 * [backup-simplify]: Simplify (- k) into (- k) 2.612 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.612 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.614 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.614 * [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)))) 2.615 * [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))))) 2.615 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.615 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.615 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.615 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.615 * [taylor]: Taking taylor expansion of 0.5 in n 2.615 * [backup-simplify]: Simplify 0.5 into 0.5 2.615 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.615 * [taylor]: Taking taylor expansion of 1.0 in n 2.615 * [backup-simplify]: Simplify 1.0 into 1.0 2.615 * [taylor]: Taking taylor expansion of k in n 2.615 * [backup-simplify]: Simplify k into k 2.615 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.615 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.615 * [taylor]: Taking taylor expansion of 2.0 in n 2.615 * [backup-simplify]: Simplify 2.0 into 2.0 2.615 * [taylor]: Taking taylor expansion of (* n PI) in n 2.615 * [taylor]: Taking taylor expansion of n in n 2.615 * [backup-simplify]: Simplify 0 into 0 2.615 * [backup-simplify]: Simplify 1 into 1 2.615 * [taylor]: Taking taylor expansion of PI in n 2.615 * [backup-simplify]: Simplify PI into PI 2.616 * [backup-simplify]: Simplify (* 0 PI) into 0 2.616 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.617 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.618 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.618 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.618 * [backup-simplify]: Simplify (- k) into (- k) 2.618 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.618 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.619 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.620 * [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)))) 2.620 * [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))))) 2.621 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.621 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.621 * [taylor]: Taking taylor expansion of 0.5 in k 2.621 * [backup-simplify]: Simplify 0.5 into 0.5 2.621 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.621 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.621 * [taylor]: Taking taylor expansion of 1.0 in k 2.621 * [backup-simplify]: Simplify 1.0 into 1.0 2.621 * [taylor]: Taking taylor expansion of k in k 2.621 * [backup-simplify]: Simplify 0 into 0 2.621 * [backup-simplify]: Simplify 1 into 1 2.621 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.621 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.621 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.621 * [taylor]: Taking taylor expansion of 2.0 in k 2.621 * [backup-simplify]: Simplify 2.0 into 2.0 2.621 * [taylor]: Taking taylor expansion of PI in k 2.621 * [backup-simplify]: Simplify PI into PI 2.621 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.622 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.622 * [taylor]: Taking taylor expansion of (log n) in k 2.622 * [taylor]: Taking taylor expansion of n in k 2.622 * [backup-simplify]: Simplify n into n 2.622 * [backup-simplify]: Simplify (log n) into (log n) 2.622 * [backup-simplify]: Simplify (- 0) into 0 2.622 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.623 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.624 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.624 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 2.625 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.626 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.626 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.627 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.628 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.628 * [backup-simplify]: Simplify (- 0) into 0 2.628 * [backup-simplify]: Simplify (+ 0 0) into 0 2.628 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 2.629 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.630 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.631 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.631 * [taylor]: Taking taylor expansion of 0 in k 2.631 * [backup-simplify]: Simplify 0 into 0 2.631 * [backup-simplify]: Simplify 0 into 0 2.632 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.632 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.633 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.633 * [backup-simplify]: Simplify (+ 0 0) into 0 2.633 * [backup-simplify]: Simplify (- 1) into -1 2.634 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.635 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.636 * [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)))) 2.638 * [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)))))) 2.639 * [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)))))) 2.640 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.641 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.643 * [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 2.643 * [backup-simplify]: Simplify (- 0) into 0 2.643 * [backup-simplify]: Simplify (+ 0 0) into 0 2.643 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.644 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.645 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.647 * [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 2.647 * [taylor]: Taking taylor expansion of 0 in k 2.647 * [backup-simplify]: Simplify 0 into 0 2.647 * [backup-simplify]: Simplify 0 into 0 2.647 * [backup-simplify]: Simplify 0 into 0 2.647 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.649 * [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 2.650 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.650 * [backup-simplify]: Simplify (+ 0 0) into 0 2.651 * [backup-simplify]: Simplify (- 0) into 0 2.651 * [backup-simplify]: Simplify (+ 0 0) into 0 2.652 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.653 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.656 * [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)))))) 2.659 * [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)))))) 2.665 * [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)))))) 2.665 * [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)))) 2.665 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.665 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.665 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.665 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.665 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.666 * [taylor]: Taking taylor expansion of 0.5 in k 2.666 * [backup-simplify]: Simplify 0.5 into 0.5 2.666 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.666 * [taylor]: Taking taylor expansion of 1.0 in k 2.666 * [backup-simplify]: Simplify 1.0 into 1.0 2.666 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.666 * [taylor]: Taking taylor expansion of k in k 2.666 * [backup-simplify]: Simplify 0 into 0 2.666 * [backup-simplify]: Simplify 1 into 1 2.666 * [backup-simplify]: Simplify (/ 1 1) into 1 2.666 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.666 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.666 * [taylor]: Taking taylor expansion of 2.0 in k 2.666 * [backup-simplify]: Simplify 2.0 into 2.0 2.666 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.666 * [taylor]: Taking taylor expansion of PI in k 2.666 * [backup-simplify]: Simplify PI into PI 2.666 * [taylor]: Taking taylor expansion of n in k 2.666 * [backup-simplify]: Simplify n into n 2.666 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.666 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.666 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.666 * [backup-simplify]: Simplify (- 1) into -1 2.667 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.667 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.667 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.667 * [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))))) 2.667 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.667 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.667 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.667 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.667 * [taylor]: Taking taylor expansion of 0.5 in n 2.667 * [backup-simplify]: Simplify 0.5 into 0.5 2.667 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.667 * [taylor]: Taking taylor expansion of 1.0 in n 2.667 * [backup-simplify]: Simplify 1.0 into 1.0 2.667 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.667 * [taylor]: Taking taylor expansion of k in n 2.667 * [backup-simplify]: Simplify k into k 2.667 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.667 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.667 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.667 * [taylor]: Taking taylor expansion of 2.0 in n 2.667 * [backup-simplify]: Simplify 2.0 into 2.0 2.667 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.667 * [taylor]: Taking taylor expansion of PI in n 2.667 * [backup-simplify]: Simplify PI into PI 2.667 * [taylor]: Taking taylor expansion of n in n 2.667 * [backup-simplify]: Simplify 0 into 0 2.667 * [backup-simplify]: Simplify 1 into 1 2.668 * [backup-simplify]: Simplify (/ PI 1) into PI 2.668 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.669 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.669 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.669 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.669 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.670 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.670 * [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)))) 2.671 * [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))))) 2.671 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.671 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.671 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.671 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.671 * [taylor]: Taking taylor expansion of 0.5 in n 2.671 * [backup-simplify]: Simplify 0.5 into 0.5 2.671 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.671 * [taylor]: Taking taylor expansion of 1.0 in n 2.671 * [backup-simplify]: Simplify 1.0 into 1.0 2.671 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.671 * [taylor]: Taking taylor expansion of k in n 2.671 * [backup-simplify]: Simplify k into k 2.671 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.671 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.671 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.671 * [taylor]: Taking taylor expansion of 2.0 in n 2.671 * [backup-simplify]: Simplify 2.0 into 2.0 2.671 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.671 * [taylor]: Taking taylor expansion of PI in n 2.671 * [backup-simplify]: Simplify PI into PI 2.672 * [taylor]: Taking taylor expansion of n in n 2.672 * [backup-simplify]: Simplify 0 into 0 2.672 * [backup-simplify]: Simplify 1 into 1 2.672 * [backup-simplify]: Simplify (/ PI 1) into PI 2.672 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.673 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.673 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.673 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.673 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.674 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.674 * [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)))) 2.675 * [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))))) 2.675 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.675 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.675 * [taylor]: Taking taylor expansion of 0.5 in k 2.675 * [backup-simplify]: Simplify 0.5 into 0.5 2.675 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.675 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.675 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.675 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.675 * [taylor]: Taking taylor expansion of 2.0 in k 2.675 * [backup-simplify]: Simplify 2.0 into 2.0 2.675 * [taylor]: Taking taylor expansion of PI in k 2.675 * [backup-simplify]: Simplify PI into PI 2.676 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.676 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.676 * [taylor]: Taking taylor expansion of (log n) in k 2.676 * [taylor]: Taking taylor expansion of n in k 2.676 * [backup-simplify]: Simplify n into n 2.676 * [backup-simplify]: Simplify (log n) into (log n) 2.676 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.676 * [taylor]: Taking taylor expansion of 1.0 in k 2.677 * [backup-simplify]: Simplify 1.0 into 1.0 2.677 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.677 * [taylor]: Taking taylor expansion of k in k 2.677 * [backup-simplify]: Simplify 0 into 0 2.677 * [backup-simplify]: Simplify 1 into 1 2.677 * [backup-simplify]: Simplify (/ 1 1) into 1 2.677 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.677 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.678 * [backup-simplify]: Simplify (- 1) into -1 2.678 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.679 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.679 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.680 * [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))))) 2.681 * [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))))) 2.681 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.682 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.683 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.683 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.683 * [backup-simplify]: Simplify (- 0) into 0 2.683 * [backup-simplify]: Simplify (+ 0 0) into 0 2.683 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.684 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.685 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.686 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.686 * [taylor]: Taking taylor expansion of 0 in k 2.686 * [backup-simplify]: Simplify 0 into 0 2.686 * [backup-simplify]: Simplify 0 into 0 2.686 * [backup-simplify]: Simplify 0 into 0 2.687 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.687 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.689 * [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 2.689 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.689 * [backup-simplify]: Simplify (- 0) into 0 2.690 * [backup-simplify]: Simplify (+ 0 0) into 0 2.690 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.691 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.692 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.701 * [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 2.701 * [taylor]: Taking taylor expansion of 0 in k 2.701 * [backup-simplify]: Simplify 0 into 0 2.701 * [backup-simplify]: Simplify 0 into 0 2.701 * [backup-simplify]: Simplify 0 into 0 2.701 * [backup-simplify]: Simplify 0 into 0 2.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.703 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.706 * [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 2.706 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.706 * [backup-simplify]: Simplify (- 0) into 0 2.707 * [backup-simplify]: Simplify (+ 0 0) into 0 2.707 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.708 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.709 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.711 * [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 2.711 * [taylor]: Taking taylor expansion of 0 in k 2.711 * [backup-simplify]: Simplify 0 into 0 2.711 * [backup-simplify]: Simplify 0 into 0 2.712 * [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)))) 2.712 * [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))) 2.712 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.712 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.712 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.712 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.712 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.712 * [taylor]: Taking taylor expansion of 0.5 in k 2.712 * [backup-simplify]: Simplify 0.5 into 0.5 2.712 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.712 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.712 * [taylor]: Taking taylor expansion of k in k 2.712 * [backup-simplify]: Simplify 0 into 0 2.712 * [backup-simplify]: Simplify 1 into 1 2.713 * [backup-simplify]: Simplify (/ 1 1) into 1 2.713 * [taylor]: Taking taylor expansion of 1.0 in k 2.713 * [backup-simplify]: Simplify 1.0 into 1.0 2.713 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.713 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.713 * [taylor]: Taking taylor expansion of -2.0 in k 2.713 * [backup-simplify]: Simplify -2.0 into -2.0 2.713 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.713 * [taylor]: Taking taylor expansion of PI in k 2.713 * [backup-simplify]: Simplify PI into PI 2.713 * [taylor]: Taking taylor expansion of n in k 2.713 * [backup-simplify]: Simplify n into n 2.713 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.713 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.713 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.713 * [backup-simplify]: Simplify (+ 1 0) into 1 2.714 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.714 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.714 * [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)))))) 2.714 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.714 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.714 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.714 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.714 * [taylor]: Taking taylor expansion of 0.5 in n 2.714 * [backup-simplify]: Simplify 0.5 into 0.5 2.714 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.714 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.714 * [taylor]: Taking taylor expansion of k in n 2.714 * [backup-simplify]: Simplify k into k 2.714 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.714 * [taylor]: Taking taylor expansion of 1.0 in n 2.714 * [backup-simplify]: Simplify 1.0 into 1.0 2.714 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.714 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.714 * [taylor]: Taking taylor expansion of -2.0 in n 2.714 * [backup-simplify]: Simplify -2.0 into -2.0 2.714 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.714 * [taylor]: Taking taylor expansion of PI in n 2.714 * [backup-simplify]: Simplify PI into PI 2.714 * [taylor]: Taking taylor expansion of n in n 2.714 * [backup-simplify]: Simplify 0 into 0 2.714 * [backup-simplify]: Simplify 1 into 1 2.715 * [backup-simplify]: Simplify (/ PI 1) into PI 2.715 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.716 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.716 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.716 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.717 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.717 * [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)))) 2.718 * [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))))) 2.718 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.718 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.718 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.718 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.718 * [taylor]: Taking taylor expansion of 0.5 in n 2.718 * [backup-simplify]: Simplify 0.5 into 0.5 2.718 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.718 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.718 * [taylor]: Taking taylor expansion of k in n 2.718 * [backup-simplify]: Simplify k into k 2.718 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.718 * [taylor]: Taking taylor expansion of 1.0 in n 2.718 * [backup-simplify]: Simplify 1.0 into 1.0 2.718 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.718 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.718 * [taylor]: Taking taylor expansion of -2.0 in n 2.718 * [backup-simplify]: Simplify -2.0 into -2.0 2.718 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.718 * [taylor]: Taking taylor expansion of PI in n 2.718 * [backup-simplify]: Simplify PI into PI 2.718 * [taylor]: Taking taylor expansion of n in n 2.718 * [backup-simplify]: Simplify 0 into 0 2.718 * [backup-simplify]: Simplify 1 into 1 2.719 * [backup-simplify]: Simplify (/ PI 1) into PI 2.719 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.720 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.720 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.720 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.721 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.721 * [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)))) 2.722 * [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))))) 2.722 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.722 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.722 * [taylor]: Taking taylor expansion of 0.5 in k 2.722 * [backup-simplify]: Simplify 0.5 into 0.5 2.722 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.722 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.722 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.722 * [taylor]: Taking taylor expansion of k in k 2.722 * [backup-simplify]: Simplify 0 into 0 2.722 * [backup-simplify]: Simplify 1 into 1 2.722 * [backup-simplify]: Simplify (/ 1 1) into 1 2.722 * [taylor]: Taking taylor expansion of 1.0 in k 2.723 * [backup-simplify]: Simplify 1.0 into 1.0 2.723 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.723 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.723 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.723 * [taylor]: Taking taylor expansion of -2.0 in k 2.723 * [backup-simplify]: Simplify -2.0 into -2.0 2.723 * [taylor]: Taking taylor expansion of PI in k 2.723 * [backup-simplify]: Simplify PI into PI 2.723 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.724 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.724 * [taylor]: Taking taylor expansion of (log n) in k 2.724 * [taylor]: Taking taylor expansion of n in k 2.724 * [backup-simplify]: Simplify n into n 2.724 * [backup-simplify]: Simplify (log n) into (log n) 2.724 * [backup-simplify]: Simplify (+ 1 0) into 1 2.724 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.725 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.725 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.726 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.727 * [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))))) 2.728 * [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))))) 2.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.729 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.730 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.730 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.730 * [backup-simplify]: Simplify (+ 0 0) into 0 2.730 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.731 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.732 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.733 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (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 0 into 0 2.734 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.734 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.736 * [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 2.736 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.736 * [backup-simplify]: Simplify (+ 0 0) into 0 2.737 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.738 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.738 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.740 * [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 2.740 * [taylor]: Taking taylor expansion of 0 in k 2.740 * [backup-simplify]: Simplify 0 into 0 2.740 * [backup-simplify]: Simplify 0 into 0 2.740 * [backup-simplify]: Simplify 0 into 0 2.740 * [backup-simplify]: Simplify 0 into 0 2.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.741 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.744 * [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 2.744 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.745 * [backup-simplify]: Simplify (+ 0 0) into 0 2.745 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.746 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.747 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.749 * [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 2.749 * [taylor]: Taking taylor expansion of 0 in k 2.749 * [backup-simplify]: Simplify 0 into 0 2.749 * [backup-simplify]: Simplify 0 into 0 2.750 * [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)))))) 2.750 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 1 2) 2.750 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 2.750 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 2.750 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.750 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.750 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.750 * [taylor]: Taking taylor expansion of 1/3 in n 2.750 * [backup-simplify]: Simplify 1/3 into 1/3 2.750 * [taylor]: Taking taylor expansion of (log n) in n 2.750 * [taylor]: Taking taylor expansion of n in n 2.750 * [backup-simplify]: Simplify 0 into 0 2.750 * [backup-simplify]: Simplify 1 into 1 2.750 * [backup-simplify]: Simplify (log 1) into 0 2.750 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.751 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.751 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.751 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.751 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.751 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.751 * [taylor]: Taking taylor expansion of 1/3 in n 2.751 * [backup-simplify]: Simplify 1/3 into 1/3 2.751 * [taylor]: Taking taylor expansion of (log n) in n 2.751 * [taylor]: Taking taylor expansion of n in n 2.751 * [backup-simplify]: Simplify 0 into 0 2.751 * [backup-simplify]: Simplify 1 into 1 2.751 * [backup-simplify]: Simplify (log 1) into 0 2.751 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.751 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.751 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.751 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.752 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.752 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.753 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 2.753 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.753 * [backup-simplify]: Simplify 0 into 0 2.755 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.755 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.755 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 2.756 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.756 * [backup-simplify]: Simplify 0 into 0 2.759 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 2.759 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.760 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 2.761 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.761 * [backup-simplify]: Simplify 0 into 0 2.766 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 2.766 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.767 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 2.769 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.769 * [backup-simplify]: Simplify 0 into 0 2.777 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 2.777 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.778 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 2.780 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.780 * [backup-simplify]: Simplify 0 into 0 2.802 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 2.803 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.804 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 2.807 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.807 * [backup-simplify]: Simplify 0 into 0 2.807 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.807 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 2.807 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 2.807 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.807 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.807 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.807 * [taylor]: Taking taylor expansion of 1/3 in n 2.807 * [backup-simplify]: Simplify 1/3 into 1/3 2.807 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.807 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.807 * [taylor]: Taking taylor expansion of n in n 2.807 * [backup-simplify]: Simplify 0 into 0 2.807 * [backup-simplify]: Simplify 1 into 1 2.808 * [backup-simplify]: Simplify (/ 1 1) into 1 2.808 * [backup-simplify]: Simplify (log 1) into 0 2.808 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.808 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.808 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.808 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.808 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.808 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.808 * [taylor]: Taking taylor expansion of 1/3 in n 2.808 * [backup-simplify]: Simplify 1/3 into 1/3 2.808 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.808 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.808 * [taylor]: Taking taylor expansion of n in n 2.808 * [backup-simplify]: Simplify 0 into 0 2.808 * [backup-simplify]: Simplify 1 into 1 2.809 * [backup-simplify]: Simplify (/ 1 1) into 1 2.809 * [backup-simplify]: Simplify (log 1) into 0 2.809 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.809 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.809 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.809 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 2.810 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.811 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.811 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.811 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 2.812 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.812 * [backup-simplify]: Simplify 0 into 0 2.812 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.814 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.814 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.815 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 2.815 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.815 * [backup-simplify]: Simplify 0 into 0 2.816 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.819 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 2.819 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.820 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 2.820 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.820 * [backup-simplify]: Simplify 0 into 0 2.821 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.826 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 2.826 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.827 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 2.829 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.829 * [backup-simplify]: Simplify 0 into 0 2.829 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.837 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 2.837 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.839 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 2.840 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.841 * [backup-simplify]: Simplify 0 into 0 2.841 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.856 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 2.856 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.858 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 2.861 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.861 * [backup-simplify]: Simplify 0 into 0 2.861 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 2.861 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.861 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 2.861 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.861 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.861 * [taylor]: Taking taylor expansion of -1 in n 2.861 * [backup-simplify]: Simplify -1 into -1 2.861 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.862 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.862 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.862 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.862 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.862 * [taylor]: Taking taylor expansion of 1/3 in n 2.862 * [backup-simplify]: Simplify 1/3 into 1/3 2.862 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.862 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.862 * [taylor]: Taking taylor expansion of n in n 2.862 * [backup-simplify]: Simplify 0 into 0 2.862 * [backup-simplify]: Simplify 1 into 1 2.862 * [backup-simplify]: Simplify (/ 1 1) into 1 2.862 * [backup-simplify]: Simplify (log 1) into 0 2.863 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.863 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.863 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.863 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.863 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.863 * [taylor]: Taking taylor expansion of -1 in n 2.863 * [backup-simplify]: Simplify -1 into -1 2.863 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.864 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.864 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.864 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.864 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.864 * [taylor]: Taking taylor expansion of 1/3 in n 2.864 * [backup-simplify]: Simplify 1/3 into 1/3 2.864 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.864 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.864 * [taylor]: Taking taylor expansion of n in n 2.864 * [backup-simplify]: Simplify 0 into 0 2.864 * [backup-simplify]: Simplify 1 into 1 2.864 * [backup-simplify]: Simplify (/ 1 1) into 1 2.864 * [backup-simplify]: Simplify (log 1) into 0 2.865 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.865 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.865 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.865 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.866 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.866 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.867 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.867 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.867 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 2.868 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.868 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 2.868 * [backup-simplify]: Simplify 0 into 0 2.869 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.877 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.877 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.878 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 2.878 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.879 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.880 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 2.880 * [backup-simplify]: Simplify 0 into 0 2.880 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.883 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 2.883 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.884 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 2.885 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.886 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.886 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 2.886 * [backup-simplify]: Simplify 0 into 0 2.887 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.892 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 2.892 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.893 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 2.895 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.896 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.897 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 2.897 * [backup-simplify]: Simplify 0 into 0 2.898 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.905 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 2.906 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.907 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 2.909 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.910 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.911 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 2.911 * [backup-simplify]: Simplify 0 into 0 2.912 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.927 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 2.927 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.929 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 2.931 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.932 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.934 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 2.934 * [backup-simplify]: Simplify 0 into 0 2.934 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 2.934 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1 1 1 2 2) 2.934 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 2.934 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 2.934 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.934 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.934 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.934 * [taylor]: Taking taylor expansion of 1/3 in n 2.934 * [backup-simplify]: Simplify 1/3 into 1/3 2.934 * [taylor]: Taking taylor expansion of (log n) in n 2.934 * [taylor]: Taking taylor expansion of n in n 2.934 * [backup-simplify]: Simplify 0 into 0 2.934 * [backup-simplify]: Simplify 1 into 1 2.935 * [backup-simplify]: Simplify (log 1) into 0 2.935 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.935 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.935 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.935 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.935 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.935 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.935 * [taylor]: Taking taylor expansion of 1/3 in n 2.935 * [backup-simplify]: Simplify 1/3 into 1/3 2.935 * [taylor]: Taking taylor expansion of (log n) in n 2.935 * [taylor]: Taking taylor expansion of n in n 2.935 * [backup-simplify]: Simplify 0 into 0 2.935 * [backup-simplify]: Simplify 1 into 1 2.935 * [backup-simplify]: Simplify (log 1) into 0 2.936 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.936 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.936 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.936 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.937 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.937 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.937 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 2.938 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.938 * [backup-simplify]: Simplify 0 into 0 2.939 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.939 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.940 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 2.941 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.941 * [backup-simplify]: Simplify 0 into 0 2.943 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 2.943 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.944 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 2.945 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.945 * [backup-simplify]: Simplify 0 into 0 2.950 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 2.950 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.951 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 2.959 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.959 * [backup-simplify]: Simplify 0 into 0 2.968 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 2.968 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.969 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 2.971 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.971 * [backup-simplify]: Simplify 0 into 0 2.986 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 2.986 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.988 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 2.990 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.990 * [backup-simplify]: Simplify 0 into 0 2.991 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.991 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 2.991 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 2.991 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.991 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.991 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.991 * [taylor]: Taking taylor expansion of 1/3 in n 2.991 * [backup-simplify]: Simplify 1/3 into 1/3 2.991 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.991 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.991 * [taylor]: Taking taylor expansion of n in n 2.991 * [backup-simplify]: Simplify 0 into 0 2.991 * [backup-simplify]: Simplify 1 into 1 2.991 * [backup-simplify]: Simplify (/ 1 1) into 1 2.991 * [backup-simplify]: Simplify (log 1) into 0 2.992 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.992 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.992 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.992 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.992 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.992 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.992 * [taylor]: Taking taylor expansion of 1/3 in n 2.992 * [backup-simplify]: Simplify 1/3 into 1/3 2.992 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.992 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.992 * [taylor]: Taking taylor expansion of n in n 2.992 * [backup-simplify]: Simplify 0 into 0 2.992 * [backup-simplify]: Simplify 1 into 1 2.992 * [backup-simplify]: Simplify (/ 1 1) into 1 2.992 * [backup-simplify]: Simplify (log 1) into 0 2.993 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.993 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.993 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.993 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 2.993 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.994 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.994 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.995 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 2.995 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.995 * [backup-simplify]: Simplify 0 into 0 2.996 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.997 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.998 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.998 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 2.999 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.999 * [backup-simplify]: Simplify 0 into 0 2.999 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.002 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 3.002 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.003 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 3.004 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.004 * [backup-simplify]: Simplify 0 into 0 3.004 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.009 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 3.009 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.010 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 3.012 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.012 * [backup-simplify]: Simplify 0 into 0 3.012 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.020 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 3.021 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.022 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 3.024 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.024 * [backup-simplify]: Simplify 0 into 0 3.024 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.045 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 3.045 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.046 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 3.049 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.049 * [backup-simplify]: Simplify 0 into 0 3.049 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 3.049 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 3.050 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 3.050 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 3.050 * [taylor]: Taking taylor expansion of (cbrt -1) in n 3.050 * [taylor]: Taking taylor expansion of -1 in n 3.050 * [backup-simplify]: Simplify -1 into -1 3.050 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 3.050 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 3.050 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 3.050 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 3.050 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 3.050 * [taylor]: Taking taylor expansion of 1/3 in n 3.050 * [backup-simplify]: Simplify 1/3 into 1/3 3.050 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 3.050 * [taylor]: Taking taylor expansion of (/ 1 n) in n 3.050 * [taylor]: Taking taylor expansion of n in n 3.050 * [backup-simplify]: Simplify 0 into 0 3.050 * [backup-simplify]: Simplify 1 into 1 3.051 * [backup-simplify]: Simplify (/ 1 1) into 1 3.051 * [backup-simplify]: Simplify (log 1) into 0 3.051 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.051 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 3.051 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 3.051 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 3.051 * [taylor]: Taking taylor expansion of (cbrt -1) in n 3.051 * [taylor]: Taking taylor expansion of -1 in n 3.051 * [backup-simplify]: Simplify -1 into -1 3.052 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 3.052 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 3.052 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 3.052 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 3.052 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 3.052 * [taylor]: Taking taylor expansion of 1/3 in n 3.052 * [backup-simplify]: Simplify 1/3 into 1/3 3.052 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 3.052 * [taylor]: Taking taylor expansion of (/ 1 n) in n 3.052 * [taylor]: Taking taylor expansion of n in n 3.052 * [backup-simplify]: Simplify 0 into 0 3.052 * [backup-simplify]: Simplify 1 into 1 3.053 * [backup-simplify]: Simplify (/ 1 1) into 1 3.053 * [backup-simplify]: Simplify (log 1) into 0 3.053 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.053 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 3.053 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 3.054 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 3.054 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 3.055 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.055 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.056 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.056 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 3.056 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 3.057 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 3.057 * [backup-simplify]: Simplify 0 into 0 3.057 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.059 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 3.059 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.060 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 3.060 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.061 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 3.062 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 3.062 * [backup-simplify]: Simplify 0 into 0 3.062 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.065 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 3.065 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.066 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 3.067 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.067 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 3.068 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 3.068 * [backup-simplify]: Simplify 0 into 0 3.069 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.074 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 3.074 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.075 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 3.076 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.077 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 3.078 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 3.078 * [backup-simplify]: Simplify 0 into 0 3.079 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.087 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 3.087 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.088 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 3.090 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.091 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 3.092 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 3.092 * [backup-simplify]: Simplify 0 into 0 3.093 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.108 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 3.108 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.109 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 3.112 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.113 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 3.115 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 3.115 * [backup-simplify]: Simplify 0 into 0 3.123 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 3.123 * * * [progress]: simplifying candidates 3.124 * [simplify]: Simplifying: (expm1 (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (+ (+ (+ (log 2.0) (log PI)) (+ (log (cbrt n)) (log (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (+ (log 2.0) (log PI)) (log (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (log (* 2.0 PI)) (+ (log (cbrt n)) (log (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (log (* 2.0 PI)) (log (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (log (* (* 2.0 PI) (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (log (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n))) (/ (- 1.0 k) 2.0)) (* (log (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1.0 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ k 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) 1) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (- 1.0 k)) (pow (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (log (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (exp (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2)) (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 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.125 (* (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)))))) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) 3.125 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (log1p (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (* (+ (+ (+ (log h0) (log PI)) (+ (log (cbrt h1)) (log (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (+ (+ (log h0) (log PI)) (log (* (cbrt h1) (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (+ (log (* h0 PI)) (+ (log (cbrt h1)) (log (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (+ (log (* h0 PI)) (log (* (cbrt h1) (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (log (* (* h0 PI) (* (cbrt h1) (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (log (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1))) (/ (- h2 h3) h0)) (* (log (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1))) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ h2 h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ h3 h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (sqrt (/ (- h2 h3) h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (sqrt (- h2 h3)) 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) 1) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (- h2 h3)) (pow (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (/ (- h2 h3) h0)) (pow (cbrt h1) (/ (- h2 h3) h0)) (log (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (exp (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (cbrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0)))) (cbrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (* (* (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (sqrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (sqrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (/ (- h2 h3) h0) 2)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (/ (- h2 h3) h0) 2)) (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ h2 h0)) (pow (* (* h0 PI) h1) (/ h3 h0)) (pow (* (* h0 PI) h1) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* h0 PI) h1) (sqrt (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) 1) (pow (* (* h0 PI) h1) (- h2 h3)) (pow (* h0 PI) (/ (- h2 h3) h0)) (pow h1 (/ (- h2 h3) h0)) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (exp (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (expm1 (cbrt h1)) (log1p (cbrt h1)) (log (cbrt h1)) (exp (cbrt h1)) (cbrt (* (cbrt h1) (cbrt h1))) (cbrt (cbrt h1)) (cbrt (sqrt h1)) (cbrt (sqrt h1)) (cbrt 1) (cbrt h1) (* (cbrt (cbrt h1)) (cbrt (cbrt h1))) (cbrt (cbrt h1)) (* (* (cbrt h1) (cbrt h1)) (cbrt h1)) (sqrt (cbrt h1)) (sqrt (cbrt h1)) (expm1 (cbrt h1)) (log1p (cbrt h1)) (log (cbrt h1)) (exp (cbrt h1)) (cbrt (* (cbrt h1) (cbrt h1))) (cbrt (cbrt h1)) (cbrt (sqrt h1)) (cbrt (sqrt h1)) (cbrt 1) (cbrt h1) (* (cbrt (cbrt h1)) (cbrt (cbrt h1))) (cbrt (cbrt h1)) (* (* (cbrt h1) (cbrt h1)) (cbrt h1)) (sqrt (cbrt h1)) (sqrt (cbrt h1)) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (pow h1 1/3) (pow (/ 1 h1) -1/3) (* (pow (* -1 h1) 1/3) (cbrt -1)) (pow h1 1/3) (pow (/ 1 h1) -1/3) (* (pow (* -1 h1) 1/3) (cbrt -1)) 3.131 * * [simplify]: iteration 0 : 511 enodes (cost 996 ) 3.139 * * [simplify]: iteration 1 : 1634 enodes (cost 936 ) 3.166 * * [simplify]: iteration 2 : 5001 enodes (cost 729 ) 3.169 * * * [progress]: adding candidates to table 3.628 * * [progress]: iteration 4 / 4 3.628 * * * [progress]: picking best candidate 3.641 * * * * [pick]: Picked # 3.641 * * * [progress]: localizing error 3.661 * * * [progress]: generating rewritten candidates 3.661 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.683 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 3.708 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 3.729 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 3.764 * * * [progress]: generating series expansions 3.764 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.765 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 3.765 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.765 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.765 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.765 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.765 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.765 * [taylor]: Taking taylor expansion of 0.5 in k 3.765 * [backup-simplify]: Simplify 0.5 into 0.5 3.765 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.765 * [taylor]: Taking taylor expansion of 1.0 in k 3.765 * [backup-simplify]: Simplify 1.0 into 1.0 3.765 * [taylor]: Taking taylor expansion of k in k 3.765 * [backup-simplify]: Simplify 0 into 0 3.765 * [backup-simplify]: Simplify 1 into 1 3.765 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.765 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.765 * [taylor]: Taking taylor expansion of 2.0 in k 3.766 * [backup-simplify]: Simplify 2.0 into 2.0 3.766 * [taylor]: Taking taylor expansion of (* n PI) in k 3.766 * [taylor]: Taking taylor expansion of n in k 3.766 * [backup-simplify]: Simplify n into n 3.766 * [taylor]: Taking taylor expansion of PI in k 3.766 * [backup-simplify]: Simplify PI into PI 3.766 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.766 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.766 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.766 * [backup-simplify]: Simplify (- 0) into 0 3.766 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.767 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.767 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.767 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.767 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.767 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.767 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.767 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.767 * [taylor]: Taking taylor expansion of 0.5 in n 3.767 * [backup-simplify]: Simplify 0.5 into 0.5 3.767 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.767 * [taylor]: Taking taylor expansion of 1.0 in n 3.767 * [backup-simplify]: Simplify 1.0 into 1.0 3.767 * [taylor]: Taking taylor expansion of k in n 3.767 * [backup-simplify]: Simplify k into k 3.767 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.767 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.767 * [taylor]: Taking taylor expansion of 2.0 in n 3.767 * [backup-simplify]: Simplify 2.0 into 2.0 3.767 * [taylor]: Taking taylor expansion of (* n PI) in n 3.767 * [taylor]: Taking taylor expansion of n in n 3.767 * [backup-simplify]: Simplify 0 into 0 3.767 * [backup-simplify]: Simplify 1 into 1 3.767 * [taylor]: Taking taylor expansion of PI in n 3.767 * [backup-simplify]: Simplify PI into PI 3.767 * [backup-simplify]: Simplify (* 0 PI) into 0 3.768 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.769 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.770 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.770 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.770 * [backup-simplify]: Simplify (- k) into (- k) 3.770 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.770 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.771 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.772 * [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)))) 3.773 * [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))))) 3.773 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.773 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.773 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.773 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.773 * [taylor]: Taking taylor expansion of 0.5 in n 3.773 * [backup-simplify]: Simplify 0.5 into 0.5 3.773 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.773 * [taylor]: Taking taylor expansion of 1.0 in n 3.773 * [backup-simplify]: Simplify 1.0 into 1.0 3.773 * [taylor]: Taking taylor expansion of k in n 3.773 * [backup-simplify]: Simplify k into k 3.773 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.773 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.773 * [taylor]: Taking taylor expansion of 2.0 in n 3.773 * [backup-simplify]: Simplify 2.0 into 2.0 3.773 * [taylor]: Taking taylor expansion of (* n PI) in n 3.773 * [taylor]: Taking taylor expansion of n in n 3.773 * [backup-simplify]: Simplify 0 into 0 3.773 * [backup-simplify]: Simplify 1 into 1 3.773 * [taylor]: Taking taylor expansion of PI in n 3.773 * [backup-simplify]: Simplify PI into PI 3.773 * [backup-simplify]: Simplify (* 0 PI) into 0 3.773 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.774 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.775 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.776 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.776 * [backup-simplify]: Simplify (- k) into (- k) 3.776 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.776 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.777 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.777 * [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)))) 3.778 * [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))))) 3.778 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.778 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.778 * [taylor]: Taking taylor expansion of 0.5 in k 3.778 * [backup-simplify]: Simplify 0.5 into 0.5 3.778 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.778 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.778 * [taylor]: Taking taylor expansion of 1.0 in k 3.778 * [backup-simplify]: Simplify 1.0 into 1.0 3.778 * [taylor]: Taking taylor expansion of k in k 3.778 * [backup-simplify]: Simplify 0 into 0 3.778 * [backup-simplify]: Simplify 1 into 1 3.778 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.779 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.779 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.779 * [taylor]: Taking taylor expansion of 2.0 in k 3.779 * [backup-simplify]: Simplify 2.0 into 2.0 3.779 * [taylor]: Taking taylor expansion of PI in k 3.779 * [backup-simplify]: Simplify PI into PI 3.779 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.780 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.780 * [taylor]: Taking taylor expansion of (log n) in k 3.780 * [taylor]: Taking taylor expansion of n in k 3.780 * [backup-simplify]: Simplify n into n 3.780 * [backup-simplify]: Simplify (log n) into (log n) 3.780 * [backup-simplify]: Simplify (- 0) into 0 3.780 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.781 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.781 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.782 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 3.783 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.783 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.784 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.785 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.786 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.786 * [backup-simplify]: Simplify (- 0) into 0 3.793 * [backup-simplify]: Simplify (+ 0 0) into 0 3.793 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.794 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.795 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.796 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.796 * [taylor]: Taking taylor expansion of 0 in k 3.796 * [backup-simplify]: Simplify 0 into 0 3.796 * [backup-simplify]: Simplify 0 into 0 3.797 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.798 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.798 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.798 * [backup-simplify]: Simplify (+ 0 0) into 0 3.799 * [backup-simplify]: Simplify (- 1) into -1 3.799 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.800 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.801 * [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)))) 3.803 * [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)))))) 3.805 * [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)))))) 3.806 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.806 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.808 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.808 * [backup-simplify]: Simplify (- 0) into 0 3.809 * [backup-simplify]: Simplify (+ 0 0) into 0 3.809 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.810 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.811 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.812 * [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 3.812 * [taylor]: Taking taylor expansion of 0 in k 3.812 * [backup-simplify]: Simplify 0 into 0 3.812 * [backup-simplify]: Simplify 0 into 0 3.812 * [backup-simplify]: Simplify 0 into 0 3.813 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.815 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.816 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.816 * [backup-simplify]: Simplify (+ 0 0) into 0 3.816 * [backup-simplify]: Simplify (- 0) into 0 3.816 * [backup-simplify]: Simplify (+ 0 0) into 0 3.817 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.819 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 3.821 * [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)))))) 3.825 * [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)))))) 3.831 * [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)))))) 3.831 * [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)))) 3.831 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.831 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.831 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.831 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.831 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.831 * [taylor]: Taking taylor expansion of 0.5 in k 3.831 * [backup-simplify]: Simplify 0.5 into 0.5 3.831 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.831 * [taylor]: Taking taylor expansion of 1.0 in k 3.831 * [backup-simplify]: Simplify 1.0 into 1.0 3.831 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.831 * [taylor]: Taking taylor expansion of k in k 3.831 * [backup-simplify]: Simplify 0 into 0 3.831 * [backup-simplify]: Simplify 1 into 1 3.832 * [backup-simplify]: Simplify (/ 1 1) into 1 3.832 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.832 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.832 * [taylor]: Taking taylor expansion of 2.0 in k 3.832 * [backup-simplify]: Simplify 2.0 into 2.0 3.832 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.832 * [taylor]: Taking taylor expansion of PI in k 3.832 * [backup-simplify]: Simplify PI into PI 3.832 * [taylor]: Taking taylor expansion of n in k 3.832 * [backup-simplify]: Simplify n into n 3.832 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.832 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.832 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.832 * [backup-simplify]: Simplify (- 1) into -1 3.833 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.833 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.833 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.833 * [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))))) 3.833 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.833 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.833 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.833 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.833 * [taylor]: Taking taylor expansion of 0.5 in n 3.833 * [backup-simplify]: Simplify 0.5 into 0.5 3.833 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.833 * [taylor]: Taking taylor expansion of 1.0 in n 3.833 * [backup-simplify]: Simplify 1.0 into 1.0 3.833 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.833 * [taylor]: Taking taylor expansion of k in n 3.833 * [backup-simplify]: Simplify k into k 3.833 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.833 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.833 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.833 * [taylor]: Taking taylor expansion of 2.0 in n 3.833 * [backup-simplify]: Simplify 2.0 into 2.0 3.833 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.833 * [taylor]: Taking taylor expansion of PI in n 3.833 * [backup-simplify]: Simplify PI into PI 3.833 * [taylor]: Taking taylor expansion of n in n 3.833 * [backup-simplify]: Simplify 0 into 0 3.833 * [backup-simplify]: Simplify 1 into 1 3.834 * [backup-simplify]: Simplify (/ PI 1) into PI 3.834 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.835 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.835 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.835 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.835 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.836 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.836 * [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)))) 3.837 * [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))))) 3.837 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.837 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.837 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.837 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.837 * [taylor]: Taking taylor expansion of 0.5 in n 3.837 * [backup-simplify]: Simplify 0.5 into 0.5 3.837 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.837 * [taylor]: Taking taylor expansion of 1.0 in n 3.837 * [backup-simplify]: Simplify 1.0 into 1.0 3.837 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.837 * [taylor]: Taking taylor expansion of k in n 3.837 * [backup-simplify]: Simplify k into k 3.837 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.837 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.837 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.837 * [taylor]: Taking taylor expansion of 2.0 in n 3.837 * [backup-simplify]: Simplify 2.0 into 2.0 3.837 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.837 * [taylor]: Taking taylor expansion of PI in n 3.837 * [backup-simplify]: Simplify PI into PI 3.837 * [taylor]: Taking taylor expansion of n in n 3.837 * [backup-simplify]: Simplify 0 into 0 3.837 * [backup-simplify]: Simplify 1 into 1 3.838 * [backup-simplify]: Simplify (/ PI 1) into PI 3.838 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.839 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.839 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.839 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.839 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.840 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.840 * [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)))) 3.841 * [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))))) 3.841 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.841 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.841 * [taylor]: Taking taylor expansion of 0.5 in k 3.841 * [backup-simplify]: Simplify 0.5 into 0.5 3.841 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.841 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.841 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.841 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.841 * [taylor]: Taking taylor expansion of 2.0 in k 3.841 * [backup-simplify]: Simplify 2.0 into 2.0 3.841 * [taylor]: Taking taylor expansion of PI in k 3.841 * [backup-simplify]: Simplify PI into PI 3.842 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.842 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.842 * [taylor]: Taking taylor expansion of (log n) in k 3.842 * [taylor]: Taking taylor expansion of n in k 3.842 * [backup-simplify]: Simplify n into n 3.842 * [backup-simplify]: Simplify (log n) into (log n) 3.842 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.842 * [taylor]: Taking taylor expansion of 1.0 in k 3.842 * [backup-simplify]: Simplify 1.0 into 1.0 3.842 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.842 * [taylor]: Taking taylor expansion of k in k 3.842 * [backup-simplify]: Simplify 0 into 0 3.842 * [backup-simplify]: Simplify 1 into 1 3.843 * [backup-simplify]: Simplify (/ 1 1) into 1 3.843 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.843 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 3.844 * [backup-simplify]: Simplify (- 1) into -1 3.844 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.844 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 3.845 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 3.846 * [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))))) 3.847 * [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))))) 3.847 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.848 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.848 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.849 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.849 * [backup-simplify]: Simplify (- 0) into 0 3.849 * [backup-simplify]: Simplify (+ 0 0) into 0 3.849 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.850 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.851 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.852 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.852 * [taylor]: Taking taylor expansion of 0 in k 3.852 * [backup-simplify]: Simplify 0 into 0 3.852 * [backup-simplify]: Simplify 0 into 0 3.852 * [backup-simplify]: Simplify 0 into 0 3.853 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.853 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.855 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.855 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.855 * [backup-simplify]: Simplify (- 0) into 0 3.856 * [backup-simplify]: Simplify (+ 0 0) into 0 3.856 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 3.857 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.858 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 3.859 * [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 3.859 * [taylor]: Taking taylor expansion of 0 in k 3.859 * [backup-simplify]: Simplify 0 into 0 3.859 * [backup-simplify]: Simplify 0 into 0 3.859 * [backup-simplify]: Simplify 0 into 0 3.859 * [backup-simplify]: Simplify 0 into 0 3.860 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.861 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.864 * [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 3.864 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.864 * [backup-simplify]: Simplify (- 0) into 0 3.864 * [backup-simplify]: Simplify (+ 0 0) into 0 3.865 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 3.866 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.867 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 3.868 * [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 3.868 * [taylor]: Taking taylor expansion of 0 in k 3.868 * [backup-simplify]: Simplify 0 into 0 3.868 * [backup-simplify]: Simplify 0 into 0 3.869 * [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)))) 3.870 * [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))) 3.870 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.870 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.870 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.870 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.870 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.870 * [taylor]: Taking taylor expansion of 0.5 in k 3.870 * [backup-simplify]: Simplify 0.5 into 0.5 3.870 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.870 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.870 * [taylor]: Taking taylor expansion of k in k 3.870 * [backup-simplify]: Simplify 0 into 0 3.870 * [backup-simplify]: Simplify 1 into 1 3.870 * [backup-simplify]: Simplify (/ 1 1) into 1 3.870 * [taylor]: Taking taylor expansion of 1.0 in k 3.870 * [backup-simplify]: Simplify 1.0 into 1.0 3.870 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.870 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.870 * [taylor]: Taking taylor expansion of -2.0 in k 3.870 * [backup-simplify]: Simplify -2.0 into -2.0 3.870 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.870 * [taylor]: Taking taylor expansion of PI in k 3.870 * [backup-simplify]: Simplify PI into PI 3.870 * [taylor]: Taking taylor expansion of n in k 3.870 * [backup-simplify]: Simplify n into n 3.870 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.870 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.871 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.871 * [backup-simplify]: Simplify (+ 1 0) into 1 3.871 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.871 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.871 * [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)))))) 3.871 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.871 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.871 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.871 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.871 * [taylor]: Taking taylor expansion of 0.5 in n 3.871 * [backup-simplify]: Simplify 0.5 into 0.5 3.871 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.871 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.871 * [taylor]: Taking taylor expansion of k in n 3.871 * [backup-simplify]: Simplify k into k 3.871 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.871 * [taylor]: Taking taylor expansion of 1.0 in n 3.872 * [backup-simplify]: Simplify 1.0 into 1.0 3.872 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.872 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.872 * [taylor]: Taking taylor expansion of -2.0 in n 3.872 * [backup-simplify]: Simplify -2.0 into -2.0 3.872 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.872 * [taylor]: Taking taylor expansion of PI in n 3.872 * [backup-simplify]: Simplify PI into PI 3.872 * [taylor]: Taking taylor expansion of n in n 3.872 * [backup-simplify]: Simplify 0 into 0 3.872 * [backup-simplify]: Simplify 1 into 1 3.872 * [backup-simplify]: Simplify (/ PI 1) into PI 3.872 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.873 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.873 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.873 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.874 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.875 * [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)))) 3.875 * [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))))) 3.875 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.875 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.875 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.875 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.875 * [taylor]: Taking taylor expansion of 0.5 in n 3.875 * [backup-simplify]: Simplify 0.5 into 0.5 3.875 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.875 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.875 * [taylor]: Taking taylor expansion of k in n 3.875 * [backup-simplify]: Simplify k into k 3.875 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.875 * [taylor]: Taking taylor expansion of 1.0 in n 3.875 * [backup-simplify]: Simplify 1.0 into 1.0 3.876 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.876 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.876 * [taylor]: Taking taylor expansion of -2.0 in n 3.876 * [backup-simplify]: Simplify -2.0 into -2.0 3.876 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.876 * [taylor]: Taking taylor expansion of PI in n 3.876 * [backup-simplify]: Simplify PI into PI 3.876 * [taylor]: Taking taylor expansion of n in n 3.876 * [backup-simplify]: Simplify 0 into 0 3.876 * [backup-simplify]: Simplify 1 into 1 3.876 * [backup-simplify]: Simplify (/ PI 1) into PI 3.876 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.877 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.877 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.877 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.878 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.878 * [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)))) 3.879 * [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))))) 3.879 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 3.879 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 3.879 * [taylor]: Taking taylor expansion of 0.5 in k 3.879 * [backup-simplify]: Simplify 0.5 into 0.5 3.879 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 3.879 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.879 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.879 * [taylor]: Taking taylor expansion of k in k 3.879 * [backup-simplify]: Simplify 0 into 0 3.879 * [backup-simplify]: Simplify 1 into 1 3.880 * [backup-simplify]: Simplify (/ 1 1) into 1 3.880 * [taylor]: Taking taylor expansion of 1.0 in k 3.880 * [backup-simplify]: Simplify 1.0 into 1.0 3.880 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.880 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.880 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.880 * [taylor]: Taking taylor expansion of -2.0 in k 3.880 * [backup-simplify]: Simplify -2.0 into -2.0 3.880 * [taylor]: Taking taylor expansion of PI in k 3.880 * [backup-simplify]: Simplify PI into PI 3.880 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.881 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.881 * [taylor]: Taking taylor expansion of (log n) in k 3.881 * [taylor]: Taking taylor expansion of n in k 3.881 * [backup-simplify]: Simplify n into n 3.881 * [backup-simplify]: Simplify (log n) into (log n) 3.881 * [backup-simplify]: Simplify (+ 1 0) into 1 3.881 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.882 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 3.882 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 3.883 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 3.884 * [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))))) 3.892 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 3.892 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.893 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.894 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.894 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.894 * [backup-simplify]: Simplify (+ 0 0) into 0 3.894 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.895 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.896 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.897 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.897 * [taylor]: Taking taylor expansion of 0 in k 3.897 * [backup-simplify]: Simplify 0 into 0 3.897 * [backup-simplify]: Simplify 0 into 0 3.897 * [backup-simplify]: Simplify 0 into 0 3.898 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.898 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.900 * [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 3.900 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.901 * [backup-simplify]: Simplify (+ 0 0) into 0 3.901 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 3.902 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.903 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 3.904 * [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 3.904 * [taylor]: Taking taylor expansion of 0 in k 3.904 * [backup-simplify]: Simplify 0 into 0 3.904 * [backup-simplify]: Simplify 0 into 0 3.904 * [backup-simplify]: Simplify 0 into 0 3.905 * [backup-simplify]: Simplify 0 into 0 3.905 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.906 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.909 * [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 3.909 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.909 * [backup-simplify]: Simplify (+ 0 0) into 0 3.910 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 3.911 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.912 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 3.913 * [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 3.913 * [taylor]: Taking taylor expansion of 0 in k 3.913 * [backup-simplify]: Simplify 0 into 0 3.913 * [backup-simplify]: Simplify 0 into 0 3.914 * [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)))))) 3.914 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 3.914 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k))) 3.914 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.914 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.914 * [taylor]: Taking taylor expansion of 1.0 in k 3.914 * [backup-simplify]: Simplify 1.0 into 1.0 3.914 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.914 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.914 * [taylor]: Taking taylor expansion of k in k 3.915 * [backup-simplify]: Simplify 0 into 0 3.915 * [backup-simplify]: Simplify 1 into 1 3.915 * [backup-simplify]: Simplify (/ 1 1) into 1 3.915 * [backup-simplify]: Simplify (sqrt 0) into 0 3.916 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.916 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.916 * [taylor]: Taking taylor expansion of 1.0 in k 3.916 * [backup-simplify]: Simplify 1.0 into 1.0 3.916 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.916 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.916 * [taylor]: Taking taylor expansion of k in k 3.916 * [backup-simplify]: Simplify 0 into 0 3.916 * [backup-simplify]: Simplify 1 into 1 3.916 * [backup-simplify]: Simplify (/ 1 1) into 1 3.916 * [backup-simplify]: Simplify (sqrt 0) into 0 3.917 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.917 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.918 * [backup-simplify]: Simplify 0 into 0 3.918 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.919 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.919 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.921 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.922 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.922 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.923 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.925 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.926 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.926 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.927 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 3.927 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k)) 3.927 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.927 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.927 * [taylor]: Taking taylor expansion of 1.0 in k 3.927 * [backup-simplify]: Simplify 1.0 into 1.0 3.927 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.927 * [taylor]: Taking taylor expansion of k in k 3.927 * [backup-simplify]: Simplify 0 into 0 3.927 * [backup-simplify]: Simplify 1 into 1 3.928 * [backup-simplify]: Simplify (sqrt 0) into 0 3.928 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.929 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.929 * [taylor]: Taking taylor expansion of 1.0 in k 3.929 * [backup-simplify]: Simplify 1.0 into 1.0 3.929 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.929 * [taylor]: Taking taylor expansion of k in k 3.929 * [backup-simplify]: Simplify 0 into 0 3.929 * [backup-simplify]: Simplify 1 into 1 3.929 * [backup-simplify]: Simplify (sqrt 0) into 0 3.930 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.930 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.930 * [backup-simplify]: Simplify 0 into 0 3.931 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.931 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.933 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.934 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.934 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.937 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.938 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.938 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.939 * [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)))))))) 3.939 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k))) 3.939 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.939 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.939 * [taylor]: Taking taylor expansion of 1.0 in k 3.939 * [backup-simplify]: Simplify 1.0 into 1.0 3.939 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.939 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.939 * [taylor]: Taking taylor expansion of -1 in k 3.939 * [backup-simplify]: Simplify -1 into -1 3.939 * [taylor]: Taking taylor expansion of k in k 3.939 * [backup-simplify]: Simplify 0 into 0 3.939 * [backup-simplify]: Simplify 1 into 1 3.940 * [backup-simplify]: Simplify (/ -1 1) into -1 3.940 * [backup-simplify]: Simplify (sqrt 0) into 0 3.941 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.941 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.941 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.941 * [taylor]: Taking taylor expansion of 1.0 in k 3.941 * [backup-simplify]: Simplify 1.0 into 1.0 3.941 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.941 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.941 * [taylor]: Taking taylor expansion of -1 in k 3.941 * [backup-simplify]: Simplify -1 into -1 3.941 * [taylor]: Taking taylor expansion of k in k 3.941 * [backup-simplify]: Simplify 0 into 0 3.941 * [backup-simplify]: Simplify 1 into 1 3.941 * [backup-simplify]: Simplify (/ -1 1) into -1 3.942 * [backup-simplify]: Simplify (sqrt 0) into 0 3.942 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.943 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.943 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.943 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.945 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.946 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.946 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.947 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.949 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.952 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 3.952 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.953 * [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))))) 3.953 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 3.953 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.953 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.953 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.953 * [taylor]: Taking taylor expansion of 2.0 in n 3.953 * [backup-simplify]: Simplify 2.0 into 2.0 3.953 * [taylor]: Taking taylor expansion of (* n PI) in n 3.953 * [taylor]: Taking taylor expansion of n in n 3.953 * [backup-simplify]: Simplify 0 into 0 3.953 * [backup-simplify]: Simplify 1 into 1 3.953 * [taylor]: Taking taylor expansion of PI in n 3.953 * [backup-simplify]: Simplify PI into PI 3.953 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.953 * [taylor]: Taking taylor expansion of 2.0 in n 3.953 * [backup-simplify]: Simplify 2.0 into 2.0 3.953 * [taylor]: Taking taylor expansion of (* n PI) in n 3.953 * [taylor]: Taking taylor expansion of n in n 3.953 * [backup-simplify]: Simplify 0 into 0 3.953 * [backup-simplify]: Simplify 1 into 1 3.953 * [taylor]: Taking taylor expansion of PI in n 3.953 * [backup-simplify]: Simplify PI into PI 3.954 * [backup-simplify]: Simplify (* 0 PI) into 0 3.954 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.954 * [backup-simplify]: Simplify 0 into 0 3.955 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.956 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.956 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.956 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.957 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.957 * [backup-simplify]: Simplify 0 into 0 3.958 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.958 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.958 * [backup-simplify]: Simplify 0 into 0 3.959 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.960 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.960 * [backup-simplify]: Simplify 0 into 0 3.961 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.961 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 3.961 * [backup-simplify]: Simplify 0 into 0 3.962 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.963 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 3.963 * [backup-simplify]: Simplify 0 into 0 3.964 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 3.965 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 3.965 * [backup-simplify]: Simplify 0 into 0 3.966 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.966 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 3.966 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.966 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.966 * [taylor]: Taking taylor expansion of 2.0 in n 3.966 * [backup-simplify]: Simplify 2.0 into 2.0 3.966 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.966 * [taylor]: Taking taylor expansion of PI in n 3.966 * [backup-simplify]: Simplify PI into PI 3.966 * [taylor]: Taking taylor expansion of n in n 3.966 * [backup-simplify]: Simplify 0 into 0 3.966 * [backup-simplify]: Simplify 1 into 1 3.966 * [backup-simplify]: Simplify (/ PI 1) into PI 3.966 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.966 * [taylor]: Taking taylor expansion of 2.0 in n 3.966 * [backup-simplify]: Simplify 2.0 into 2.0 3.967 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.967 * [taylor]: Taking taylor expansion of PI in n 3.967 * [backup-simplify]: Simplify PI into PI 3.967 * [taylor]: Taking taylor expansion of n in n 3.967 * [backup-simplify]: Simplify 0 into 0 3.967 * [backup-simplify]: Simplify 1 into 1 3.967 * [backup-simplify]: Simplify (/ PI 1) into PI 3.967 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.968 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.968 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.968 * [backup-simplify]: Simplify 0 into 0 3.969 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.970 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.970 * [backup-simplify]: Simplify 0 into 0 3.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.971 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.971 * [backup-simplify]: Simplify 0 into 0 3.971 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.972 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.972 * [backup-simplify]: Simplify 0 into 0 3.973 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.974 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.974 * [backup-simplify]: Simplify 0 into 0 3.974 * [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 3.975 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.975 * [backup-simplify]: Simplify 0 into 0 3.976 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 3.976 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 3.976 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.976 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.976 * [taylor]: Taking taylor expansion of -2.0 in n 3.976 * [backup-simplify]: Simplify -2.0 into -2.0 3.976 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.976 * [taylor]: Taking taylor expansion of PI in n 3.976 * [backup-simplify]: Simplify PI into PI 3.976 * [taylor]: Taking taylor expansion of n in n 3.976 * [backup-simplify]: Simplify 0 into 0 3.976 * [backup-simplify]: Simplify 1 into 1 3.976 * [backup-simplify]: Simplify (/ PI 1) into PI 3.976 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.976 * [taylor]: Taking taylor expansion of -2.0 in n 3.976 * [backup-simplify]: Simplify -2.0 into -2.0 3.976 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.976 * [taylor]: Taking taylor expansion of PI in n 3.976 * [backup-simplify]: Simplify PI into PI 3.976 * [taylor]: Taking taylor expansion of n in n 3.976 * [backup-simplify]: Simplify 0 into 0 3.977 * [backup-simplify]: Simplify 1 into 1 3.977 * [backup-simplify]: Simplify (/ PI 1) into PI 3.977 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.978 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.978 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.979 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.979 * [backup-simplify]: Simplify 0 into 0 3.986 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.986 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.986 * [backup-simplify]: Simplify 0 into 0 3.987 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.988 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.988 * [backup-simplify]: Simplify 0 into 0 3.988 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.989 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.989 * [backup-simplify]: Simplify 0 into 0 3.990 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.990 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.990 * [backup-simplify]: Simplify 0 into 0 3.991 * [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 3.992 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.992 * [backup-simplify]: Simplify 0 into 0 3.992 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 3.993 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 3.993 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4)) 3.993 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 3.993 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 3.993 * [taylor]: Taking taylor expansion of 1.0 in k 3.993 * [backup-simplify]: Simplify 1.0 into 1.0 3.993 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 3.993 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 3.993 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 3.993 * [taylor]: Taking taylor expansion of 1/4 in k 3.993 * [backup-simplify]: Simplify 1/4 into 1/4 3.993 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.993 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.993 * [taylor]: Taking taylor expansion of k in k 3.993 * [backup-simplify]: Simplify 0 into 0 3.993 * [backup-simplify]: Simplify 1 into 1 3.993 * [backup-simplify]: Simplify (/ 1 1) into 1 3.993 * [backup-simplify]: Simplify (log 1) into 0 3.994 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.994 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 3.994 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 3.994 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 3.994 * [taylor]: Taking taylor expansion of 1.0 in k 3.994 * [backup-simplify]: Simplify 1.0 into 1.0 3.994 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 3.994 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 3.994 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 3.994 * [taylor]: Taking taylor expansion of 1/4 in k 3.994 * [backup-simplify]: Simplify 1/4 into 1/4 3.994 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.994 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.994 * [taylor]: Taking taylor expansion of k in k 3.994 * [backup-simplify]: Simplify 0 into 0 3.994 * [backup-simplify]: Simplify 1 into 1 3.994 * [backup-simplify]: Simplify (/ 1 1) into 1 3.994 * [backup-simplify]: Simplify (log 1) into 0 3.995 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.995 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 3.995 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 3.995 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 3.995 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 3.996 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.997 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.997 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.998 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 3.998 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 3.998 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0 3.998 * [backup-simplify]: Simplify 0 into 0 3.999 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.000 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 4.001 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 4.001 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 4.002 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.003 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0 4.003 * [backup-simplify]: Simplify 0 into 0 4.003 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.006 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 4.006 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 4.007 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 4.008 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.009 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0 4.009 * [backup-simplify]: Simplify 0 into 0 4.009 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.014 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 4.014 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 4.015 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 4.017 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.018 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0 4.018 * [backup-simplify]: Simplify 0 into 0 4.018 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.026 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 4.027 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 4.028 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 4.030 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.031 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0 4.031 * [backup-simplify]: Simplify 0 into 0 4.032 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.046 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 4.047 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 4.048 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 4.051 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.053 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0 4.053 * [backup-simplify]: Simplify 0 into 0 4.053 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 4.053 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4)) 4.053 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 4.053 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 4.053 * [taylor]: Taking taylor expansion of 1.0 in k 4.053 * [backup-simplify]: Simplify 1.0 into 1.0 4.053 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 4.053 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 4.053 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 4.053 * [taylor]: Taking taylor expansion of 1/4 in k 4.053 * [backup-simplify]: Simplify 1/4 into 1/4 4.053 * [taylor]: Taking taylor expansion of (log k) in k 4.053 * [taylor]: Taking taylor expansion of k in k 4.053 * [backup-simplify]: Simplify 0 into 0 4.053 * [backup-simplify]: Simplify 1 into 1 4.054 * [backup-simplify]: Simplify (log 1) into 0 4.054 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 4.054 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 4.054 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 4.054 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 4.054 * [taylor]: Taking taylor expansion of 1.0 in k 4.054 * [backup-simplify]: Simplify 1.0 into 1.0 4.054 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 4.054 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 4.054 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 4.054 * [taylor]: Taking taylor expansion of 1/4 in k 4.054 * [backup-simplify]: Simplify 1/4 into 1/4 4.054 * [taylor]: Taking taylor expansion of (log k) in k 4.054 * [taylor]: Taking taylor expansion of k in k 4.054 * [backup-simplify]: Simplify 0 into 0 4.054 * [backup-simplify]: Simplify 1 into 1 4.054 * [backup-simplify]: Simplify (log 1) into 0 4.055 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 4.055 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 4.055 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 4.055 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 4.055 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 4.056 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 4.056 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 4.056 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 4.057 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 4.057 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0 4.057 * [backup-simplify]: Simplify 0 into 0 4.059 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 4.059 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 4.059 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 4.060 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.061 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 4.061 * [backup-simplify]: Simplify 0 into 0 4.063 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 4.064 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 4.064 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 4.065 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.066 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 4.066 * [backup-simplify]: Simplify 0 into 0 4.077 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 4.078 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 4.079 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 4.080 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.081 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0 4.081 * [backup-simplify]: Simplify 0 into 0 4.089 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 4.090 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 4.091 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 4.093 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.094 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0 4.094 * [backup-simplify]: Simplify 0 into 0 4.109 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 4.109 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 4.110 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 4.113 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.115 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0 4.115 * [backup-simplify]: Simplify 0 into 0 4.115 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 4.115 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) 4.115 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 4.115 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 4.115 * [taylor]: Taking taylor expansion of 1.0 in k 4.115 * [backup-simplify]: Simplify 1.0 into 1.0 4.115 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 4.115 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 4.115 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.115 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.115 * [taylor]: Taking taylor expansion of -1 in k 4.115 * [backup-simplify]: Simplify -1 into -1 4.115 * [taylor]: Taking taylor expansion of k in k 4.115 * [backup-simplify]: Simplify 0 into 0 4.115 * [backup-simplify]: Simplify 1 into 1 4.116 * [backup-simplify]: Simplify (/ -1 1) into -1 4.116 * [backup-simplify]: Simplify (sqrt 0) into 0 4.117 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.117 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 4.117 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 4.118 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.119 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.120 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.122 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 4.122 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 4.122 * [taylor]: Taking taylor expansion of 1.0 in k 4.122 * [backup-simplify]: Simplify 1.0 into 1.0 4.122 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 4.122 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 4.122 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.122 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.122 * [taylor]: Taking taylor expansion of -1 in k 4.122 * [backup-simplify]: Simplify -1 into -1 4.122 * [taylor]: Taking taylor expansion of k in k 4.122 * [backup-simplify]: Simplify 0 into 0 4.122 * [backup-simplify]: Simplify 1 into 1 4.122 * [backup-simplify]: Simplify (/ -1 1) into -1 4.122 * [backup-simplify]: Simplify (sqrt 0) into 0 4.123 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.123 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 4.124 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 4.124 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.126 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.127 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.128 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 4.129 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 4.129 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 4.131 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 4.132 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 4.133 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.135 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.137 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.140 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 4.147 * [backup-simplify]: Simplify (+ (* 1.0 (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) 4.159 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) 4.165 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (sqrt +nan.0)))) (/ 1 (- k))) (* 1.0 (sqrt +nan.0)))) into (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) 4.165 * * * [progress]: simplifying candidates 4.173 * [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))) 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k))))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt 1))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt 1)) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 1) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 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(sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt k)))) (* (sqrt (sqrt k)) (sqrt (sqrt k))) (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 (sqrt k)))) (log1p (/ 1.0 (sqrt (sqrt k)))) (- (log 1.0) (log (sqrt (sqrt k)))) (log (/ 1.0 (sqrt (sqrt k)))) (exp (/ 1.0 (sqrt (sqrt k)))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (cbrt (/ 1.0 (sqrt (sqrt k)))) (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (- 1.0) (- (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt 1))) (/ (sqrt 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(sqrt h3)) (/ (cbrt h2) (cbrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (cbrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt (cbrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (cbrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (cbrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt (cbrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ h2 (cbrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (cbrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt (cbrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ 1 (sqrt (sqrt h3)))) (* (sqrt (sqrt h3)) (sqrt (sqrt h3))) (expm1 (* (* h0 PI) h1)) (log1p (* (* h0 PI) h1)) (* (* h0 PI) h1) (* (* h0 PI) h1) (+ (+ (log h0) (log PI)) (log h1)) (+ (log (* h0 PI)) (log h1)) (log (* (* h0 PI) h1)) (exp (* (* h0 PI) h1)) (* (* (* (* h0 h0) h0) (* (* PI PI) PI)) (* (* h1 h1) h1)) (* (* (* (* h0 PI) (* h0 PI)) (* h0 PI)) (* (* h1 h1) h1)) (* (cbrt (* (* h0 PI) h1)) (cbrt (* (* h0 PI) h1))) (cbrt (* (* h0 PI) h1)) (* (* (* (* h0 PI) h1) (* (* h0 PI) h1)) (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (* (* h0 PI) (sqrt h1)) (* (* h0 PI) 1) (* PI h1) (expm1 (/ h2 (sqrt (sqrt h3)))) (log1p (/ h2 (sqrt (sqrt h3)))) (- (log h2) (log (sqrt (sqrt h3)))) (log (/ h2 (sqrt (sqrt h3)))) (exp (/ h2 (sqrt (sqrt h3)))) (/ (* (* h2 h2) h2) (* (* (sqrt (sqrt h3)) (sqrt (sqrt h3))) (sqrt (sqrt h3)))) (* (cbrt (/ h2 (sqrt (sqrt h3)))) (cbrt (/ h2 (sqrt (sqrt h3))))) (cbrt (/ h2 (sqrt (sqrt h3)))) (* (* (/ h2 (sqrt (sqrt h3))) (/ h2 (sqrt (sqrt h3)))) (/ h2 (sqrt (sqrt h3)))) (sqrt (/ h2 (sqrt (sqrt h3)))) (sqrt (/ h2 (sqrt (sqrt h3)))) (- h2) (- (sqrt (sqrt h3))) (/ (* (cbrt h2) (cbrt h2)) (* (cbrt (sqrt (sqrt h3))) (cbrt (sqrt (sqrt h3))))) (/ (cbrt h2) (cbrt (sqrt (sqrt h3)))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (* (cbrt (sqrt h3)) (cbrt (sqrt h3))))) (/ (cbrt h2) (sqrt (cbrt (sqrt h3)))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt (* (cbrt h3) (cbrt h3))))) (/ (cbrt h2) (sqrt (sqrt (cbrt h3)))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt (sqrt h3)))) (/ (cbrt h2) (sqrt (sqrt (sqrt h3)))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt 1))) (/ (cbrt h2) (sqrt (sqrt h3))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt (sqrt h3)))) (/ (cbrt h2) (sqrt (sqrt (sqrt h3)))) (/ (* (cbrt h2) (cbrt h2)) (sqrt 1)) (/ (cbrt h2) (sqrt (sqrt h3))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt (sqrt h3)))) (/ (cbrt h2) (sqrt (sqrt (sqrt h3)))) (/ (* (cbrt h2) (cbrt h2)) 1) (/ (cbrt h2) (sqrt (sqrt h3))) (/ (sqrt h2) (* (cbrt (sqrt (sqrt h3))) (cbrt (sqrt (sqrt h3))))) (/ (sqrt h2) (cbrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt (* (cbrt (sqrt h3)) (cbrt (sqrt h3))))) (/ (sqrt h2) (sqrt (cbrt (sqrt h3)))) (/ (sqrt h2) (sqrt (sqrt (* (cbrt h3) (cbrt h3))))) (/ (sqrt h2) (sqrt (sqrt (cbrt h3)))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt (sqrt 1))) (/ (sqrt h2) (sqrt (sqrt h3))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt 1)) (/ (sqrt h2) (sqrt (sqrt h3))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) 1) (/ (sqrt h2) (sqrt (sqrt h3))) (/ 1 (* (cbrt (sqrt (sqrt h3))) (cbrt (sqrt (sqrt h3))))) (/ h2 (cbrt (sqrt (sqrt h3)))) (/ 1 (sqrt (* (cbrt (sqrt h3)) (cbrt (sqrt h3))))) (/ h2 (sqrt (cbrt (sqrt h3)))) (/ 1 (sqrt (sqrt (* (cbrt h3) (cbrt h3))))) (/ h2 (sqrt (sqrt (cbrt h3)))) (/ 1 (sqrt (sqrt (sqrt h3)))) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ 1 (sqrt (sqrt 1))) (/ h2 (sqrt (sqrt h3))) (/ 1 (sqrt (sqrt (sqrt h3)))) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ 1 (sqrt 1)) (/ h2 (sqrt (sqrt h3))) (/ 1 (sqrt (sqrt (sqrt h3)))) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ 1 1) (/ h2 (sqrt (sqrt h3))) (/ 1 (sqrt (sqrt h3))) (/ (sqrt (sqrt h3)) h2) (/ h2 (* (cbrt (sqrt (sqrt h3))) (cbrt (sqrt (sqrt h3))))) (/ h2 (sqrt (* (cbrt (sqrt h3)) (cbrt (sqrt h3))))) (/ h2 (sqrt (sqrt (* (cbrt h3) (cbrt h3))))) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ h2 (sqrt (sqrt 1))) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ h2 1) (/ (sqrt (sqrt h3)) (cbrt h2)) (/ (sqrt (sqrt h3)) (sqrt h2)) (/ (sqrt (sqrt h3)) h2) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (- (+ (* h8 h3) (- (+ (* h8 (pow h3 2)) (- h8))))) (- (+ (* h8 (/ 1 (pow h3 2))) (- (+ (* h8 (/ 1 h3)) (- (* h8 (/ 1 (pow h3 3)))))))) (- (+ (* h8 (/ 1 (pow h3 2))) (- (+ (* h8 (/ 1 h3)) (- h8))))) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h2 (pow (/ 1 h3) 1/4)) (* h2 (pow (/ 1 h3) 1/4)) (- (* h2 (sqrt h8)) (+ (* h8 (/ 1 (* (sqrt h8) (pow h3 2)))) (- (+ (* h8 (/ 1 (* (sqrt h8) h3))) (- (* h8 (/ 1 (* (pow (sqrt h8) 3) (pow h3 2))))))))) 4.193 * * [simplify]: iteration 0 : 1355 enodes (cost 5833 ) 4.215 * * [simplify]: iteration 1 : 5001 enodes (cost 5050 ) 4.234 * * * [progress]: adding candidates to table 4.999 * [progress]: [Phase 3 of 3] Extracting. 4.999 * * [regime]: Finding splitpoints for: (# # # # # # #) 5.002 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 5.002 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 5.032 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 5.068 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 5.102 * * * [regime]: Found split indices: #