16.661 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.087 * * * [progress]: [2/2] Setting up program. 0.089 * [progress]: [Phase 2 of 3] Improving. 0.090 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.090 * [simplify]: Sending expressions to egg_math: (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) 0.092 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.093 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.095 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.097 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.103 * * [simplify]: iteration 4 : 1034 enodes (cost 8 ) 0.125 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.126 * * [progress]: iteration 1 / 4 0.126 * * * [progress]: picking best candidate 0.128 * * * * [pick]: Picked # 0.128 * * * [progress]: localizing error 0.141 * * * [progress]: generating rewritten candidates 0.141 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.165 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.182 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.188 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.232 * * * [progress]: generating series expansions 0.232 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.233 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 0.233 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.233 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.233 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.233 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.233 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.233 * [taylor]: Taking taylor expansion of 0.5 in k 0.233 * [backup-simplify]: Simplify 0.5 into 0.5 0.233 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.233 * [taylor]: Taking taylor expansion of 1.0 in k 0.233 * [backup-simplify]: Simplify 1.0 into 1.0 0.233 * [taylor]: Taking taylor expansion of k in k 0.233 * [backup-simplify]: Simplify 0 into 0 0.233 * [backup-simplify]: Simplify 1 into 1 0.233 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.233 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.233 * [taylor]: Taking taylor expansion of 2.0 in k 0.233 * [backup-simplify]: Simplify 2.0 into 2.0 0.233 * [taylor]: Taking taylor expansion of (* n PI) in k 0.233 * [taylor]: Taking taylor expansion of n in k 0.233 * [backup-simplify]: Simplify n into n 0.233 * [taylor]: Taking taylor expansion of PI in k 0.233 * [backup-simplify]: Simplify PI into PI 0.233 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.233 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.233 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.234 * [backup-simplify]: Simplify (- 0) into 0 0.234 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.234 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.234 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.234 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.234 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.234 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.234 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.234 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.234 * [taylor]: Taking taylor expansion of 0.5 in n 0.234 * [backup-simplify]: Simplify 0.5 into 0.5 0.234 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.235 * [taylor]: Taking taylor expansion of 1.0 in n 0.235 * [backup-simplify]: Simplify 1.0 into 1.0 0.235 * [taylor]: Taking taylor expansion of k in n 0.235 * [backup-simplify]: Simplify k into k 0.235 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.235 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.235 * [taylor]: Taking taylor expansion of 2.0 in n 0.235 * [backup-simplify]: Simplify 2.0 into 2.0 0.235 * [taylor]: Taking taylor expansion of (* n PI) in n 0.235 * [taylor]: Taking taylor expansion of n in n 0.235 * [backup-simplify]: Simplify 0 into 0 0.235 * [backup-simplify]: Simplify 1 into 1 0.235 * [taylor]: Taking taylor expansion of PI in n 0.235 * [backup-simplify]: Simplify PI into PI 0.235 * [backup-simplify]: Simplify (* 0 PI) into 0 0.235 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.236 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.237 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.238 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.238 * [backup-simplify]: Simplify (- k) into (- k) 0.238 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.238 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.239 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.239 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.240 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.240 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.240 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.240 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.240 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.240 * [taylor]: Taking taylor expansion of 0.5 in n 0.240 * [backup-simplify]: Simplify 0.5 into 0.5 0.240 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.240 * [taylor]: Taking taylor expansion of 1.0 in n 0.240 * [backup-simplify]: Simplify 1.0 into 1.0 0.240 * [taylor]: Taking taylor expansion of k in n 0.240 * [backup-simplify]: Simplify k into k 0.240 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.240 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.240 * [taylor]: Taking taylor expansion of 2.0 in n 0.240 * [backup-simplify]: Simplify 2.0 into 2.0 0.240 * [taylor]: Taking taylor expansion of (* n PI) in n 0.240 * [taylor]: Taking taylor expansion of n in n 0.240 * [backup-simplify]: Simplify 0 into 0 0.240 * [backup-simplify]: Simplify 1 into 1 0.240 * [taylor]: Taking taylor expansion of PI in n 0.240 * [backup-simplify]: Simplify PI into PI 0.241 * [backup-simplify]: Simplify (* 0 PI) into 0 0.241 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.242 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.243 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.243 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.243 * [backup-simplify]: Simplify (- k) into (- k) 0.243 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.243 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.244 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.245 * [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)))) 0.246 * [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))))) 0.246 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.246 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.246 * [taylor]: Taking taylor expansion of 0.5 in k 0.246 * [backup-simplify]: Simplify 0.5 into 0.5 0.246 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.246 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.246 * [taylor]: Taking taylor expansion of 1.0 in k 0.246 * [backup-simplify]: Simplify 1.0 into 1.0 0.246 * [taylor]: Taking taylor expansion of k in k 0.246 * [backup-simplify]: Simplify 0 into 0 0.246 * [backup-simplify]: Simplify 1 into 1 0.246 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.246 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.246 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.246 * [taylor]: Taking taylor expansion of 2.0 in k 0.246 * [backup-simplify]: Simplify 2.0 into 2.0 0.246 * [taylor]: Taking taylor expansion of PI in k 0.246 * [backup-simplify]: Simplify PI into PI 0.246 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.247 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.247 * [taylor]: Taking taylor expansion of (log n) in k 0.247 * [taylor]: Taking taylor expansion of n in k 0.247 * [backup-simplify]: Simplify n into n 0.247 * [backup-simplify]: Simplify (log n) into (log n) 0.247 * [backup-simplify]: Simplify (- 0) into 0 0.247 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.248 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.249 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.249 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.250 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.251 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.251 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.252 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.253 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.253 * [backup-simplify]: Simplify (- 0) into 0 0.253 * [backup-simplify]: Simplify (+ 0 0) into 0 0.253 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 0.254 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.255 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.256 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.256 * [taylor]: Taking taylor expansion of 0 in k 0.256 * [backup-simplify]: Simplify 0 into 0 0.256 * [backup-simplify]: Simplify 0 into 0 0.257 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.258 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.258 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.258 * [backup-simplify]: Simplify (+ 0 0) into 0 0.258 * [backup-simplify]: Simplify (- 1) into -1 0.259 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.260 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.261 * [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)))) 0.264 * [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)))))) 0.266 * [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)))))) 0.267 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.268 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.269 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.269 * [backup-simplify]: Simplify (- 0) into 0 0.270 * [backup-simplify]: Simplify (+ 0 0) into 0 0.270 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 0.271 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.272 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.273 * [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 0.273 * [taylor]: Taking taylor expansion of 0 in k 0.273 * [backup-simplify]: Simplify 0 into 0 0.273 * [backup-simplify]: Simplify 0 into 0 0.273 * [backup-simplify]: Simplify 0 into 0 0.274 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.276 * [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 0.277 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 0.277 * [backup-simplify]: Simplify (+ 0 0) into 0 0.277 * [backup-simplify]: Simplify (- 0) into 0 0.278 * [backup-simplify]: Simplify (+ 0 0) into 0 0.279 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.280 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 0.283 * [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)))))) 0.286 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 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)))))) 0.298 * [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)))))) 0.299 * [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)))) 0.299 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.299 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.299 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.299 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.299 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.299 * [taylor]: Taking taylor expansion of 0.5 in k 0.299 * [backup-simplify]: Simplify 0.5 into 0.5 0.299 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.299 * [taylor]: Taking taylor expansion of 1.0 in k 0.299 * [backup-simplify]: Simplify 1.0 into 1.0 0.299 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.299 * [taylor]: Taking taylor expansion of k in k 0.299 * [backup-simplify]: Simplify 0 into 0 0.299 * [backup-simplify]: Simplify 1 into 1 0.299 * [backup-simplify]: Simplify (/ 1 1) into 1 0.299 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.299 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.299 * [taylor]: Taking taylor expansion of 2.0 in k 0.299 * [backup-simplify]: Simplify 2.0 into 2.0 0.299 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.299 * [taylor]: Taking taylor expansion of PI in k 0.299 * [backup-simplify]: Simplify PI into PI 0.299 * [taylor]: Taking taylor expansion of n in k 0.299 * [backup-simplify]: Simplify n into n 0.299 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.299 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.299 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.300 * [backup-simplify]: Simplify (- 1) into -1 0.300 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.300 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.300 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.301 * [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))))) 0.301 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.301 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.301 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.301 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.301 * [taylor]: Taking taylor expansion of 0.5 in n 0.301 * [backup-simplify]: Simplify 0.5 into 0.5 0.301 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.301 * [taylor]: Taking taylor expansion of 1.0 in n 0.301 * [backup-simplify]: Simplify 1.0 into 1.0 0.301 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.301 * [taylor]: Taking taylor expansion of k in n 0.301 * [backup-simplify]: Simplify k into k 0.301 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.301 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.301 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.301 * [taylor]: Taking taylor expansion of 2.0 in n 0.301 * [backup-simplify]: Simplify 2.0 into 2.0 0.301 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.301 * [taylor]: Taking taylor expansion of PI in n 0.301 * [backup-simplify]: Simplify PI into PI 0.301 * [taylor]: Taking taylor expansion of n in n 0.301 * [backup-simplify]: Simplify 0 into 0 0.301 * [backup-simplify]: Simplify 1 into 1 0.301 * [backup-simplify]: Simplify (/ PI 1) into PI 0.302 * [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 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.302 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.302 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.303 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.304 * [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)))) 0.305 * [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))))) 0.305 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.305 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.305 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.305 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.305 * [taylor]: Taking taylor expansion of 0.5 in n 0.305 * [backup-simplify]: Simplify 0.5 into 0.5 0.305 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.305 * [taylor]: Taking taylor expansion of 1.0 in n 0.305 * [backup-simplify]: Simplify 1.0 into 1.0 0.305 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.305 * [taylor]: Taking taylor expansion of k in n 0.305 * [backup-simplify]: Simplify k into k 0.305 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.305 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.305 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.305 * [taylor]: Taking taylor expansion of 2.0 in n 0.305 * [backup-simplify]: Simplify 2.0 into 2.0 0.305 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.305 * [taylor]: Taking taylor expansion of PI in n 0.305 * [backup-simplify]: Simplify PI into PI 0.305 * [taylor]: Taking taylor expansion of n in n 0.305 * [backup-simplify]: Simplify 0 into 0 0.305 * [backup-simplify]: Simplify 1 into 1 0.305 * [backup-simplify]: Simplify (/ PI 1) into PI 0.306 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.306 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.306 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.306 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.306 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.308 * [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)))) 0.309 * [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))))) 0.309 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.309 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.309 * [taylor]: Taking taylor expansion of 0.5 in k 0.309 * [backup-simplify]: Simplify 0.5 into 0.5 0.309 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.309 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.309 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.309 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.309 * [taylor]: Taking taylor expansion of 2.0 in k 0.309 * [backup-simplify]: Simplify 2.0 into 2.0 0.309 * [taylor]: Taking taylor expansion of PI in k 0.309 * [backup-simplify]: Simplify PI into PI 0.309 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.310 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.310 * [taylor]: Taking taylor expansion of (log n) in k 0.310 * [taylor]: Taking taylor expansion of n in k 0.310 * [backup-simplify]: Simplify n into n 0.310 * [backup-simplify]: Simplify (log n) into (log n) 0.310 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.310 * [taylor]: Taking taylor expansion of 1.0 in k 0.310 * [backup-simplify]: Simplify 1.0 into 1.0 0.310 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.310 * [taylor]: Taking taylor expansion of k in k 0.310 * [backup-simplify]: Simplify 0 into 0 0.310 * [backup-simplify]: Simplify 1 into 1 0.310 * [backup-simplify]: Simplify (/ 1 1) into 1 0.310 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.311 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.311 * [backup-simplify]: Simplify (- 1) into -1 0.311 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.312 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.313 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 0.313 * [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))))) 0.314 * [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))))) 0.315 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.315 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.316 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.317 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.317 * [backup-simplify]: Simplify (- 0) into 0 0.317 * [backup-simplify]: Simplify (+ 0 0) into 0 0.317 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.318 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.319 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.320 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.320 * [taylor]: Taking taylor expansion of 0 in k 0.320 * [backup-simplify]: Simplify 0 into 0 0.320 * [backup-simplify]: Simplify 0 into 0 0.320 * [backup-simplify]: Simplify 0 into 0 0.321 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.321 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.323 * [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 0.323 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.323 * [backup-simplify]: Simplify (- 0) into 0 0.323 * [backup-simplify]: Simplify (+ 0 0) into 0 0.324 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 0.325 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.326 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 0.327 * [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 0.327 * [taylor]: Taking taylor expansion of 0 in k 0.327 * [backup-simplify]: Simplify 0 into 0 0.327 * [backup-simplify]: Simplify 0 into 0 0.327 * [backup-simplify]: Simplify 0 into 0 0.327 * [backup-simplify]: Simplify 0 into 0 0.328 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.329 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.331 * [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 0.332 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.332 * [backup-simplify]: Simplify (- 0) into 0 0.332 * [backup-simplify]: Simplify (+ 0 0) into 0 0.333 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 0.334 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.335 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 0.336 * [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 0.336 * [taylor]: Taking taylor expansion of 0 in k 0.336 * [backup-simplify]: Simplify 0 into 0 0.336 * [backup-simplify]: Simplify 0 into 0 0.337 * [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)))) 0.338 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 0.338 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.338 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.338 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.338 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.338 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.338 * [taylor]: Taking taylor expansion of 0.5 in k 0.338 * [backup-simplify]: Simplify 0.5 into 0.5 0.338 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.338 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.338 * [taylor]: Taking taylor expansion of k in k 0.338 * [backup-simplify]: Simplify 0 into 0 0.338 * [backup-simplify]: Simplify 1 into 1 0.338 * [backup-simplify]: Simplify (/ 1 1) into 1 0.338 * [taylor]: Taking taylor expansion of 1.0 in k 0.338 * [backup-simplify]: Simplify 1.0 into 1.0 0.338 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.338 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.338 * [taylor]: Taking taylor expansion of -2.0 in k 0.338 * [backup-simplify]: Simplify -2.0 into -2.0 0.338 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.338 * [taylor]: Taking taylor expansion of PI in k 0.338 * [backup-simplify]: Simplify PI into PI 0.338 * [taylor]: Taking taylor expansion of n in k 0.338 * [backup-simplify]: Simplify n into n 0.338 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.338 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.338 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.339 * [backup-simplify]: Simplify (+ 1 0) into 1 0.339 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.339 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.339 * [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)))))) 0.339 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.339 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.339 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.339 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.339 * [taylor]: Taking taylor expansion of 0.5 in n 0.339 * [backup-simplify]: Simplify 0.5 into 0.5 0.339 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.339 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.339 * [taylor]: Taking taylor expansion of k in n 0.339 * [backup-simplify]: Simplify k into k 0.339 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.339 * [taylor]: Taking taylor expansion of 1.0 in n 0.339 * [backup-simplify]: Simplify 1.0 into 1.0 0.339 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.340 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.340 * [taylor]: Taking taylor expansion of -2.0 in n 0.340 * [backup-simplify]: Simplify -2.0 into -2.0 0.340 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.340 * [taylor]: Taking taylor expansion of PI in n 0.340 * [backup-simplify]: Simplify PI into PI 0.340 * [taylor]: Taking taylor expansion of n in n 0.340 * [backup-simplify]: Simplify 0 into 0 0.340 * [backup-simplify]: Simplify 1 into 1 0.340 * [backup-simplify]: Simplify (/ PI 1) into PI 0.340 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.341 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.341 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.341 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.342 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.342 * [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)))) 0.343 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.343 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.343 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.343 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.343 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.343 * [taylor]: Taking taylor expansion of 0.5 in n 0.343 * [backup-simplify]: Simplify 0.5 into 0.5 0.343 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.343 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.343 * [taylor]: Taking taylor expansion of k in n 0.343 * [backup-simplify]: Simplify k into k 0.343 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.343 * [taylor]: Taking taylor expansion of 1.0 in n 0.343 * [backup-simplify]: Simplify 1.0 into 1.0 0.343 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.343 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.343 * [taylor]: Taking taylor expansion of -2.0 in n 0.343 * [backup-simplify]: Simplify -2.0 into -2.0 0.344 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.344 * [taylor]: Taking taylor expansion of PI in n 0.344 * [backup-simplify]: Simplify PI into PI 0.344 * [taylor]: Taking taylor expansion of n in n 0.344 * [backup-simplify]: Simplify 0 into 0 0.344 * [backup-simplify]: Simplify 1 into 1 0.344 * [backup-simplify]: Simplify (/ PI 1) into PI 0.344 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.345 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.345 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.345 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.346 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.346 * [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)))) 0.347 * [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))))) 0.347 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.347 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.347 * [taylor]: Taking taylor expansion of 0.5 in k 0.347 * [backup-simplify]: Simplify 0.5 into 0.5 0.347 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.347 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.347 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.347 * [taylor]: Taking taylor expansion of k in k 0.347 * [backup-simplify]: Simplify 0 into 0 0.347 * [backup-simplify]: Simplify 1 into 1 0.348 * [backup-simplify]: Simplify (/ 1 1) into 1 0.348 * [taylor]: Taking taylor expansion of 1.0 in k 0.348 * [backup-simplify]: Simplify 1.0 into 1.0 0.348 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.348 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.348 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.348 * [taylor]: Taking taylor expansion of -2.0 in k 0.348 * [backup-simplify]: Simplify -2.0 into -2.0 0.348 * [taylor]: Taking taylor expansion of PI in k 0.348 * [backup-simplify]: Simplify PI into PI 0.348 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.349 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.349 * [taylor]: Taking taylor expansion of (log n) in k 0.349 * [taylor]: Taking taylor expansion of n in k 0.349 * [backup-simplify]: Simplify n into n 0.349 * [backup-simplify]: Simplify (log n) into (log n) 0.349 * [backup-simplify]: Simplify (+ 1 0) into 1 0.349 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.350 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 0.350 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 0.351 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 0.352 * [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))))) 0.352 * [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))))) 0.353 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.353 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.354 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.354 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.354 * [backup-simplify]: Simplify (+ 0 0) into 0 0.355 * [backup-simplify]: Simplify (+ (* 0.5 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)) 0.356 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.357 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.357 * [taylor]: Taking taylor expansion of 0 in k 0.358 * [backup-simplify]: Simplify 0 into 0 0.358 * [backup-simplify]: Simplify 0 into 0 0.358 * [backup-simplify]: Simplify 0 into 0 0.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.359 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.360 * [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 0.360 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.361 * [backup-simplify]: Simplify (+ 0 0) into 0 0.361 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 0.362 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.363 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (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 0.365 * [backup-simplify]: Simplify 0 into 0 0.365 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.366 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.369 * [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 0.369 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.369 * [backup-simplify]: Simplify (+ 0 0) into 0 0.370 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.371 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.372 * [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 0.374 * [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) 0.375 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.375 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.375 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.375 * [taylor]: Taking taylor expansion of 2.0 in n 0.375 * [backup-simplify]: Simplify 2.0 into 2.0 0.375 * [taylor]: Taking taylor expansion of (* n PI) in n 0.375 * [taylor]: Taking taylor expansion of n in n 0.375 * [backup-simplify]: Simplify 0 into 0 0.375 * [backup-simplify]: Simplify 1 into 1 0.375 * [taylor]: Taking taylor expansion of PI in n 0.375 * [backup-simplify]: Simplify PI into PI 0.375 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.375 * [taylor]: Taking taylor expansion of 2.0 in n 0.375 * [backup-simplify]: Simplify 2.0 into 2.0 0.375 * [taylor]: Taking taylor expansion of (* n PI) in n 0.375 * [taylor]: Taking taylor expansion of n in n 0.375 * [backup-simplify]: Simplify 0 into 0 0.375 * [backup-simplify]: Simplify 1 into 1 0.375 * [taylor]: Taking taylor expansion of PI in n 0.375 * [backup-simplify]: Simplify PI into PI 0.375 * [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) 0.378 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.378 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.379 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.379 * [backup-simplify]: Simplify 0 into 0 0.380 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.380 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.380 * [backup-simplify]: Simplify 0 into 0 0.381 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.382 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.382 * [backup-simplify]: Simplify 0 into 0 0.383 * [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 0.390 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.391 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.391 * [backup-simplify]: Simplify 0 into 0 0.392 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.393 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.393 * [backup-simplify]: Simplify 0 into 0 0.394 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.394 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 0.394 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.394 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.394 * [taylor]: Taking taylor expansion of 2.0 in n 0.394 * [backup-simplify]: Simplify 2.0 into 2.0 0.394 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.394 * [taylor]: Taking taylor expansion of PI in n 0.394 * [backup-simplify]: Simplify PI into PI 0.394 * [taylor]: Taking taylor expansion of n in n 0.394 * [backup-simplify]: Simplify 0 into 0 0.394 * [backup-simplify]: Simplify 1 into 1 0.395 * [backup-simplify]: Simplify (/ PI 1) into PI 0.395 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.395 * [taylor]: Taking taylor expansion of 2.0 in n 0.395 * [backup-simplify]: Simplify 2.0 into 2.0 0.395 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.395 * [taylor]: Taking taylor expansion of PI in n 0.395 * [backup-simplify]: Simplify PI into PI 0.395 * [taylor]: Taking taylor expansion of n in n 0.395 * [backup-simplify]: Simplify 0 into 0 0.395 * [backup-simplify]: Simplify 1 into 1 0.395 * [backup-simplify]: Simplify (/ PI 1) into PI 0.395 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.396 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.396 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.396 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.397 * [backup-simplify]: Simplify 0 into 0 0.397 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.398 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.398 * [backup-simplify]: Simplify 0 into 0 0.398 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.399 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.399 * [backup-simplify]: Simplify 0 into 0 0.399 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.400 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.400 * [backup-simplify]: Simplify 0 into 0 0.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.401 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.401 * [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)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.403 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.403 * [backup-simplify]: Simplify 0 into 0 0.403 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.404 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.404 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.404 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.404 * [taylor]: Taking taylor expansion of -2.0 in n 0.404 * [backup-simplify]: Simplify -2.0 into -2.0 0.404 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.404 * [taylor]: Taking taylor expansion of PI in n 0.404 * [backup-simplify]: Simplify PI into PI 0.404 * [taylor]: Taking taylor expansion of n in n 0.404 * [backup-simplify]: Simplify 0 into 0 0.404 * [backup-simplify]: Simplify 1 into 1 0.404 * [backup-simplify]: Simplify (/ PI 1) into PI 0.404 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.404 * [taylor]: Taking taylor expansion of -2.0 in n 0.404 * [backup-simplify]: Simplify -2.0 into -2.0 0.404 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.404 * [taylor]: Taking taylor expansion of PI in n 0.404 * [backup-simplify]: Simplify PI into PI 0.404 * [taylor]: Taking taylor expansion of n in n 0.404 * [backup-simplify]: Simplify 0 into 0 0.404 * [backup-simplify]: Simplify 1 into 1 0.404 * [backup-simplify]: Simplify (/ PI 1) into PI 0.405 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.405 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.406 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.406 * [backup-simplify]: Simplify 0 into 0 0.407 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.407 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.407 * [backup-simplify]: Simplify 0 into 0 0.408 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.408 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.408 * [backup-simplify]: Simplify 0 into 0 0.409 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.410 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.410 * [backup-simplify]: Simplify 0 into 0 0.410 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.411 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.411 * [backup-simplify]: Simplify 0 into 0 0.412 * [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 0.412 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.412 * [backup-simplify]: Simplify 0 into 0 0.413 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.413 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.413 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.413 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.413 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.413 * [taylor]: Taking taylor expansion of 1.0 in k 0.413 * [backup-simplify]: Simplify 1.0 into 1.0 0.413 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.413 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.413 * [taylor]: Taking taylor expansion of k in k 0.413 * [backup-simplify]: Simplify 0 into 0 0.413 * [backup-simplify]: Simplify 1 into 1 0.413 * [backup-simplify]: Simplify (/ 1 1) into 1 0.414 * [backup-simplify]: Simplify (sqrt 0) into 0 0.414 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.414 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.414 * [taylor]: Taking taylor expansion of 1.0 in k 0.414 * [backup-simplify]: Simplify 1.0 into 1.0 0.414 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.414 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.414 * [taylor]: Taking taylor expansion of k in k 0.414 * [backup-simplify]: Simplify 0 into 0 0.414 * [backup-simplify]: Simplify 1 into 1 0.415 * [backup-simplify]: Simplify (/ 1 1) into 1 0.415 * [backup-simplify]: Simplify (sqrt 0) into 0 0.416 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.416 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.416 * [backup-simplify]: Simplify 0 into 0 0.417 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.417 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.417 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.419 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.420 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.420 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.421 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.423 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.424 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.424 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.425 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 0.425 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 0.425 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.425 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.425 * [taylor]: Taking taylor expansion of 1.0 in k 0.425 * [backup-simplify]: Simplify 1.0 into 1.0 0.425 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.425 * [taylor]: Taking taylor expansion of k in k 0.425 * [backup-simplify]: Simplify 0 into 0 0.425 * [backup-simplify]: Simplify 1 into 1 0.426 * [backup-simplify]: Simplify (sqrt 0) into 0 0.426 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.426 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.426 * [taylor]: Taking taylor expansion of 1.0 in k 0.426 * [backup-simplify]: Simplify 1.0 into 1.0 0.426 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.426 * [taylor]: Taking taylor expansion of k in k 0.426 * [backup-simplify]: Simplify 0 into 0 0.426 * [backup-simplify]: Simplify 1 into 1 0.427 * [backup-simplify]: Simplify (sqrt 0) into 0 0.428 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.428 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.428 * [backup-simplify]: Simplify 0 into 0 0.429 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.429 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.431 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.432 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.432 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.434 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.435 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.435 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.436 * [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)))))))) 0.437 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.437 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.437 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.437 * [taylor]: Taking taylor expansion of 1.0 in k 0.437 * [backup-simplify]: Simplify 1.0 into 1.0 0.437 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.437 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.437 * [taylor]: Taking taylor expansion of -1 in k 0.437 * [backup-simplify]: Simplify -1 into -1 0.437 * [taylor]: Taking taylor expansion of k in k 0.437 * [backup-simplify]: Simplify 0 into 0 0.437 * [backup-simplify]: Simplify 1 into 1 0.437 * [backup-simplify]: Simplify (/ -1 1) into -1 0.437 * [backup-simplify]: Simplify (sqrt 0) into 0 0.438 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.438 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.438 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.438 * [taylor]: Taking taylor expansion of 1.0 in k 0.438 * [backup-simplify]: Simplify 1.0 into 1.0 0.438 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.438 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.438 * [taylor]: Taking taylor expansion of -1 in k 0.438 * [backup-simplify]: Simplify -1 into -1 0.438 * [taylor]: Taking taylor expansion of k in k 0.438 * [backup-simplify]: Simplify 0 into 0 0.438 * [backup-simplify]: Simplify 1 into 1 0.439 * [backup-simplify]: Simplify (/ -1 1) into -1 0.439 * [backup-simplify]: Simplify (sqrt 0) into 0 0.440 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.440 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.440 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.440 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.442 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.443 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 0.443 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.444 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.446 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.448 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 0.448 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.449 * [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))))) 0.449 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.450 * [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))))) 0.450 * [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 0.450 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.450 * [taylor]: Taking taylor expansion of 1.0 in n 0.450 * [backup-simplify]: Simplify 1.0 into 1.0 0.450 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.450 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.450 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.450 * [taylor]: Taking taylor expansion of k in n 0.450 * [backup-simplify]: Simplify k into k 0.450 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.450 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 0.450 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.450 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 0.450 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.450 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.450 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.450 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.450 * [taylor]: Taking taylor expansion of 0.5 in n 0.450 * [backup-simplify]: Simplify 0.5 into 0.5 0.450 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.450 * [taylor]: Taking taylor expansion of 1.0 in n 0.450 * [backup-simplify]: Simplify 1.0 into 1.0 0.450 * [taylor]: Taking taylor expansion of k in n 0.450 * [backup-simplify]: Simplify k into k 0.450 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.450 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.450 * [taylor]: Taking taylor expansion of 2.0 in n 0.450 * [backup-simplify]: Simplify 2.0 into 2.0 0.450 * [taylor]: Taking taylor expansion of (* n PI) in n 0.450 * [taylor]: Taking taylor expansion of n in n 0.450 * [backup-simplify]: Simplify 0 into 0 0.450 * [backup-simplify]: Simplify 1 into 1 0.450 * [taylor]: Taking taylor expansion of PI in n 0.450 * [backup-simplify]: Simplify PI into PI 0.451 * [backup-simplify]: Simplify (* 0 PI) into 0 0.451 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.452 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.453 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.453 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.453 * [backup-simplify]: Simplify (- k) into (- k) 0.453 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.453 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.454 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.455 * [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)))) 0.455 * [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))))) 0.456 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.456 * [taylor]: Taking taylor expansion of 1.0 in k 0.456 * [backup-simplify]: Simplify 1.0 into 1.0 0.456 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.456 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.456 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.456 * [taylor]: Taking taylor expansion of k in k 0.456 * [backup-simplify]: Simplify 0 into 0 0.456 * [backup-simplify]: Simplify 1 into 1 0.456 * [backup-simplify]: Simplify (/ 1 1) into 1 0.456 * [backup-simplify]: Simplify (sqrt 0) into 0 0.457 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.457 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.457 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.457 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.457 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.457 * [taylor]: Taking taylor expansion of 0.5 in k 0.457 * [backup-simplify]: Simplify 0.5 into 0.5 0.457 * [taylor]: Taking taylor expansion of (- 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 k in k 0.457 * [backup-simplify]: Simplify 0 into 0 0.457 * [backup-simplify]: Simplify 1 into 1 0.457 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.457 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.457 * [taylor]: Taking taylor expansion of 2.0 in k 0.457 * [backup-simplify]: Simplify 2.0 into 2.0 0.457 * [taylor]: Taking taylor expansion of (* n PI) in k 0.457 * [taylor]: Taking taylor expansion of n in k 0.457 * [backup-simplify]: Simplify n into n 0.457 * [taylor]: Taking taylor expansion of PI in k 0.457 * [backup-simplify]: Simplify PI into PI 0.457 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.457 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.457 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.458 * [backup-simplify]: Simplify (- 0) into 0 0.458 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.458 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.458 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.458 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.458 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.458 * [taylor]: Taking taylor expansion of 1.0 in k 0.458 * [backup-simplify]: Simplify 1.0 into 1.0 0.458 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.458 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.458 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.458 * [taylor]: Taking taylor expansion of k in k 0.458 * [backup-simplify]: Simplify 0 into 0 0.458 * [backup-simplify]: Simplify 1 into 1 0.459 * [backup-simplify]: Simplify (/ 1 1) into 1 0.459 * [backup-simplify]: Simplify (sqrt 0) into 0 0.459 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.460 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.460 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.460 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.460 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.460 * [taylor]: Taking taylor expansion of 0.5 in k 0.460 * [backup-simplify]: Simplify 0.5 into 0.5 0.460 * [taylor]: Taking taylor expansion of (- 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 k in k 0.460 * [backup-simplify]: Simplify 0 into 0 0.460 * [backup-simplify]: Simplify 1 into 1 0.460 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.460 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.460 * [taylor]: Taking taylor expansion of 2.0 in k 0.460 * [backup-simplify]: Simplify 2.0 into 2.0 0.460 * [taylor]: Taking taylor expansion of (* n PI) in k 0.460 * [taylor]: Taking taylor expansion of n in k 0.460 * [backup-simplify]: Simplify n into n 0.460 * [taylor]: Taking taylor expansion of PI in k 0.460 * [backup-simplify]: Simplify PI into PI 0.460 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.460 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.460 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.460 * [backup-simplify]: Simplify (- 0) into 0 0.460 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.461 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.461 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.461 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.461 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 0.461 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.461 * [taylor]: Taking taylor expansion of 0 in n 0.461 * [backup-simplify]: Simplify 0 into 0 0.461 * [backup-simplify]: Simplify 0 into 0 0.462 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 0.462 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 0.462 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 0.463 * [backup-simplify]: Simplify (- 1) into -1 0.463 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.464 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 0.464 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 0.465 * [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))) 0.466 * [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))) 0.467 * [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))) 0.467 * [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 0.467 * [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 0.467 * [taylor]: Taking taylor expansion of +nan.0 in n 0.467 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.467 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.467 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.467 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.467 * [taylor]: Taking taylor expansion of 0.5 in n 0.467 * [backup-simplify]: Simplify 0.5 into 0.5 0.467 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.467 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.467 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.467 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.467 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.467 * [taylor]: Taking taylor expansion of 1.0 in n 0.467 * [backup-simplify]: Simplify 1.0 into 1.0 0.467 * [taylor]: Taking taylor expansion of (log PI) in n 0.467 * [taylor]: Taking taylor expansion of PI in n 0.467 * [backup-simplify]: Simplify PI into PI 0.467 * [backup-simplify]: Simplify (log PI) into (log PI) 0.468 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.469 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.469 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.469 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.469 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.469 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) 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 n) in n 0.469 * [taylor]: Taking taylor expansion of n in n 0.469 * [backup-simplify]: Simplify 0 into 0 0.469 * [backup-simplify]: Simplify 1 into 1 0.469 * [backup-simplify]: Simplify (log 1) into 0 0.469 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.469 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.470 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.470 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.470 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.470 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.470 * [taylor]: Taking taylor expansion of 1.0 in n 0.470 * [backup-simplify]: Simplify 1.0 into 1.0 0.470 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.470 * [taylor]: Taking taylor expansion of 2.0 in n 0.470 * [backup-simplify]: Simplify 2.0 into 2.0 0.470 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.470 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.471 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.472 * [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) 0.472 * [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) 0.473 * [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)) 0.474 * [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))) 0.475 * [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) 0.476 * [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)) 0.477 * [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))) 0.478 * [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))) 0.478 * [backup-simplify]: Simplify 0 into 0 0.478 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 0.479 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 0.486 * [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 0.486 * [backup-simplify]: Simplify (- 0) into 0 0.487 * [backup-simplify]: Simplify (+ 0 0) into 0 0.487 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.488 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 0.488 * [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))) 0.489 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.491 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.493 * [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)))))))) 0.496 * [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)))))))) 0.496 * [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 0.496 * [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 0.496 * [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 0.496 * [taylor]: Taking taylor expansion of +nan.0 in n 0.496 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.496 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.496 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.496 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.496 * [taylor]: Taking taylor expansion of 0.5 in n 0.496 * [backup-simplify]: Simplify 0.5 into 0.5 0.496 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.496 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.496 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.496 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.496 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.496 * [taylor]: Taking taylor expansion of 1.0 in n 0.496 * [backup-simplify]: Simplify 1.0 into 1.0 0.496 * [taylor]: Taking taylor expansion of (log PI) in n 0.496 * [taylor]: Taking taylor expansion of PI in n 0.496 * [backup-simplify]: Simplify PI into PI 0.496 * [backup-simplify]: Simplify (log PI) into (log PI) 0.497 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.498 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.498 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.498 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.498 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.498 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.498 * [taylor]: Taking taylor expansion of 1.0 in n 0.498 * [backup-simplify]: Simplify 1.0 into 1.0 0.498 * [taylor]: Taking taylor expansion of (log n) in n 0.498 * [taylor]: Taking taylor expansion of n in n 0.498 * [backup-simplify]: Simplify 0 into 0 0.498 * [backup-simplify]: Simplify 1 into 1 0.498 * [backup-simplify]: Simplify (log 1) into 0 0.498 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.498 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.498 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.498 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.498 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.499 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.499 * [taylor]: Taking taylor expansion of 1.0 in n 0.499 * [backup-simplify]: Simplify 1.0 into 1.0 0.499 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.499 * [taylor]: Taking taylor expansion of 2.0 in n 0.499 * [backup-simplify]: Simplify 2.0 into 2.0 0.499 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.499 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.500 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.501 * [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) 0.501 * [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) 0.502 * [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)) 0.503 * [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))) 0.504 * [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) 0.504 * [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 0.504 * [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 0.504 * [taylor]: Taking taylor expansion of +nan.0 in n 0.504 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.504 * [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 0.504 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.504 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.504 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.504 * [taylor]: Taking taylor expansion of 0.5 in n 0.504 * [backup-simplify]: Simplify 0.5 into 0.5 0.504 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.504 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.504 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.504 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.504 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) 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 2.0) in n 0.504 * [taylor]: Taking taylor expansion of 2.0 in n 0.504 * [backup-simplify]: Simplify 2.0 into 2.0 0.504 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.505 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.506 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.506 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.506 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.506 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.506 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.506 * [taylor]: Taking taylor expansion of 1.0 in n 0.506 * [backup-simplify]: Simplify 1.0 into 1.0 0.506 * [taylor]: Taking taylor expansion of (log PI) in n 0.506 * [taylor]: Taking taylor expansion of PI in n 0.506 * [backup-simplify]: Simplify PI into PI 0.506 * [backup-simplify]: Simplify (log PI) into (log PI) 0.507 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.508 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.508 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.508 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.508 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.508 * [taylor]: Taking taylor expansion of 1.0 in n 0.508 * [backup-simplify]: Simplify 1.0 into 1.0 0.508 * [taylor]: Taking taylor expansion of (log n) 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 * [backup-simplify]: Simplify (log 1) into 0 0.508 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.508 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.508 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.509 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.509 * [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) 0.510 * [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)) 0.511 * [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))) 0.512 * [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) 0.512 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.512 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.512 * [taylor]: Taking taylor expansion of 2.0 in n 0.512 * [backup-simplify]: Simplify 2.0 into 2.0 0.512 * [taylor]: Taking taylor expansion of (* n PI) in n 0.512 * [taylor]: Taking taylor expansion of n in n 0.512 * [backup-simplify]: Simplify 0 into 0 0.512 * [backup-simplify]: Simplify 1 into 1 0.512 * [taylor]: Taking taylor expansion of PI in n 0.512 * [backup-simplify]: Simplify PI into PI 0.512 * [backup-simplify]: Simplify (* 0 PI) into 0 0.513 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.513 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.514 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.515 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.516 * [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)) 0.517 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.518 * [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)) 0.520 * [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))) 0.521 * [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)))))) 0.525 * [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)))))))) 0.529 * [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)))))))) 0.532 * [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)))))))) 0.533 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 0.533 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 0.534 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 0.535 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 0.535 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.536 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.536 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 0.536 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 0.537 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 0.538 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 0.538 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 0.539 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 0.540 * [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 0.542 * [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 0.543 * [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 0.544 * [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 0.544 * [backup-simplify]: Simplify (- 0) into 0 0.544 * [backup-simplify]: Simplify 0 into 0 0.544 * [backup-simplify]: Simplify 0 into 0 0.545 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.546 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 0.547 * [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 0.548 * [backup-simplify]: Simplify (- 0) into 0 0.548 * [backup-simplify]: Simplify (+ 0 0) into 0 0.548 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 0.549 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 0.550 * [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))) 0.551 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.553 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.556 * [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)))))))) 0.562 * [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)))))))) 0.562 * [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 0.562 * [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 0.563 * [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 0.563 * [taylor]: Taking taylor expansion of +nan.0 in n 0.563 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.563 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.563 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.563 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.563 * [taylor]: Taking taylor expansion of 0.5 in n 0.563 * [backup-simplify]: Simplify 0.5 into 0.5 0.563 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.563 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.563 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.563 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.563 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.563 * [taylor]: Taking taylor expansion of 1.0 in n 0.563 * [backup-simplify]: Simplify 1.0 into 1.0 0.563 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.563 * [taylor]: Taking taylor expansion of 2.0 in n 0.563 * [backup-simplify]: Simplify 2.0 into 2.0 0.563 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.564 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.564 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.564 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.564 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.565 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.565 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.565 * [taylor]: Taking taylor expansion of 1.0 in n 0.565 * [backup-simplify]: Simplify 1.0 into 1.0 0.565 * [taylor]: Taking taylor expansion of (log n) in n 0.565 * [taylor]: Taking taylor expansion of n in n 0.565 * [backup-simplify]: Simplify 0 into 0 0.565 * [backup-simplify]: Simplify 1 into 1 0.565 * [backup-simplify]: Simplify (log 1) into 0 0.565 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.565 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.565 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.565 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.565 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.565 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) 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 PI) in n 0.565 * [taylor]: Taking taylor expansion of PI in n 0.565 * [backup-simplify]: Simplify PI into PI 0.566 * [backup-simplify]: Simplify (log PI) into (log PI) 0.566 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.567 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.568 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.568 * [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) 0.569 * [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)) 0.570 * [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))) 0.571 * [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) 0.571 * [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 0.571 * [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 0.571 * [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 0.571 * [taylor]: Taking taylor expansion of +nan.0 in n 0.571 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.571 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 0.571 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.571 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.571 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.571 * [taylor]: Taking taylor expansion of 0.5 in n 0.571 * [backup-simplify]: Simplify 0.5 into 0.5 0.571 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.571 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.571 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.571 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.571 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.571 * [taylor]: Taking taylor expansion of 1.0 in n 0.571 * [backup-simplify]: Simplify 1.0 into 1.0 0.571 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.571 * [taylor]: Taking taylor expansion of 2.0 in n 0.571 * [backup-simplify]: Simplify 2.0 into 2.0 0.571 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.572 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.573 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.573 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.573 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.573 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.573 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.573 * [taylor]: Taking taylor expansion of 1.0 in n 0.573 * [backup-simplify]: Simplify 1.0 into 1.0 0.573 * [taylor]: Taking taylor expansion of (log PI) in n 0.573 * [taylor]: Taking taylor expansion of PI in n 0.573 * [backup-simplify]: Simplify PI into PI 0.573 * [backup-simplify]: Simplify (log PI) into (log PI) 0.574 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.575 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.575 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.575 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.575 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) 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 n) in n 0.575 * [taylor]: Taking taylor expansion of n in n 0.575 * [backup-simplify]: Simplify 0 into 0 0.575 * [backup-simplify]: Simplify 1 into 1 0.575 * [backup-simplify]: Simplify (log 1) into 0 0.575 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.576 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.576 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.576 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.577 * [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) 0.578 * [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)) 0.585 * [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))) 0.586 * [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) 0.586 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.586 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.586 * [taylor]: Taking taylor expansion of 2.0 in n 0.586 * [backup-simplify]: Simplify 2.0 into 2.0 0.586 * [taylor]: Taking taylor expansion of (* n PI) in n 0.586 * [taylor]: Taking taylor expansion of n in n 0.586 * [backup-simplify]: Simplify 0 into 0 0.586 * [backup-simplify]: Simplify 1 into 1 0.586 * [taylor]: Taking taylor expansion of PI in n 0.586 * [backup-simplify]: Simplify PI into PI 0.586 * [backup-simplify]: Simplify (* 0 PI) into 0 0.586 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.587 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.588 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.589 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.589 * [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 0.589 * [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 0.589 * [taylor]: Taking taylor expansion of +nan.0 in n 0.589 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.589 * [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 0.589 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.589 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.589 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.589 * [taylor]: Taking taylor expansion of 0.5 in n 0.589 * [backup-simplify]: Simplify 0.5 into 0.5 0.589 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.589 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.589 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.589 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.589 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) 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 2.0) in n 0.589 * [taylor]: Taking taylor expansion of 2.0 in n 0.589 * [backup-simplify]: Simplify 2.0 into 2.0 0.589 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.590 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.591 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.591 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.591 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.591 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.591 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.591 * [taylor]: Taking taylor expansion of 1.0 in n 0.591 * [backup-simplify]: Simplify 1.0 into 1.0 0.591 * [taylor]: Taking taylor expansion of (log PI) in n 0.591 * [taylor]: Taking taylor expansion of PI in n 0.591 * [backup-simplify]: Simplify PI into PI 0.591 * [backup-simplify]: Simplify (log PI) into (log PI) 0.592 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.593 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.593 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.593 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.593 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.593 * [taylor]: Taking taylor expansion of 1.0 in n 0.593 * [backup-simplify]: Simplify 1.0 into 1.0 0.593 * [taylor]: Taking taylor expansion of (log n) 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 * [backup-simplify]: Simplify (log 1) into 0 0.593 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.593 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.593 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.594 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.595 * [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) 0.595 * [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)) 0.596 * [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))) 0.597 * [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) 0.597 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.597 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.597 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.597 * [taylor]: Taking taylor expansion of 2.0 in n 0.597 * [backup-simplify]: Simplify 2.0 into 2.0 0.597 * [taylor]: Taking taylor expansion of (* n PI) in n 0.597 * [taylor]: Taking taylor expansion of n in n 0.597 * [backup-simplify]: Simplify 0 into 0 0.597 * [backup-simplify]: Simplify 1 into 1 0.597 * [taylor]: Taking taylor expansion of PI in n 0.597 * [backup-simplify]: Simplify PI into PI 0.597 * [backup-simplify]: Simplify (* 0 PI) into 0 0.598 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.599 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.599 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.600 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.601 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.602 * [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)) 0.603 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.604 * [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)) 0.606 * [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))) 0.606 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.607 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.608 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 0.610 * [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)) 0.612 * [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))) 0.613 * [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)))))))) 0.620 * [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)))))))))))) 0.628 * [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)))))))))))) 0.637 * [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)))))))))))))) 0.646 * [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)))))))))))))) 0.655 * [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)))))))))))))) 0.670 * [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)))))))))))))))))))))) 0.671 * [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)))))) 0.671 * [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 0.671 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.671 * [taylor]: Taking taylor expansion of 1.0 in n 0.671 * [backup-simplify]: Simplify 1.0 into 1.0 0.671 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.671 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.671 * [taylor]: Taking taylor expansion of k in n 0.671 * [backup-simplify]: Simplify k into k 0.671 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 0.671 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 0.671 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.671 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.671 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.671 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.671 * [taylor]: Taking taylor expansion of 0.5 in n 0.671 * [backup-simplify]: Simplify 0.5 into 0.5 0.671 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.671 * [taylor]: Taking taylor expansion of 1.0 in n 0.671 * [backup-simplify]: Simplify 1.0 into 1.0 0.671 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.671 * [taylor]: Taking taylor expansion of k in n 0.671 * [backup-simplify]: Simplify k into k 0.671 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.671 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.671 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.671 * [taylor]: Taking taylor expansion of 2.0 in n 0.671 * [backup-simplify]: Simplify 2.0 into 2.0 0.671 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.671 * [taylor]: Taking taylor expansion of PI in n 0.671 * [backup-simplify]: Simplify PI into PI 0.671 * [taylor]: Taking taylor expansion of n in n 0.671 * [backup-simplify]: Simplify 0 into 0 0.671 * [backup-simplify]: Simplify 1 into 1 0.677 * [backup-simplify]: Simplify (/ PI 1) into PI 0.677 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.678 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.678 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.678 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.678 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.679 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.680 * [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)))) 0.681 * [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))))) 0.681 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.681 * [taylor]: Taking taylor expansion of 1.0 in k 0.681 * [backup-simplify]: Simplify 1.0 into 1.0 0.681 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.681 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.681 * [taylor]: Taking taylor expansion of k in k 0.681 * [backup-simplify]: Simplify 0 into 0 0.681 * [backup-simplify]: Simplify 1 into 1 0.681 * [backup-simplify]: Simplify (sqrt 0) into 0 0.682 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.682 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.682 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.682 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.682 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.682 * [taylor]: Taking taylor expansion of 0.5 in k 0.682 * [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)) 0.683 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.683 * [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))))) 0.684 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.684 * [taylor]: Taking taylor expansion of 1.0 in k 0.684 * [backup-simplify]: Simplify 1.0 into 1.0 0.684 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.684 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.684 * [taylor]: Taking taylor expansion of k in k 0.684 * [backup-simplify]: Simplify 0 into 0 0.684 * [backup-simplify]: Simplify 1 into 1 0.684 * [backup-simplify]: Simplify (sqrt 0) into 0 0.685 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.685 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.685 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.685 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.685 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.685 * [taylor]: Taking taylor expansion of 0.5 in k 0.685 * [backup-simplify]: Simplify 0.5 into 0.5 0.685 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.685 * [taylor]: Taking taylor expansion of 1.0 in k 0.685 * [backup-simplify]: Simplify 1.0 into 1.0 0.685 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.685 * [taylor]: Taking taylor expansion of k in k 0.685 * [backup-simplify]: Simplify 0 into 0 0.685 * [backup-simplify]: Simplify 1 into 1 0.685 * [backup-simplify]: Simplify (/ 1 1) into 1 0.685 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.685 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.685 * [taylor]: Taking taylor expansion of 2.0 in k 0.685 * [backup-simplify]: Simplify 2.0 into 2.0 0.685 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.685 * [taylor]: Taking taylor expansion of PI in k 0.685 * [backup-simplify]: Simplify PI into PI 0.685 * [taylor]: Taking taylor expansion of n in k 0.685 * [backup-simplify]: Simplify n into n 0.685 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.685 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.685 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.686 * [backup-simplify]: Simplify (- 1) into -1 0.686 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.686 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.686 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.686 * [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))))) 0.687 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 0.687 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.687 * [taylor]: Taking taylor expansion of 0 in n 0.687 * [backup-simplify]: Simplify 0 into 0 0.687 * [backup-simplify]: Simplify 0 into 0 0.687 * [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))))))) 0.688 * [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))))))) 0.688 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.688 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.688 * [taylor]: Taking taylor expansion of +nan.0 in n 0.688 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.688 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.688 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.688 * [taylor]: Taking taylor expansion of 0.5 in n 0.688 * [backup-simplify]: Simplify 0.5 into 0.5 0.688 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.688 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.688 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.688 * [taylor]: Taking taylor expansion of 2.0 in n 0.688 * [backup-simplify]: Simplify 2.0 into 2.0 0.688 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.688 * [taylor]: Taking taylor expansion of PI in n 0.688 * [backup-simplify]: Simplify PI into PI 0.688 * [taylor]: Taking taylor expansion of n in n 0.688 * [backup-simplify]: Simplify 0 into 0 0.688 * [backup-simplify]: Simplify 1 into 1 0.688 * [backup-simplify]: Simplify (/ PI 1) into PI 0.689 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.689 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.689 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.689 * [taylor]: Taking taylor expansion of 1.0 in n 0.689 * [backup-simplify]: Simplify 1.0 into 1.0 0.689 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.689 * [taylor]: Taking taylor expansion of k in n 0.689 * [backup-simplify]: Simplify k into k 0.689 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.690 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.690 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.690 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.691 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.692 * [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)))) 0.692 * [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))))) 0.693 * [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)))))) 0.694 * [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))))))) 0.695 * [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))))))) 0.695 * [backup-simplify]: Simplify 0 into 0 0.696 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.697 * [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))))))) 0.698 * [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))))))) 0.698 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.698 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.698 * [taylor]: Taking taylor expansion of +nan.0 in n 0.698 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.698 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.698 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.698 * [taylor]: Taking taylor expansion of 0.5 in n 0.698 * [backup-simplify]: Simplify 0.5 into 0.5 0.698 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.698 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.698 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.698 * [taylor]: Taking taylor expansion of 2.0 in n 0.698 * [backup-simplify]: Simplify 2.0 into 2.0 0.698 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.698 * [taylor]: Taking taylor expansion of PI in n 0.698 * [backup-simplify]: Simplify PI into PI 0.698 * [taylor]: Taking taylor expansion of n in n 0.698 * [backup-simplify]: Simplify 0 into 0 0.698 * [backup-simplify]: Simplify 1 into 1 0.698 * [backup-simplify]: Simplify (/ PI 1) into PI 0.698 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.699 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.699 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.699 * [taylor]: Taking taylor expansion of 1.0 in n 0.699 * [backup-simplify]: Simplify 1.0 into 1.0 0.699 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.699 * [taylor]: Taking taylor expansion of k in n 0.699 * [backup-simplify]: Simplify k into k 0.699 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.700 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.700 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.700 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.701 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.702 * [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)))) 0.703 * [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))))) 0.703 * [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)))))) 0.704 * [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))))))) 0.705 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.706 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.706 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.706 * [backup-simplify]: Simplify (- 0) into 0 0.707 * [backup-simplify]: Simplify (+ 0 0) into 0 0.707 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.707 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.708 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.709 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.710 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 0.711 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.712 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 0.712 * [backup-simplify]: Simplify (- 0) into 0 0.712 * [backup-simplify]: Simplify 0 into 0 0.712 * [backup-simplify]: Simplify 0 into 0 0.714 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.715 * [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))))))) 0.716 * [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))))))) 0.716 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.716 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.716 * [taylor]: Taking taylor expansion of +nan.0 in n 0.716 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.716 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.716 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.716 * [taylor]: Taking taylor expansion of 0.5 in n 0.716 * [backup-simplify]: Simplify 0.5 into 0.5 0.716 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.716 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.716 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.716 * [taylor]: Taking taylor expansion of 2.0 in n 0.716 * [backup-simplify]: Simplify 2.0 into 2.0 0.716 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.716 * [taylor]: Taking taylor expansion of PI in n 0.716 * [backup-simplify]: Simplify PI into PI 0.716 * [taylor]: Taking taylor expansion of n in n 0.716 * [backup-simplify]: Simplify 0 into 0 0.716 * [backup-simplify]: Simplify 1 into 1 0.717 * [backup-simplify]: Simplify (/ PI 1) into PI 0.717 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.718 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.718 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.718 * [taylor]: Taking taylor expansion of 1.0 in n 0.718 * [backup-simplify]: Simplify 1.0 into 1.0 0.718 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.718 * [taylor]: Taking taylor expansion of k in n 0.718 * [backup-simplify]: Simplify k into k 0.718 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.719 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.719 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.719 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.719 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.720 * [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)))) 0.721 * [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))))) 0.722 * [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)))))) 0.722 * [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 n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.726 * [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)))))))) 0.726 * [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)))) 0.726 * [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 0.726 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.726 * [taylor]: Taking taylor expansion of 1.0 in n 0.726 * [backup-simplify]: Simplify 1.0 into 1.0 0.726 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.727 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.727 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.727 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.727 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.727 * [taylor]: Taking taylor expansion of 0.5 in n 0.727 * [backup-simplify]: Simplify 0.5 into 0.5 0.727 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.727 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.727 * [taylor]: Taking taylor expansion of k in n 0.727 * [backup-simplify]: Simplify k into k 0.727 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.727 * [taylor]: Taking taylor expansion of 1.0 in n 0.727 * [backup-simplify]: Simplify 1.0 into 1.0 0.727 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.727 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.727 * [taylor]: Taking taylor expansion of -2.0 in n 0.727 * [backup-simplify]: Simplify -2.0 into -2.0 0.727 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.727 * [taylor]: Taking taylor expansion of PI in n 0.727 * [backup-simplify]: Simplify PI into PI 0.727 * [taylor]: Taking taylor expansion of n in n 0.727 * [backup-simplify]: Simplify 0 into 0 0.727 * [backup-simplify]: Simplify 1 into 1 0.727 * [backup-simplify]: Simplify (/ PI 1) into PI 0.727 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.728 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.728 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.728 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.729 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.730 * [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)))) 0.731 * [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))))) 0.731 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.731 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.731 * [taylor]: Taking taylor expansion of -1 in n 0.731 * [backup-simplify]: Simplify -1 into -1 0.731 * [taylor]: Taking taylor expansion of k in n 0.731 * [backup-simplify]: Simplify k into k 0.731 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 0.731 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 0.731 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 0.731 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 0.732 * [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))) 0.732 * [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 0.732 * [backup-simplify]: Simplify (/ 1 1) into 1 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 (log (* -2.0 (/ PI n))) in k 0.732 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.732 * [taylor]: Taking taylor expansion of -2.0 in k 0.732 * [backup-simplify]: Simplify -2.0 into -2.0 0.732 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.732 * [taylor]: Taking taylor expansion of PI in k 0.732 * [backup-simplify]: Simplify PI into PI 0.732 * [taylor]: Taking taylor expansion of n in k 0.732 * [backup-simplify]: Simplify n into n 0.732 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.732 * [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)))) 0.733 * [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)))))) 0.733 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.733 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.733 * [taylor]: Taking taylor expansion of -1 in k 0.733 * [backup-simplify]: Simplify -1 into -1 0.733 * [taylor]: Taking taylor expansion of k in k 0.733 * [backup-simplify]: Simplify 0 into 0 0.733 * [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 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.735 * [taylor]: Taking taylor expansion of 1.0 in k 0.735 * [backup-simplify]: Simplify 1.0 into 1.0 0.735 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.735 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.735 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.735 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.735 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.735 * [taylor]: Taking taylor expansion of 0.5 in k 0.735 * [backup-simplify]: Simplify 0.5 into 0.5 0.735 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.735 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.735 * [taylor]: Taking taylor expansion of k in k 0.735 * [backup-simplify]: Simplify 0 into 0 0.735 * [backup-simplify]: Simplify 1 into 1 0.735 * [backup-simplify]: Simplify (/ 1 1) into 1 0.735 * [taylor]: Taking taylor expansion of 1.0 in k 0.735 * [backup-simplify]: Simplify 1.0 into 1.0 0.735 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.735 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.735 * [taylor]: Taking taylor expansion of -2.0 in k 0.735 * [backup-simplify]: Simplify -2.0 into -2.0 0.735 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.735 * [taylor]: Taking taylor expansion of PI in k 0.735 * [backup-simplify]: Simplify PI into PI 0.735 * [taylor]: Taking taylor expansion of n in k 0.736 * [backup-simplify]: Simplify n into n 0.736 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.736 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.736 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.736 * [backup-simplify]: Simplify (+ 1 0) into 1 0.736 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.736 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.736 * [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)))))) 0.736 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.736 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.736 * [taylor]: Taking taylor expansion of -1 in k 0.736 * [backup-simplify]: Simplify -1 into -1 0.736 * [taylor]: Taking taylor expansion of k in k 0.737 * [backup-simplify]: Simplify 0 into 0 0.737 * [backup-simplify]: Simplify 1 into 1 0.737 * [backup-simplify]: Simplify (/ -1 1) into -1 0.737 * [backup-simplify]: Simplify (sqrt 0) into 0 0.738 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.738 * [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))))))) 0.738 * [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))))))) 0.738 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.738 * [taylor]: Taking taylor expansion of +nan.0 in n 0.738 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.738 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.738 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.738 * [taylor]: Taking taylor expansion of 0.5 in n 0.738 * [backup-simplify]: Simplify 0.5 into 0.5 0.738 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.738 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.738 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.738 * [taylor]: Taking taylor expansion of k in n 0.738 * [backup-simplify]: Simplify k into k 0.738 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.738 * [taylor]: Taking taylor expansion of 1.0 in n 0.738 * [backup-simplify]: Simplify 1.0 into 1.0 0.738 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.738 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.738 * [taylor]: Taking taylor expansion of -2.0 in n 0.738 * [backup-simplify]: Simplify -2.0 into -2.0 0.738 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.738 * [taylor]: Taking taylor expansion of PI in n 0.739 * [backup-simplify]: Simplify PI into PI 0.739 * [taylor]: Taking taylor expansion of n in n 0.739 * [backup-simplify]: Simplify 0 into 0 0.739 * [backup-simplify]: Simplify 1 into 1 0.739 * [backup-simplify]: Simplify (/ PI 1) into PI 0.739 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.740 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.740 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.741 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.741 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.742 * [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)))) 0.743 * [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))))) 0.743 * [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)))))) 0.744 * [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)))))) 0.745 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.746 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.747 * [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)))))))) 0.747 * [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)))))))) 0.747 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.747 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.747 * [taylor]: Taking taylor expansion of +nan.0 in n 0.747 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.747 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.747 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.747 * [taylor]: Taking taylor expansion of 0.5 in n 0.747 * [backup-simplify]: Simplify 0.5 into 0.5 0.748 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.748 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.748 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.748 * [taylor]: Taking taylor expansion of k in n 0.748 * [backup-simplify]: Simplify k into k 0.748 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.748 * [taylor]: Taking taylor expansion of 1.0 in n 0.748 * [backup-simplify]: Simplify 1.0 into 1.0 0.748 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.748 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.748 * [taylor]: Taking taylor expansion of -2.0 in n 0.748 * [backup-simplify]: Simplify -2.0 into -2.0 0.748 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.748 * [taylor]: Taking taylor expansion of PI in n 0.748 * [backup-simplify]: Simplify PI into PI 0.748 * [taylor]: Taking taylor expansion of n in n 0.748 * [backup-simplify]: Simplify 0 into 0 0.748 * [backup-simplify]: Simplify 1 into 1 0.748 * [backup-simplify]: Simplify (/ PI 1) into PI 0.748 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.749 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.749 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.750 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.750 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.751 * [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)))) 0.752 * [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))))) 0.753 * [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)))))) 0.753 * [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))))))) 0.754 * [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))))))) 0.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.755 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.756 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.756 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.756 * [backup-simplify]: Simplify (+ 0 0) into 0 0.757 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.758 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.759 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 0.760 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.761 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 0.761 * [backup-simplify]: Simplify 0 into 0 0.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.763 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.765 * [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)))))))) 0.765 * [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)))))))) 0.765 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.765 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.765 * [taylor]: Taking taylor expansion of +nan.0 in n 0.765 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.765 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.765 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.765 * [taylor]: Taking taylor expansion of 0.5 in n 0.765 * [backup-simplify]: Simplify 0.5 into 0.5 0.765 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.765 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.765 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.765 * [taylor]: Taking taylor expansion of k in n 0.765 * [backup-simplify]: Simplify k into k 0.765 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.765 * [taylor]: Taking taylor expansion of 1.0 in n 0.765 * [backup-simplify]: Simplify 1.0 into 1.0 0.765 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.765 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.765 * [taylor]: Taking taylor expansion of -2.0 in n 0.765 * [backup-simplify]: Simplify -2.0 into -2.0 0.765 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.765 * [taylor]: Taking taylor expansion of PI in n 0.765 * [backup-simplify]: Simplify PI into PI 0.766 * [taylor]: Taking taylor expansion of n in n 0.766 * [backup-simplify]: Simplify 0 into 0 0.766 * [backup-simplify]: Simplify 1 into 1 0.766 * [backup-simplify]: Simplify (/ PI 1) into PI 0.766 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.767 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.767 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.768 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.768 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.769 * [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)))) 0.770 * [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))))) 0.770 * [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)))))) 0.777 * [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 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))))))) 0.781 * [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)))))))))))) 0.781 * * * [progress]: simplifying candidates 0.783 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 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+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) 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(log (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (+ (log (/ h2 (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (log (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (exp (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 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h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ h2 (sqrt h1)) (pow (* h0 h4) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (* (/ h2 (sqrt h1)) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ h2 (sqrt h1)) 1) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ 1 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ h2 h0))) (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (- (+ (* h7 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h7 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (+ (* h6 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (- (+ (* h9 h1) (- (+ (* h9 (pow h1 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- (* h9 (/ 1 (pow h1 3)))))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- h9))))) (- (+ (* h9 (* (* (pow h1 2) (pow (log (* h0 h4)) 2)) (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log (* h0 h4))) (pow (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (* (log (* h0 h4)) (log h3))) (pow (* (pow h4 h2) (* (pow h0 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log h3)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* h1 (log (* h0 h4))) (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (pow (log h3) 2)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* h1 (log h3)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5)) (- (+ (* h9 (* (pow h1 2) (pow (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2))) h5))) (- (* h9 (* h1 (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5)))))))))))))))))))))) (- (+ (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (pow h1 3))) (- (+ (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) h1)) (- (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (pow h1 2)))))))) (- (+ (* h9 (/ (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) h1)) (- (+ (* h9 (/ (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (pow h1 2))) (- (* h9 (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))))))))) 0.793 * * [simplify]: iteration 0 : 950 enodes (cost 1461 ) 0.808 * * [simplify]: iteration 1 : 3924 enodes (cost 1358 ) 0.870 * * [simplify]: iteration 2 : 5002 enodes (cost 1344 ) 0.876 * * * [progress]: adding candidates to table 1.285 * * [progress]: iteration 2 / 4 1.285 * * * [progress]: picking best candidate 1.310 * * * * [pick]: Picked # 1.311 * * * [progress]: localizing error 1.326 * * * [progress]: generating rewritten candidates 1.326 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 1.350 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 1.367 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 1.373 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 1.383 * * * [progress]: generating series expansions 1.383 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 1.384 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.384 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.384 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.384 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.384 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.384 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.384 * [taylor]: Taking taylor expansion of 0.5 in k 1.384 * [backup-simplify]: Simplify 0.5 into 0.5 1.384 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.384 * [taylor]: Taking taylor expansion of 1.0 in k 1.384 * [backup-simplify]: Simplify 1.0 into 1.0 1.384 * [taylor]: Taking taylor expansion of k in k 1.384 * [backup-simplify]: Simplify 0 into 0 1.385 * [backup-simplify]: Simplify 1 into 1 1.385 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.385 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.385 * [taylor]: Taking taylor expansion of 2.0 in k 1.385 * [backup-simplify]: Simplify 2.0 into 2.0 1.385 * [taylor]: Taking taylor expansion of (* n PI) in k 1.385 * [taylor]: Taking taylor expansion of n in k 1.385 * [backup-simplify]: Simplify n into n 1.385 * [taylor]: Taking taylor expansion of PI in k 1.385 * [backup-simplify]: Simplify PI into PI 1.385 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.385 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.385 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.385 * [backup-simplify]: Simplify (- 0) into 0 1.385 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.386 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.386 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.386 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.386 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.386 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.386 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.386 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.386 * [taylor]: Taking taylor expansion of 0.5 in n 1.386 * [backup-simplify]: Simplify 0.5 into 0.5 1.386 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.386 * [taylor]: Taking taylor expansion of 1.0 in n 1.386 * [backup-simplify]: Simplify 1.0 into 1.0 1.386 * [taylor]: Taking taylor expansion of k in n 1.386 * [backup-simplify]: Simplify k into k 1.386 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.386 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.386 * [taylor]: Taking taylor expansion of 2.0 in n 1.386 * [backup-simplify]: Simplify 2.0 into 2.0 1.386 * [taylor]: Taking taylor expansion of (* n PI) in n 1.386 * [taylor]: Taking taylor expansion of n in n 1.386 * [backup-simplify]: Simplify 0 into 0 1.386 * [backup-simplify]: Simplify 1 into 1 1.386 * [taylor]: Taking taylor expansion of PI in n 1.386 * [backup-simplify]: Simplify PI into PI 1.386 * [backup-simplify]: Simplify (* 0 PI) into 0 1.387 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.388 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.389 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.389 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.389 * [backup-simplify]: Simplify (- k) into (- k) 1.389 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.389 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.390 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.391 * [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)))) 1.391 * [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))))) 1.391 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.391 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.391 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.391 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.392 * [taylor]: Taking taylor expansion of 0.5 in n 1.392 * [backup-simplify]: Simplify 0.5 into 0.5 1.392 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.392 * [taylor]: Taking taylor expansion of 1.0 in n 1.392 * [backup-simplify]: Simplify 1.0 into 1.0 1.392 * [taylor]: Taking taylor expansion of k in n 1.392 * [backup-simplify]: Simplify k into k 1.392 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.392 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.392 * [taylor]: Taking taylor expansion of 2.0 in n 1.392 * [backup-simplify]: Simplify 2.0 into 2.0 1.392 * [taylor]: Taking taylor expansion of (* n PI) in n 1.392 * [taylor]: Taking taylor expansion of n in n 1.392 * [backup-simplify]: Simplify 0 into 0 1.392 * [backup-simplify]: Simplify 1 into 1 1.392 * [taylor]: Taking taylor expansion of PI in n 1.392 * [backup-simplify]: Simplify PI into PI 1.392 * [backup-simplify]: Simplify (* 0 PI) into 0 1.392 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.393 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.394 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.395 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.395 * [backup-simplify]: Simplify (- k) into (- k) 1.395 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.395 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.396 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.396 * [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)))) 1.397 * [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))))) 1.397 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.397 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.397 * [taylor]: Taking taylor expansion of 0.5 in k 1.397 * [backup-simplify]: Simplify 0.5 into 0.5 1.397 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.397 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.397 * [taylor]: Taking taylor expansion of 1.0 in k 1.397 * [backup-simplify]: Simplify 1.0 into 1.0 1.397 * [taylor]: Taking taylor expansion of k in k 1.397 * [backup-simplify]: Simplify 0 into 0 1.397 * [backup-simplify]: Simplify 1 into 1 1.397 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.397 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.397 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.397 * [taylor]: Taking taylor expansion of 2.0 in k 1.397 * [backup-simplify]: Simplify 2.0 into 2.0 1.397 * [taylor]: Taking taylor expansion of PI in k 1.397 * [backup-simplify]: Simplify PI into PI 1.398 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.398 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.398 * [taylor]: Taking taylor expansion of (log n) in k 1.398 * [taylor]: Taking taylor expansion of n in k 1.398 * [backup-simplify]: Simplify n into n 1.398 * [backup-simplify]: Simplify (log n) into (log n) 1.398 * [backup-simplify]: Simplify (- 0) into 0 1.399 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.399 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.400 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.401 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.401 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.402 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.407 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.407 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.408 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.409 * [backup-simplify]: Simplify (- 0) into 0 1.409 * [backup-simplify]: Simplify (+ 0 0) into 0 1.409 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.410 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.411 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.412 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.412 * [taylor]: Taking taylor expansion of 0 in k 1.412 * [backup-simplify]: Simplify 0 into 0 1.412 * [backup-simplify]: Simplify 0 into 0 1.412 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.413 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.414 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.414 * [backup-simplify]: Simplify (+ 0 0) into 0 1.414 * [backup-simplify]: Simplify (- 1) into -1 1.414 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.415 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.417 * [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)))) 1.418 * [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)))))) 1.420 * [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)))))) 1.421 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.421 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.423 * [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 1.423 * [backup-simplify]: Simplify (- 0) into 0 1.424 * [backup-simplify]: Simplify (+ 0 0) into 0 1.424 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.425 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.426 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.427 * [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 1.427 * [taylor]: Taking taylor expansion of 0 in k 1.427 * [backup-simplify]: Simplify 0 into 0 1.427 * [backup-simplify]: Simplify 0 into 0 1.427 * [backup-simplify]: Simplify 0 into 0 1.428 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.430 * [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 1.431 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.431 * [backup-simplify]: Simplify (+ 0 0) into 0 1.431 * [backup-simplify]: Simplify (- 0) into 0 1.431 * [backup-simplify]: Simplify (+ 0 0) into 0 1.432 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.434 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.436 * [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)))))) 1.439 * [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)))))) 1.445 * [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)))))) 1.445 * [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)))) 1.445 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.445 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.445 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.445 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.445 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.445 * [taylor]: Taking taylor expansion of 0.5 in k 1.446 * [backup-simplify]: Simplify 0.5 into 0.5 1.446 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.446 * [taylor]: Taking taylor expansion of 1.0 in k 1.446 * [backup-simplify]: Simplify 1.0 into 1.0 1.446 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.446 * [taylor]: Taking taylor expansion of k in k 1.446 * [backup-simplify]: Simplify 0 into 0 1.446 * [backup-simplify]: Simplify 1 into 1 1.446 * [backup-simplify]: Simplify (/ 1 1) into 1 1.446 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.446 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.446 * [taylor]: Taking taylor expansion of 2.0 in k 1.446 * [backup-simplify]: Simplify 2.0 into 2.0 1.446 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.446 * [taylor]: Taking taylor expansion of PI in k 1.446 * [backup-simplify]: Simplify PI into PI 1.446 * [taylor]: Taking taylor expansion of n in k 1.446 * [backup-simplify]: Simplify n into n 1.446 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.446 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.446 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.446 * [backup-simplify]: Simplify (- 1) into -1 1.447 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.447 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.447 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.447 * [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))))) 1.447 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.447 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.447 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.447 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.447 * [taylor]: Taking taylor expansion of 0.5 in n 1.447 * [backup-simplify]: Simplify 0.5 into 0.5 1.447 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.447 * [taylor]: Taking taylor expansion of 1.0 in n 1.447 * [backup-simplify]: Simplify 1.0 into 1.0 1.447 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.447 * [taylor]: Taking taylor expansion of k in n 1.447 * [backup-simplify]: Simplify k into k 1.447 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.447 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.447 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.447 * [taylor]: Taking taylor expansion of 2.0 in n 1.447 * [backup-simplify]: Simplify 2.0 into 2.0 1.447 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.447 * [taylor]: Taking taylor expansion of PI in n 1.447 * [backup-simplify]: Simplify PI into PI 1.447 * [taylor]: Taking taylor expansion of n in n 1.447 * [backup-simplify]: Simplify 0 into 0 1.447 * [backup-simplify]: Simplify 1 into 1 1.448 * [backup-simplify]: Simplify (/ PI 1) into PI 1.448 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.449 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.449 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.449 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.449 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.450 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.450 * [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)))) 1.451 * [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))))) 1.451 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.451 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.451 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.451 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.451 * [taylor]: Taking taylor expansion of 0.5 in n 1.451 * [backup-simplify]: Simplify 0.5 into 0.5 1.451 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.451 * [taylor]: Taking taylor expansion of 1.0 in n 1.451 * [backup-simplify]: Simplify 1.0 into 1.0 1.451 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.451 * [taylor]: Taking taylor expansion of k in n 1.451 * [backup-simplify]: Simplify k into k 1.451 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.451 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.451 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.451 * [taylor]: Taking taylor expansion of 2.0 in n 1.451 * [backup-simplify]: Simplify 2.0 into 2.0 1.451 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.451 * [taylor]: Taking taylor expansion of PI in n 1.451 * [backup-simplify]: Simplify PI into PI 1.451 * [taylor]: Taking taylor expansion of n in n 1.451 * [backup-simplify]: Simplify 0 into 0 1.451 * [backup-simplify]: Simplify 1 into 1 1.452 * [backup-simplify]: Simplify (/ PI 1) into PI 1.452 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.453 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.453 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.453 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.453 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 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 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.455 * [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))))) 1.455 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.455 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 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 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 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 1.455 * [taylor]: Taking taylor expansion of 2.0 in k 1.455 * [backup-simplify]: Simplify 2.0 into 2.0 1.455 * [taylor]: Taking taylor expansion of PI in k 1.455 * [backup-simplify]: Simplify PI into PI 1.456 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.456 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.456 * [taylor]: Taking taylor expansion of (log n) in k 1.456 * [taylor]: Taking taylor expansion of n in k 1.456 * [backup-simplify]: Simplify n into n 1.456 * [backup-simplify]: Simplify (log n) into (log n) 1.456 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.456 * [taylor]: Taking taylor expansion of 1.0 in k 1.456 * [backup-simplify]: Simplify 1.0 into 1.0 1.456 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.456 * [taylor]: Taking taylor expansion of k in k 1.456 * [backup-simplify]: Simplify 0 into 0 1.456 * [backup-simplify]: Simplify 1 into 1 1.457 * [backup-simplify]: Simplify (/ 1 1) into 1 1.457 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.457 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.457 * [backup-simplify]: Simplify (- 1) into -1 1.458 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.458 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.459 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (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)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.460 * [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))))) 1.461 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.461 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.462 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.462 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.463 * [backup-simplify]: Simplify (- 0) into 0 1.463 * [backup-simplify]: Simplify (+ 0 0) into 0 1.463 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 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 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.466 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (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 1.466 * [backup-simplify]: Simplify 0 into 0 1.466 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.467 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.469 * [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 1.469 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.469 * [backup-simplify]: Simplify (- 0) into 0 1.469 * [backup-simplify]: Simplify (+ 0 0) into 0 1.470 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.471 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.471 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.473 * [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 1.473 * [taylor]: Taking taylor expansion of 0 in k 1.473 * [backup-simplify]: Simplify 0 into 0 1.473 * [backup-simplify]: Simplify 0 into 0 1.473 * [backup-simplify]: Simplify 0 into 0 1.473 * [backup-simplify]: Simplify 0 into 0 1.474 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.474 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.477 * [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 1.477 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) 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 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.479 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.480 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.482 * [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 1.482 * [taylor]: Taking taylor expansion of 0 in k 1.482 * [backup-simplify]: Simplify 0 into 0 1.482 * [backup-simplify]: Simplify 0 into 0 1.483 * [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)))) 1.483 * [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))) 1.483 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.483 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.483 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.483 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.483 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.483 * [taylor]: Taking taylor expansion of 0.5 in k 1.483 * [backup-simplify]: Simplify 0.5 into 0.5 1.483 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.483 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.483 * [taylor]: Taking taylor expansion of k in k 1.483 * [backup-simplify]: Simplify 0 into 0 1.484 * [backup-simplify]: Simplify 1 into 1 1.484 * [backup-simplify]: Simplify (/ 1 1) into 1 1.484 * [taylor]: Taking taylor expansion of 1.0 in k 1.484 * [backup-simplify]: Simplify 1.0 into 1.0 1.484 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.484 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.484 * [taylor]: Taking taylor expansion of -2.0 in k 1.484 * [backup-simplify]: Simplify -2.0 into -2.0 1.484 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.484 * [taylor]: Taking taylor expansion of PI in k 1.484 * [backup-simplify]: Simplify PI into PI 1.484 * [taylor]: Taking taylor expansion of n in k 1.484 * [backup-simplify]: Simplify n into n 1.484 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.484 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.484 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.484 * [backup-simplify]: Simplify (+ 1 0) into 1 1.485 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.485 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.485 * [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)))))) 1.485 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.485 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.485 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.485 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.485 * [taylor]: Taking taylor expansion of 0.5 in n 1.485 * [backup-simplify]: Simplify 0.5 into 0.5 1.485 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.485 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.485 * [taylor]: Taking taylor expansion of k in n 1.485 * [backup-simplify]: Simplify k into k 1.485 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.485 * [taylor]: Taking taylor expansion of 1.0 in n 1.485 * [backup-simplify]: Simplify 1.0 into 1.0 1.485 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.485 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.485 * [taylor]: Taking taylor expansion of -2.0 in n 1.485 * [backup-simplify]: Simplify -2.0 into -2.0 1.485 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.485 * [taylor]: Taking taylor expansion of PI in n 1.485 * [backup-simplify]: Simplify PI into PI 1.485 * [taylor]: Taking taylor expansion of n in n 1.485 * [backup-simplify]: Simplify 0 into 0 1.485 * [backup-simplify]: Simplify 1 into 1 1.485 * [backup-simplify]: Simplify (/ PI 1) into PI 1.486 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.486 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.486 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.486 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.487 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.488 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.489 * [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))))) 1.489 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.489 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.489 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.489 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.489 * [taylor]: Taking taylor expansion of 0.5 in n 1.489 * [backup-simplify]: Simplify 0.5 into 0.5 1.489 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.489 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.489 * [taylor]: Taking taylor expansion of k in n 1.489 * [backup-simplify]: Simplify k into k 1.489 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.489 * [taylor]: Taking taylor expansion of 1.0 in n 1.489 * [backup-simplify]: Simplify 1.0 into 1.0 1.489 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.489 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.489 * [taylor]: Taking taylor expansion of -2.0 in n 1.489 * [backup-simplify]: Simplify -2.0 into -2.0 1.489 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.489 * [taylor]: Taking taylor expansion of PI in n 1.489 * [backup-simplify]: Simplify PI into PI 1.489 * [taylor]: Taking taylor expansion of n in n 1.489 * [backup-simplify]: Simplify 0 into 0 1.489 * [backup-simplify]: Simplify 1 into 1 1.489 * [backup-simplify]: Simplify (/ PI 1) into PI 1.490 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.490 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.490 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.490 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.491 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.492 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.493 * [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))))) 1.493 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.493 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.493 * [taylor]: Taking taylor expansion of 0.5 in k 1.493 * [backup-simplify]: Simplify 0.5 into 0.5 1.493 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.493 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.493 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.493 * [taylor]: Taking taylor expansion of k in k 1.493 * [backup-simplify]: Simplify 0 into 0 1.493 * [backup-simplify]: Simplify 1 into 1 1.493 * [backup-simplify]: Simplify (/ 1 1) into 1 1.493 * [taylor]: Taking taylor expansion of 1.0 in k 1.493 * [backup-simplify]: Simplify 1.0 into 1.0 1.493 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.493 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.493 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.493 * [taylor]: Taking taylor expansion of -2.0 in k 1.493 * [backup-simplify]: Simplify -2.0 into -2.0 1.493 * [taylor]: Taking taylor expansion of PI in k 1.493 * [backup-simplify]: Simplify PI into PI 1.494 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.494 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.494 * [taylor]: Taking taylor expansion of (log n) in k 1.494 * [taylor]: Taking taylor expansion of n in k 1.494 * [backup-simplify]: Simplify n into n 1.494 * [backup-simplify]: Simplify (log n) into (log n) 1.500 * [backup-simplify]: Simplify (+ 1 0) into 1 1.500 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.501 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.502 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.503 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.503 * [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))))) 1.504 * [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))))) 1.505 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.505 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.506 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.506 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.506 * [backup-simplify]: Simplify (+ 0 0) into 0 1.507 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.507 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.508 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.509 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.509 * [taylor]: Taking taylor expansion of 0 in k 1.509 * [backup-simplify]: Simplify 0 into 0 1.509 * [backup-simplify]: Simplify 0 into 0 1.509 * [backup-simplify]: Simplify 0 into 0 1.510 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.510 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.512 * [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 1.512 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.512 * [backup-simplify]: Simplify (+ 0 0) into 0 1.513 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.514 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.515 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.516 * [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 1.516 * [taylor]: Taking taylor expansion of 0 in k 1.516 * [backup-simplify]: Simplify 0 into 0 1.516 * [backup-simplify]: Simplify 0 into 0 1.516 * [backup-simplify]: Simplify 0 into 0 1.516 * [backup-simplify]: Simplify 0 into 0 1.517 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.518 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.521 * [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 1.521 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.521 * [backup-simplify]: Simplify (+ 0 0) into 0 1.522 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.522 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.524 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.525 * [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 1.525 * [taylor]: Taking taylor expansion of 0 in k 1.525 * [backup-simplify]: Simplify 0 into 0 1.525 * [backup-simplify]: Simplify 0 into 0 1.526 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 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)))))) 1.526 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 1.527 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.527 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.527 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.527 * [taylor]: Taking taylor expansion of 2.0 in n 1.527 * [backup-simplify]: Simplify 2.0 into 2.0 1.527 * [taylor]: Taking taylor expansion of (* n PI) in n 1.527 * [taylor]: Taking taylor expansion of n in n 1.527 * [backup-simplify]: Simplify 0 into 0 1.527 * [backup-simplify]: Simplify 1 into 1 1.527 * [taylor]: Taking taylor expansion of PI in n 1.527 * [backup-simplify]: Simplify PI into PI 1.527 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.527 * [taylor]: Taking taylor expansion of 2.0 in n 1.527 * [backup-simplify]: Simplify 2.0 into 2.0 1.527 * [taylor]: Taking taylor expansion of (* n PI) in n 1.527 * [taylor]: Taking taylor expansion of n in n 1.527 * [backup-simplify]: Simplify 0 into 0 1.527 * [backup-simplify]: Simplify 1 into 1 1.527 * [taylor]: Taking taylor expansion of PI in n 1.527 * [backup-simplify]: Simplify PI into PI 1.527 * [backup-simplify]: Simplify (* 0 PI) into 0 1.527 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.527 * [backup-simplify]: Simplify 0 into 0 1.528 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.529 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.529 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.530 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.531 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.531 * [backup-simplify]: Simplify 0 into 0 1.531 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.532 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.532 * [backup-simplify]: Simplify 0 into 0 1.533 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.533 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.533 * [backup-simplify]: Simplify 0 into 0 1.534 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.535 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.535 * [backup-simplify]: Simplify 0 into 0 1.536 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.537 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.537 * [backup-simplify]: Simplify 0 into 0 1.537 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.538 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.538 * [backup-simplify]: Simplify 0 into 0 1.539 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.539 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.539 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.539 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.539 * [taylor]: Taking taylor expansion of 2.0 in n 1.539 * [backup-simplify]: Simplify 2.0 into 2.0 1.539 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.539 * [taylor]: Taking taylor expansion of PI in n 1.539 * [backup-simplify]: Simplify PI into PI 1.539 * [taylor]: Taking taylor expansion of n in n 1.539 * [backup-simplify]: Simplify 0 into 0 1.539 * [backup-simplify]: Simplify 1 into 1 1.540 * [backup-simplify]: Simplify (/ PI 1) into PI 1.540 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.540 * [taylor]: Taking taylor expansion of 2.0 in n 1.540 * [backup-simplify]: Simplify 2.0 into 2.0 1.540 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.540 * [taylor]: Taking taylor expansion of PI in n 1.540 * [backup-simplify]: Simplify PI into PI 1.540 * [taylor]: Taking taylor expansion of n in n 1.540 * [backup-simplify]: Simplify 0 into 0 1.540 * [backup-simplify]: Simplify 1 into 1 1.540 * [backup-simplify]: Simplify (/ PI 1) into PI 1.540 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.541 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.541 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.542 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.542 * [backup-simplify]: Simplify 0 into 0 1.542 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.543 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.543 * [backup-simplify]: Simplify 0 into 0 1.543 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.544 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.544 * [backup-simplify]: Simplify 0 into 0 1.544 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.545 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.545 * [backup-simplify]: Simplify 0 into 0 1.546 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.547 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.547 * [backup-simplify]: Simplify 0 into 0 1.547 * [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 1.548 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.548 * [backup-simplify]: Simplify 0 into 0 1.548 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.549 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.549 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.549 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.549 * [taylor]: Taking taylor expansion of -2.0 in n 1.549 * [backup-simplify]: Simplify -2.0 into -2.0 1.549 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.549 * [taylor]: Taking taylor expansion of PI in n 1.549 * [backup-simplify]: Simplify PI into PI 1.549 * [taylor]: Taking taylor expansion of n in n 1.549 * [backup-simplify]: Simplify 0 into 0 1.549 * [backup-simplify]: Simplify 1 into 1 1.549 * [backup-simplify]: Simplify (/ PI 1) into PI 1.549 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.549 * [taylor]: Taking taylor expansion of -2.0 in n 1.549 * [backup-simplify]: Simplify -2.0 into -2.0 1.549 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.549 * [taylor]: Taking taylor expansion of PI in n 1.549 * [backup-simplify]: Simplify PI into PI 1.549 * [taylor]: Taking taylor expansion of n in n 1.549 * [backup-simplify]: Simplify 0 into 0 1.549 * [backup-simplify]: Simplify 1 into 1 1.550 * [backup-simplify]: Simplify (/ PI 1) into PI 1.550 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.550 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.551 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.551 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.551 * [backup-simplify]: Simplify 0 into 0 1.552 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.552 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.552 * [backup-simplify]: Simplify 0 into 0 1.553 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.553 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.554 * [backup-simplify]: Simplify 0 into 0 1.554 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.555 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.555 * [backup-simplify]: Simplify 0 into 0 1.555 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.556 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.556 * [backup-simplify]: Simplify 0 into 0 1.557 * [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 1.558 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.558 * [backup-simplify]: Simplify 0 into 0 1.558 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.558 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 1.558 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 1.558 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.558 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.558 * [taylor]: Taking taylor expansion of 1.0 in k 1.558 * [backup-simplify]: Simplify 1.0 into 1.0 1.558 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.558 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.558 * [taylor]: Taking taylor expansion of k in k 1.558 * [backup-simplify]: Simplify 0 into 0 1.558 * [backup-simplify]: Simplify 1 into 1 1.558 * [backup-simplify]: Simplify (/ 1 1) into 1 1.559 * [backup-simplify]: Simplify (sqrt 0) into 0 1.560 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.560 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.560 * [taylor]: Taking taylor expansion of 1.0 in k 1.560 * [backup-simplify]: Simplify 1.0 into 1.0 1.560 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.560 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.560 * [taylor]: Taking taylor expansion of k in k 1.560 * [backup-simplify]: Simplify 0 into 0 1.560 * [backup-simplify]: Simplify 1 into 1 1.560 * [backup-simplify]: Simplify (/ 1 1) into 1 1.560 * [backup-simplify]: Simplify (sqrt 0) into 0 1.561 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.561 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.561 * [backup-simplify]: Simplify 0 into 0 1.562 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.562 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.563 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.564 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.565 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.565 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.566 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.568 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.569 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.569 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.570 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 1.570 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 1.570 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.570 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.570 * [taylor]: Taking taylor expansion of 1.0 in k 1.570 * [backup-simplify]: Simplify 1.0 into 1.0 1.570 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.570 * [taylor]: Taking taylor expansion of k in k 1.570 * [backup-simplify]: Simplify 0 into 0 1.570 * [backup-simplify]: Simplify 1 into 1 1.571 * [backup-simplify]: Simplify (sqrt 0) into 0 1.571 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.571 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.571 * [taylor]: Taking taylor expansion of 1.0 in k 1.571 * [backup-simplify]: Simplify 1.0 into 1.0 1.571 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.571 * [taylor]: Taking taylor expansion of k in k 1.571 * [backup-simplify]: Simplify 0 into 0 1.571 * [backup-simplify]: Simplify 1 into 1 1.572 * [backup-simplify]: Simplify (sqrt 0) into 0 1.572 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.573 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.573 * [backup-simplify]: Simplify 0 into 0 1.573 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.574 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.576 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.577 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.577 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.579 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.580 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.580 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.581 * [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)))))))) 1.581 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 1.581 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.581 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.581 * [taylor]: Taking taylor expansion of 1.0 in k 1.581 * [backup-simplify]: Simplify 1.0 into 1.0 1.581 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.581 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.582 * [taylor]: Taking taylor expansion of -1 in k 1.582 * [backup-simplify]: Simplify -1 into -1 1.582 * [taylor]: Taking taylor expansion of k in k 1.582 * [backup-simplify]: Simplify 0 into 0 1.582 * [backup-simplify]: Simplify 1 into 1 1.582 * [backup-simplify]: Simplify (/ -1 1) into -1 1.582 * [backup-simplify]: Simplify (sqrt 0) into 0 1.583 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.583 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.583 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.583 * [taylor]: Taking taylor expansion of 1.0 in k 1.583 * [backup-simplify]: Simplify 1.0 into 1.0 1.583 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.583 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.583 * [taylor]: Taking taylor expansion of -1 in k 1.583 * [backup-simplify]: Simplify -1 into -1 1.583 * [taylor]: Taking taylor expansion of k in k 1.583 * [backup-simplify]: Simplify 0 into 0 1.583 * [backup-simplify]: Simplify 1 into 1 1.583 * [backup-simplify]: Simplify (/ -1 1) into -1 1.584 * [backup-simplify]: Simplify (sqrt 0) into 0 1.584 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.585 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.585 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.591 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.593 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.595 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1.595 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.595 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.597 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.600 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1.600 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.600 * [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))))) 1.601 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 1.601 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 1.601 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.601 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.601 * [taylor]: Taking taylor expansion of 1.0 in k 1.601 * [backup-simplify]: Simplify 1.0 into 1.0 1.601 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.601 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.601 * [taylor]: Taking taylor expansion of k in k 1.601 * [backup-simplify]: Simplify 0 into 0 1.601 * [backup-simplify]: Simplify 1 into 1 1.601 * [backup-simplify]: Simplify (/ 1 1) into 1 1.601 * [backup-simplify]: Simplify (sqrt 0) into 0 1.602 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.602 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.602 * [taylor]: Taking taylor expansion of 1.0 in k 1.602 * [backup-simplify]: Simplify 1.0 into 1.0 1.602 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.602 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.602 * [taylor]: Taking taylor expansion of k in k 1.602 * [backup-simplify]: Simplify 0 into 0 1.602 * [backup-simplify]: Simplify 1 into 1 1.602 * [backup-simplify]: Simplify (/ 1 1) into 1 1.603 * [backup-simplify]: Simplify (sqrt 0) into 0 1.603 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.604 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.604 * [backup-simplify]: Simplify 0 into 0 1.604 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.605 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.605 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.607 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.608 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.608 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.608 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.610 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.611 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.612 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.613 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 1.613 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 1.613 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.613 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.613 * [taylor]: Taking taylor expansion of 1.0 in k 1.613 * [backup-simplify]: Simplify 1.0 into 1.0 1.613 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.613 * [taylor]: Taking taylor expansion of k in k 1.613 * [backup-simplify]: Simplify 0 into 0 1.613 * [backup-simplify]: Simplify 1 into 1 1.613 * [backup-simplify]: Simplify (sqrt 0) into 0 1.614 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.614 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.614 * [taylor]: Taking taylor expansion of 1.0 in k 1.614 * [backup-simplify]: Simplify 1.0 into 1.0 1.614 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.614 * [taylor]: Taking taylor expansion of k in k 1.614 * [backup-simplify]: Simplify 0 into 0 1.614 * [backup-simplify]: Simplify 1 into 1 1.614 * [backup-simplify]: Simplify (sqrt 0) into 0 1.615 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.615 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.615 * [backup-simplify]: Simplify 0 into 0 1.616 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.616 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.618 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.619 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.619 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.621 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.622 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.622 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.623 * [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)))))))) 1.623 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 1.623 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.623 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.623 * [taylor]: Taking taylor expansion of 1.0 in k 1.623 * [backup-simplify]: Simplify 1.0 into 1.0 1.623 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.623 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.623 * [taylor]: Taking taylor expansion of -1 in k 1.623 * [backup-simplify]: Simplify -1 into -1 1.623 * [taylor]: Taking taylor expansion of k in k 1.624 * [backup-simplify]: Simplify 0 into 0 1.624 * [backup-simplify]: Simplify 1 into 1 1.624 * [backup-simplify]: Simplify (/ -1 1) into -1 1.624 * [backup-simplify]: Simplify (sqrt 0) into 0 1.625 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.625 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.625 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.625 * [taylor]: Taking taylor expansion of 1.0 in k 1.625 * [backup-simplify]: Simplify 1.0 into 1.0 1.625 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.625 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.625 * [taylor]: Taking taylor expansion of -1 in k 1.625 * [backup-simplify]: Simplify -1 into -1 1.625 * [taylor]: Taking taylor expansion of k in k 1.625 * [backup-simplify]: Simplify 0 into 0 1.625 * [backup-simplify]: Simplify 1 into 1 1.626 * [backup-simplify]: Simplify (/ -1 1) into -1 1.626 * [backup-simplify]: Simplify (sqrt 0) into 0 1.627 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.627 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.627 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.627 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.629 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.630 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1.631 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.631 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.633 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.635 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1.636 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.636 * [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))))) 1.636 * * * [progress]: simplifying candidates 1.638 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (+ (* 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 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))))) 1.639 * [simplify]: Sending expressions to egg_math: (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0)) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0)) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0)) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0)) (* 1 (/ (- h2 h1) h0)) (* 1 (/ (- h2 h1) h0)) (* 1 (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ h2 h0)) (pow (* (* h0 h4) h3) (/ h1 h0)) (pow (* (* h0 h4) h3) (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0)))) (pow (* (* h0 h4) h3) (sqrt (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 h4) h3) (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0))) (pow (* (* h0 h4) h3) (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1)) (pow (* (* h0 h4) h3) (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 h4) h3) (/ (sqrt (- h2 h1)) (sqrt h0))) (pow (* (* h0 h4) h3) (/ (sqrt (- h2 h1)) 1)) (pow (* (* h0 h4) h3) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 h4) h3) (/ 1 (sqrt h0))) (pow (* (* h0 h4) h3) (/ 1 1)) (pow (* (* h0 h4) h3) (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 h4) h3) (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0))) (pow (* (* h0 h4) h3) (/ (+ (sqrt h2) (sqrt h1)) 1)) (pow (* (* h0 h4) h3) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 h4) h3) (/ 1 (sqrt h0))) (pow (* (* h0 h4) h3) (/ 1 1)) (pow (* (* h0 h4) h3) 1) (pow (* (* h0 h4) h3) (- h2 h1)) (pow (* h0 h4) (/ (- h2 h1) h0)) (pow h3 (/ (- h2 h1) h0)) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (exp (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (- (log h2) (log (sqrt h1))) (log (/ h2 (sqrt h1))) (exp (/ h2 (sqrt h1))) (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (cbrt (/ h2 (sqrt h1))) (cbrt (/ h2 (sqrt h1)))) (cbrt (/ h2 (sqrt h1))) (* (* (/ h2 (sqrt h1)) (/ h2 (sqrt h1))) (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (- h2) (- (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (cbrt h2) (cbrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (cbrt h2) (sqrt (cbrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt 1)) (/ (cbrt h2) (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) 1) (/ (cbrt h2) (sqrt h1)) (/ (sqrt h2) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (sqrt h2) (cbrt (sqrt h1))) (/ (sqrt h2) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (sqrt h2) (sqrt (cbrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt 1)) (/ (sqrt h2) (sqrt h1)) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) 1) (/ (sqrt h2) (sqrt h1)) (/ 1 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (cbrt (sqrt h1))) (/ 1 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (cbrt h1))) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 (sqrt 1)) (/ h2 (sqrt h1)) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 1) (/ h2 (sqrt h1)) (/ 1 (sqrt h1)) (/ (sqrt h1) h2) (/ h2 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (sqrt h1))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h1))) (/ h2 1) (/ (sqrt h1) (cbrt h2)) (/ (sqrt h1) (sqrt h2)) (/ (sqrt h1) h2) (- (log h2) (log (sqrt h1))) (log (/ h2 (sqrt h1))) (exp (/ h2 (sqrt h1))) (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (cbrt (/ h2 (sqrt h1))) (cbrt (/ h2 (sqrt h1)))) (cbrt (/ h2 (sqrt h1))) (* (* (/ h2 (sqrt h1)) (/ h2 (sqrt h1))) (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (- h2) (- (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (cbrt h2) (cbrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (cbrt h2) (sqrt (cbrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt 1)) (/ (cbrt h2) (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) 1) (/ (cbrt h2) (sqrt h1)) (/ (sqrt h2) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (sqrt h2) (cbrt (sqrt h1))) (/ (sqrt h2) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (sqrt h2) (sqrt (cbrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt 1)) (/ (sqrt h2) (sqrt h1)) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) 1) (/ (sqrt h2) (sqrt h1)) (/ 1 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (cbrt (sqrt h1))) (/ 1 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (cbrt h1))) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 (sqrt 1)) (/ h2 (sqrt h1)) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 1) (/ h2 (sqrt h1)) (/ 1 (sqrt h1)) (/ (sqrt h1) h2) (/ h2 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (sqrt h1))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h1))) (/ h2 1) (/ (sqrt h1) (cbrt h2)) (/ (sqrt h1) (sqrt h2)) (/ (sqrt h1) h2) (- (+ (* h7 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h7 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (+ (* h6 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (- (+ (* h9 h1) (- (+ (* h9 (pow h1 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- (* h9 (/ 1 (pow h1 3)))))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- h9))))) (- (+ (* h9 h1) (- (+ (* h9 (pow h1 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- (* h9 (/ 1 (pow h1 3)))))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- h9))))) 1.645 * * [simplify]: iteration 0 : 563 enodes (cost 883 ) 1.654 * * [simplify]: iteration 1 : 2197 enodes (cost 815 ) 1.692 * * [simplify]: iteration 2 : 5001 enodes (cost 791 ) 1.696 * * * [progress]: adding candidates to table 2.127 * * [progress]: iteration 3 / 4 2.127 * * * [progress]: picking best candidate 2.156 * * * * [pick]: Picked # 2.156 * * * [progress]: localizing error 2.171 * * * [progress]: generating rewritten candidates 2.171 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 2.196 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 2.224 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 2.265 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1) 2.295 * * * [progress]: generating series expansions 2.295 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 2.296 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2.296 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.296 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.296 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.296 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.296 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.296 * [taylor]: Taking taylor expansion of 0.25 in k 2.296 * [backup-simplify]: Simplify 0.25 into 0.25 2.296 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.296 * [taylor]: Taking taylor expansion of 1.0 in k 2.296 * [backup-simplify]: Simplify 1.0 into 1.0 2.296 * [taylor]: Taking taylor expansion of k in k 2.296 * [backup-simplify]: Simplify 0 into 0 2.296 * [backup-simplify]: Simplify 1 into 1 2.296 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.296 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.296 * [taylor]: Taking taylor expansion of 2.0 in k 2.296 * [backup-simplify]: Simplify 2.0 into 2.0 2.296 * [taylor]: Taking taylor expansion of (* n PI) in k 2.296 * [taylor]: Taking taylor expansion of n in k 2.296 * [backup-simplify]: Simplify n into n 2.296 * [taylor]: Taking taylor expansion of PI in k 2.296 * [backup-simplify]: Simplify PI into PI 2.297 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.297 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.297 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.297 * [backup-simplify]: Simplify (- 0) into 0 2.297 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.298 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.298 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.298 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.298 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.298 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.298 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.298 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.298 * [taylor]: Taking taylor expansion of 0.25 in n 2.298 * [backup-simplify]: Simplify 0.25 into 0.25 2.298 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.298 * [taylor]: Taking taylor expansion of 1.0 in n 2.298 * [backup-simplify]: Simplify 1.0 into 1.0 2.298 * [taylor]: Taking taylor expansion of k in n 2.298 * [backup-simplify]: Simplify k into k 2.298 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.298 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.298 * [taylor]: Taking taylor expansion of 2.0 in n 2.298 * [backup-simplify]: Simplify 2.0 into 2.0 2.298 * [taylor]: Taking taylor expansion of (* n PI) in n 2.298 * [taylor]: Taking taylor expansion of n in n 2.298 * [backup-simplify]: Simplify 0 into 0 2.298 * [backup-simplify]: Simplify 1 into 1 2.298 * [taylor]: Taking taylor expansion of PI in n 2.298 * [backup-simplify]: Simplify PI into PI 2.298 * [backup-simplify]: Simplify (* 0 PI) into 0 2.299 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.300 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.300 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.301 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.301 * [backup-simplify]: Simplify (- k) into (- k) 2.301 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.301 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.302 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.303 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.303 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.303 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.303 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.303 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.303 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.303 * [taylor]: Taking taylor expansion of 0.25 in n 2.304 * [backup-simplify]: Simplify 0.25 into 0.25 2.304 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.304 * [taylor]: Taking taylor expansion of 1.0 in n 2.304 * [backup-simplify]: Simplify 1.0 into 1.0 2.304 * [taylor]: Taking taylor expansion of k in n 2.304 * [backup-simplify]: Simplify k into k 2.304 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.304 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.304 * [taylor]: Taking taylor expansion of 2.0 in n 2.304 * [backup-simplify]: Simplify 2.0 into 2.0 2.304 * [taylor]: Taking taylor expansion of (* n PI) in n 2.304 * [taylor]: Taking taylor expansion of n in n 2.304 * [backup-simplify]: Simplify 0 into 0 2.304 * [backup-simplify]: Simplify 1 into 1 2.304 * [taylor]: Taking taylor expansion of PI in n 2.304 * [backup-simplify]: Simplify PI into PI 2.304 * [backup-simplify]: Simplify (* 0 PI) into 0 2.304 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.305 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.306 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.307 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.307 * [backup-simplify]: Simplify (- k) into (- k) 2.307 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.307 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.308 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.308 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.309 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.309 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.309 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.309 * [taylor]: Taking taylor expansion of 0.25 in k 2.309 * [backup-simplify]: Simplify 0.25 into 0.25 2.309 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.309 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.309 * [taylor]: Taking taylor expansion of 1.0 in k 2.309 * [backup-simplify]: Simplify 1.0 into 1.0 2.309 * [taylor]: Taking taylor expansion of k in k 2.309 * [backup-simplify]: Simplify 0 into 0 2.309 * [backup-simplify]: Simplify 1 into 1 2.309 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.309 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.309 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.309 * [taylor]: Taking taylor expansion of 2.0 in k 2.309 * [backup-simplify]: Simplify 2.0 into 2.0 2.309 * [taylor]: Taking taylor expansion of PI in k 2.309 * [backup-simplify]: Simplify PI into PI 2.310 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.310 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.310 * [taylor]: Taking taylor expansion of (log n) in k 2.310 * [taylor]: Taking taylor expansion of n in k 2.310 * [backup-simplify]: Simplify n into n 2.310 * [backup-simplify]: Simplify (log n) into (log n) 2.311 * [backup-simplify]: Simplify (- 0) into 0 2.311 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.311 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.312 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.313 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.313 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.314 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.315 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.315 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.316 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.316 * [backup-simplify]: Simplify (- 0) into 0 2.317 * [backup-simplify]: Simplify (+ 0 0) into 0 2.317 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.318 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.318 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.320 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.320 * [taylor]: Taking taylor expansion of 0 in k 2.320 * [backup-simplify]: Simplify 0 into 0 2.320 * [backup-simplify]: Simplify 0 into 0 2.320 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.321 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.321 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.322 * [backup-simplify]: Simplify (+ 0 0) into 0 2.322 * [backup-simplify]: Simplify (- 1) into -1 2.322 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.323 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.324 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2.326 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.328 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.329 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.329 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.331 * [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 2.331 * [backup-simplify]: Simplify (- 0) into 0 2.331 * [backup-simplify]: Simplify (+ 0 0) into 0 2.332 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.333 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.334 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.335 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.335 * [taylor]: Taking taylor expansion of 0 in k 2.335 * [backup-simplify]: Simplify 0 into 0 2.335 * [backup-simplify]: Simplify 0 into 0 2.335 * [backup-simplify]: Simplify 0 into 0 2.336 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.337 * [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 2.339 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.339 * [backup-simplify]: Simplify (+ 0 0) into 0 2.346 * [backup-simplify]: Simplify (- 0) into 0 2.346 * [backup-simplify]: Simplify (+ 0 0) into 0 2.348 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.349 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.352 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.355 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.360 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.361 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2.361 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.361 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.361 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.361 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.361 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.361 * [taylor]: Taking taylor expansion of 0.25 in k 2.361 * [backup-simplify]: Simplify 0.25 into 0.25 2.361 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.361 * [taylor]: Taking taylor expansion of 1.0 in k 2.361 * [backup-simplify]: Simplify 1.0 into 1.0 2.361 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.361 * [taylor]: Taking taylor expansion of k in k 2.361 * [backup-simplify]: Simplify 0 into 0 2.361 * [backup-simplify]: Simplify 1 into 1 2.361 * [backup-simplify]: Simplify (/ 1 1) into 1 2.361 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.361 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.361 * [taylor]: Taking taylor expansion of 2.0 in k 2.361 * [backup-simplify]: Simplify 2.0 into 2.0 2.361 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.361 * [taylor]: Taking taylor expansion of PI in k 2.361 * [backup-simplify]: Simplify PI into PI 2.361 * [taylor]: Taking taylor expansion of n in k 2.362 * [backup-simplify]: Simplify n into n 2.362 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.362 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.362 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.362 * [backup-simplify]: Simplify (- 1) into -1 2.362 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.362 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.362 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.363 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.363 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.363 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.363 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.363 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.363 * [taylor]: Taking taylor expansion of 0.25 in n 2.363 * [backup-simplify]: Simplify 0.25 into 0.25 2.363 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.363 * [taylor]: Taking taylor expansion of 1.0 in n 2.363 * [backup-simplify]: Simplify 1.0 into 1.0 2.363 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.363 * [taylor]: Taking taylor expansion of k in n 2.363 * [backup-simplify]: Simplify k into k 2.363 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.363 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.363 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.363 * [taylor]: Taking taylor expansion of 2.0 in n 2.363 * [backup-simplify]: Simplify 2.0 into 2.0 2.363 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.363 * [taylor]: Taking taylor expansion of PI in n 2.363 * [backup-simplify]: Simplify PI into PI 2.363 * [taylor]: Taking taylor expansion of n in n 2.363 * [backup-simplify]: Simplify 0 into 0 2.363 * [backup-simplify]: Simplify 1 into 1 2.363 * [backup-simplify]: Simplify (/ PI 1) into PI 2.364 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.364 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.364 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.364 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.364 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.365 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.366 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.367 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.367 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.367 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.367 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.367 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.367 * [taylor]: Taking taylor expansion of 0.25 in n 2.367 * [backup-simplify]: Simplify 0.25 into 0.25 2.367 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.367 * [taylor]: Taking taylor expansion of 1.0 in n 2.367 * [backup-simplify]: Simplify 1.0 into 1.0 2.367 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.367 * [taylor]: Taking taylor expansion of k in n 2.367 * [backup-simplify]: Simplify k into k 2.367 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.367 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.367 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.367 * [taylor]: Taking taylor expansion of 2.0 in n 2.367 * [backup-simplify]: Simplify 2.0 into 2.0 2.367 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.367 * [taylor]: Taking taylor expansion of PI in n 2.367 * [backup-simplify]: Simplify PI into PI 2.367 * [taylor]: Taking taylor expansion of n in n 2.367 * [backup-simplify]: Simplify 0 into 0 2.367 * [backup-simplify]: Simplify 1 into 1 2.367 * [backup-simplify]: Simplify (/ PI 1) into PI 2.368 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.368 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.368 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.368 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.368 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.369 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.370 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.371 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.371 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.371 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.371 * [taylor]: Taking taylor expansion of 0.25 in k 2.371 * [backup-simplify]: Simplify 0.25 into 0.25 2.371 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.371 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.371 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.371 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.371 * [taylor]: Taking taylor expansion of 2.0 in k 2.371 * [backup-simplify]: Simplify 2.0 into 2.0 2.371 * [taylor]: Taking taylor expansion of PI in k 2.371 * [backup-simplify]: Simplify PI into PI 2.371 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.372 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.372 * [taylor]: Taking taylor expansion of (log n) in k 2.372 * [taylor]: Taking taylor expansion of n in k 2.372 * [backup-simplify]: Simplify n into n 2.372 * [backup-simplify]: Simplify (log n) into (log n) 2.372 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.372 * [taylor]: Taking taylor expansion of 1.0 in k 2.372 * [backup-simplify]: Simplify 1.0 into 1.0 2.372 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.372 * [taylor]: Taking taylor expansion of k in k 2.372 * [backup-simplify]: Simplify 0 into 0 2.372 * [backup-simplify]: Simplify 1 into 1 2.372 * [backup-simplify]: Simplify (/ 1 1) into 1 2.372 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.373 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.373 * [backup-simplify]: Simplify (- 1) into -1 2.374 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.374 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.375 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.376 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.376 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.377 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.378 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.378 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.378 * [backup-simplify]: Simplify (- 0) into 0 2.379 * [backup-simplify]: Simplify (+ 0 0) into 0 2.379 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.380 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.380 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.382 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.382 * [taylor]: Taking taylor expansion of 0 in k 2.382 * [backup-simplify]: Simplify 0 into 0 2.382 * [backup-simplify]: Simplify 0 into 0 2.382 * [backup-simplify]: Simplify 0 into 0 2.382 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.383 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.385 * [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 2.385 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.385 * [backup-simplify]: Simplify (- 0) into 0 2.385 * [backup-simplify]: Simplify (+ 0 0) into 0 2.386 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.387 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.388 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.389 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.389 * [taylor]: Taking taylor expansion of 0 in k 2.389 * [backup-simplify]: Simplify 0 into 0 2.389 * [backup-simplify]: Simplify 0 into 0 2.389 * [backup-simplify]: Simplify 0 into 0 2.389 * [backup-simplify]: Simplify 0 into 0 2.390 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.390 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.393 * [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 2.393 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.394 * [backup-simplify]: Simplify (- 0) into 0 2.394 * [backup-simplify]: Simplify (+ 0 0) into 0 2.395 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.395 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.396 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.398 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.398 * [taylor]: Taking taylor expansion of 0 in k 2.398 * [backup-simplify]: Simplify 0 into 0 2.398 * [backup-simplify]: Simplify 0 into 0 2.399 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.399 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2.399 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.399 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.399 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.399 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.399 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.399 * [taylor]: Taking taylor expansion of 0.25 in k 2.399 * [backup-simplify]: Simplify 0.25 into 0.25 2.399 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.400 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.400 * [taylor]: Taking taylor expansion of k in k 2.400 * [backup-simplify]: Simplify 0 into 0 2.400 * [backup-simplify]: Simplify 1 into 1 2.400 * [backup-simplify]: Simplify (/ 1 1) into 1 2.400 * [taylor]: Taking taylor expansion of 1.0 in k 2.400 * [backup-simplify]: Simplify 1.0 into 1.0 2.400 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.400 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.400 * [taylor]: Taking taylor expansion of -2.0 in k 2.400 * [backup-simplify]: Simplify -2.0 into -2.0 2.400 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.400 * [taylor]: Taking taylor expansion of PI in k 2.400 * [backup-simplify]: Simplify PI into PI 2.400 * [taylor]: Taking taylor expansion of n in k 2.400 * [backup-simplify]: Simplify n into n 2.400 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.400 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.400 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.400 * [backup-simplify]: Simplify (+ 1 0) into 1 2.401 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.401 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.401 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.401 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.401 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.401 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.401 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.401 * [taylor]: Taking taylor expansion of 0.25 in n 2.401 * [backup-simplify]: Simplify 0.25 into 0.25 2.401 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.401 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.401 * [taylor]: Taking taylor expansion of k in n 2.401 * [backup-simplify]: Simplify k into k 2.401 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.401 * [taylor]: Taking taylor expansion of 1.0 in n 2.401 * [backup-simplify]: Simplify 1.0 into 1.0 2.401 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.401 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.401 * [taylor]: Taking taylor expansion of -2.0 in n 2.401 * [backup-simplify]: Simplify -2.0 into -2.0 2.401 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.401 * [taylor]: Taking taylor expansion of PI in n 2.401 * [backup-simplify]: Simplify PI into PI 2.401 * [taylor]: Taking taylor expansion of n in n 2.401 * [backup-simplify]: Simplify 0 into 0 2.401 * [backup-simplify]: Simplify 1 into 1 2.402 * [backup-simplify]: Simplify (/ PI 1) into PI 2.402 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.402 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.402 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.403 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.403 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.404 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.405 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.405 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.405 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.405 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.405 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.405 * [taylor]: Taking taylor expansion of 0.25 in n 2.405 * [backup-simplify]: Simplify 0.25 into 0.25 2.405 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.405 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.405 * [taylor]: Taking taylor expansion of k in n 2.405 * [backup-simplify]: Simplify k into k 2.405 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.405 * [taylor]: Taking taylor expansion of 1.0 in n 2.405 * [backup-simplify]: Simplify 1.0 into 1.0 2.405 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.405 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.405 * [taylor]: Taking taylor expansion of -2.0 in n 2.405 * [backup-simplify]: Simplify -2.0 into -2.0 2.405 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.405 * [taylor]: Taking taylor expansion of PI in n 2.405 * [backup-simplify]: Simplify PI into PI 2.405 * [taylor]: Taking taylor expansion of n in n 2.405 * [backup-simplify]: Simplify 0 into 0 2.405 * [backup-simplify]: Simplify 1 into 1 2.406 * [backup-simplify]: Simplify (/ PI 1) into PI 2.406 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.407 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.407 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.407 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.408 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.408 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.409 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.409 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.409 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.409 * [taylor]: Taking taylor expansion of 0.25 in k 2.409 * [backup-simplify]: Simplify 0.25 into 0.25 2.409 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.409 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.409 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.409 * [taylor]: Taking taylor expansion of k in k 2.409 * [backup-simplify]: Simplify 0 into 0 2.409 * [backup-simplify]: Simplify 1 into 1 2.409 * [backup-simplify]: Simplify (/ 1 1) into 1 2.409 * [taylor]: Taking taylor expansion of 1.0 in k 2.409 * [backup-simplify]: Simplify 1.0 into 1.0 2.410 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.410 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.410 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.410 * [taylor]: Taking taylor expansion of -2.0 in k 2.410 * [backup-simplify]: Simplify -2.0 into -2.0 2.410 * [taylor]: Taking taylor expansion of PI in k 2.410 * [backup-simplify]: Simplify PI into PI 2.410 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.410 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.410 * [taylor]: Taking taylor expansion of (log n) in k 2.411 * [taylor]: Taking taylor expansion of n in k 2.411 * [backup-simplify]: Simplify n into n 2.411 * [backup-simplify]: Simplify (log n) into (log n) 2.411 * [backup-simplify]: Simplify (+ 1 0) into 1 2.411 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.411 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.412 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.413 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.413 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.414 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.415 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.415 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.416 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.416 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.416 * [backup-simplify]: Simplify (+ 0 0) into 0 2.417 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.418 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.418 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.419 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.419 * [taylor]: Taking taylor expansion of 0 in k 2.419 * [backup-simplify]: Simplify 0 into 0 2.419 * [backup-simplify]: Simplify 0 into 0 2.419 * [backup-simplify]: Simplify 0 into 0 2.420 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.421 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.422 * [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 2.422 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.423 * [backup-simplify]: Simplify (+ 0 0) into 0 2.423 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.424 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.425 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.426 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.426 * [taylor]: Taking taylor expansion of 0 in k 2.426 * [backup-simplify]: Simplify 0 into 0 2.426 * [backup-simplify]: Simplify 0 into 0 2.426 * [backup-simplify]: Simplify 0 into 0 2.426 * [backup-simplify]: Simplify 0 into 0 2.427 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.428 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.430 * [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 2.430 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.431 * [backup-simplify]: Simplify (+ 0 0) into 0 2.431 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.432 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.433 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.441 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.441 * [taylor]: Taking taylor expansion of 0 in k 2.441 * [backup-simplify]: Simplify 0 into 0 2.441 * [backup-simplify]: Simplify 0 into 0 2.442 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.442 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 2.443 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2.443 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.443 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.443 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.443 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.443 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.443 * [taylor]: Taking taylor expansion of 0.25 in k 2.443 * [backup-simplify]: Simplify 0.25 into 0.25 2.443 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.443 * [taylor]: Taking taylor expansion of 1.0 in k 2.443 * [backup-simplify]: Simplify 1.0 into 1.0 2.443 * [taylor]: Taking taylor expansion of k in k 2.443 * [backup-simplify]: Simplify 0 into 0 2.443 * [backup-simplify]: Simplify 1 into 1 2.443 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.443 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.443 * [taylor]: Taking taylor expansion of 2.0 in k 2.443 * [backup-simplify]: Simplify 2.0 into 2.0 2.443 * [taylor]: Taking taylor expansion of (* n PI) in k 2.443 * [taylor]: Taking taylor expansion of n in k 2.443 * [backup-simplify]: Simplify n into n 2.443 * [taylor]: Taking taylor expansion of PI in k 2.443 * [backup-simplify]: Simplify PI into PI 2.443 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.443 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.443 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.444 * [backup-simplify]: Simplify (- 0) into 0 2.444 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.444 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.444 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.444 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.444 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.444 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.444 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.445 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.445 * [taylor]: Taking taylor expansion of 0.25 in n 2.445 * [backup-simplify]: Simplify 0.25 into 0.25 2.445 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.445 * [taylor]: Taking taylor expansion of 1.0 in n 2.445 * [backup-simplify]: Simplify 1.0 into 1.0 2.445 * [taylor]: Taking taylor expansion of k in n 2.445 * [backup-simplify]: Simplify k into k 2.445 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.445 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.445 * [taylor]: Taking taylor expansion of 2.0 in n 2.445 * [backup-simplify]: Simplify 2.0 into 2.0 2.445 * [taylor]: Taking taylor expansion of (* n PI) in n 2.445 * [taylor]: Taking taylor expansion of n in n 2.445 * [backup-simplify]: Simplify 0 into 0 2.445 * [backup-simplify]: Simplify 1 into 1 2.445 * [taylor]: Taking taylor expansion of PI in n 2.445 * [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) 2.448 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.448 * [backup-simplify]: Simplify (- k) into (- k) 2.448 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.448 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.449 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.449 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.450 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.450 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.450 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.450 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.450 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.450 * [taylor]: Taking taylor expansion of 0.25 in n 2.450 * [backup-simplify]: Simplify 0.25 into 0.25 2.450 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.450 * [taylor]: Taking taylor expansion of 1.0 in n 2.450 * [backup-simplify]: Simplify 1.0 into 1.0 2.450 * [taylor]: Taking taylor expansion of k in n 2.450 * [backup-simplify]: Simplify k into k 2.450 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.450 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.450 * [taylor]: Taking taylor expansion of 2.0 in n 2.450 * [backup-simplify]: Simplify 2.0 into 2.0 2.450 * [taylor]: Taking taylor expansion of (* n PI) in n 2.450 * [taylor]: Taking taylor expansion of n in n 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 1 into 1 2.450 * [taylor]: Taking taylor expansion of PI in n 2.450 * [backup-simplify]: Simplify PI into PI 2.451 * [backup-simplify]: Simplify (* 0 PI) into 0 2.451 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.452 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.452 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.453 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.453 * [backup-simplify]: Simplify (- k) into (- k) 2.453 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.453 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.454 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.455 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.455 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.455 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.456 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.456 * [taylor]: Taking taylor expansion of 0.25 in k 2.456 * [backup-simplify]: Simplify 0.25 into 0.25 2.456 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.456 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.456 * [taylor]: Taking taylor expansion of 1.0 in k 2.456 * [backup-simplify]: Simplify 1.0 into 1.0 2.456 * [taylor]: Taking taylor expansion of k in k 2.456 * [backup-simplify]: Simplify 0 into 0 2.456 * [backup-simplify]: Simplify 1 into 1 2.456 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.456 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.456 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.456 * [taylor]: Taking taylor expansion of 2.0 in k 2.456 * [backup-simplify]: Simplify 2.0 into 2.0 2.456 * [taylor]: Taking taylor expansion of PI in k 2.456 * [backup-simplify]: Simplify PI into PI 2.456 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.457 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.457 * [taylor]: Taking taylor expansion of (log n) in k 2.457 * [taylor]: Taking taylor expansion of n in k 2.457 * [backup-simplify]: Simplify n into n 2.457 * [backup-simplify]: Simplify (log n) into (log n) 2.457 * [backup-simplify]: Simplify (- 0) into 0 2.458 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.458 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.459 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.459 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.460 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.461 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.461 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.462 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.463 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.463 * [backup-simplify]: Simplify (- 0) into 0 2.463 * [backup-simplify]: Simplify (+ 0 0) into 0 2.464 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.464 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.465 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.466 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.466 * [taylor]: Taking taylor expansion of 0 in k 2.466 * [backup-simplify]: Simplify 0 into 0 2.466 * [backup-simplify]: Simplify 0 into 0 2.467 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.468 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.468 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.468 * [backup-simplify]: Simplify (+ 0 0) into 0 2.468 * [backup-simplify]: Simplify (- 1) into -1 2.469 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.470 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.471 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2.473 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.474 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.475 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.476 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.477 * [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 2.478 * [backup-simplify]: Simplify (- 0) into 0 2.478 * [backup-simplify]: Simplify (+ 0 0) into 0 2.478 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.479 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.480 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.481 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.482 * [taylor]: Taking taylor expansion of 0 in k 2.482 * [backup-simplify]: Simplify 0 into 0 2.482 * [backup-simplify]: Simplify 0 into 0 2.482 * [backup-simplify]: Simplify 0 into 0 2.482 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.484 * [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 2.485 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.485 * [backup-simplify]: Simplify (+ 0 0) into 0 2.485 * [backup-simplify]: Simplify (- 0) into 0 2.485 * [backup-simplify]: Simplify (+ 0 0) into 0 2.487 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.488 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.490 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.493 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.499 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.500 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2.500 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.500 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.500 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.500 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.500 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.500 * [taylor]: Taking taylor expansion of 0.25 in k 2.500 * [backup-simplify]: Simplify 0.25 into 0.25 2.500 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.500 * [taylor]: Taking taylor expansion of 1.0 in k 2.500 * [backup-simplify]: Simplify 1.0 into 1.0 2.500 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.500 * [taylor]: Taking taylor expansion of k in k 2.500 * [backup-simplify]: Simplify 0 into 0 2.500 * [backup-simplify]: Simplify 1 into 1 2.500 * [backup-simplify]: Simplify (/ 1 1) into 1 2.500 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.500 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.500 * [taylor]: Taking taylor expansion of 2.0 in k 2.500 * [backup-simplify]: Simplify 2.0 into 2.0 2.500 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.500 * [taylor]: Taking taylor expansion of PI in k 2.500 * [backup-simplify]: Simplify PI into PI 2.500 * [taylor]: Taking taylor expansion of n in k 2.500 * [backup-simplify]: Simplify n into n 2.500 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.500 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.500 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.501 * [backup-simplify]: Simplify (- 1) into -1 2.501 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.501 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.501 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.501 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.501 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.501 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.501 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.502 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.502 * [taylor]: Taking taylor expansion of 0.25 in n 2.502 * [backup-simplify]: Simplify 0.25 into 0.25 2.502 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.502 * [taylor]: Taking taylor expansion of 1.0 in n 2.502 * [backup-simplify]: Simplify 1.0 into 1.0 2.502 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.502 * [taylor]: Taking taylor expansion of k in n 2.502 * [backup-simplify]: Simplify k into k 2.502 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.502 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.502 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.502 * [taylor]: Taking taylor expansion of 2.0 in n 2.502 * [backup-simplify]: Simplify 2.0 into 2.0 2.502 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.502 * [taylor]: Taking taylor expansion of PI in n 2.502 * [backup-simplify]: Simplify PI into PI 2.502 * [taylor]: Taking taylor expansion of n in n 2.502 * [backup-simplify]: Simplify 0 into 0 2.502 * [backup-simplify]: Simplify 1 into 1 2.502 * [backup-simplify]: Simplify (/ PI 1) into PI 2.502 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.503 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.503 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.503 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.503 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.504 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.505 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.505 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.505 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.505 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.505 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.506 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.506 * [taylor]: Taking taylor expansion of 0.25 in n 2.506 * [backup-simplify]: Simplify 0.25 into 0.25 2.506 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.506 * [taylor]: Taking taylor expansion of 1.0 in n 2.506 * [backup-simplify]: Simplify 1.0 into 1.0 2.506 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.506 * [taylor]: Taking taylor expansion of k in n 2.506 * [backup-simplify]: Simplify k into k 2.506 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.506 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.506 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.506 * [taylor]: Taking taylor expansion of 2.0 in n 2.506 * [backup-simplify]: Simplify 2.0 into 2.0 2.506 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.506 * [taylor]: Taking taylor expansion of PI in n 2.506 * [backup-simplify]: Simplify PI into PI 2.506 * [taylor]: Taking taylor expansion of n in n 2.506 * [backup-simplify]: Simplify 0 into 0 2.506 * [backup-simplify]: Simplify 1 into 1 2.506 * [backup-simplify]: Simplify (/ PI 1) into PI 2.507 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.507 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.507 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.507 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.507 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.508 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.509 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.510 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.510 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.510 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.510 * [taylor]: Taking taylor expansion of 0.25 in k 2.510 * [backup-simplify]: Simplify 0.25 into 0.25 2.510 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.510 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.510 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.510 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.510 * [taylor]: Taking taylor expansion of 2.0 in k 2.510 * [backup-simplify]: Simplify 2.0 into 2.0 2.510 * [taylor]: Taking taylor expansion of PI in k 2.510 * [backup-simplify]: Simplify PI into PI 2.510 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.511 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.511 * [taylor]: Taking taylor expansion of (log n) in k 2.511 * [taylor]: Taking taylor expansion of n in k 2.511 * [backup-simplify]: Simplify n into n 2.511 * [backup-simplify]: Simplify (log n) into (log n) 2.511 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.511 * [taylor]: Taking taylor expansion of 1.0 in k 2.511 * [backup-simplify]: Simplify 1.0 into 1.0 2.511 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.511 * [taylor]: Taking taylor expansion of k in k 2.511 * [backup-simplify]: Simplify 0 into 0 2.511 * [backup-simplify]: Simplify 1 into 1 2.511 * [backup-simplify]: Simplify (/ 1 1) into 1 2.511 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.512 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.512 * [backup-simplify]: Simplify (- 1) into -1 2.512 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.513 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.514 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.514 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.515 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.516 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.516 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.517 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.517 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.517 * [backup-simplify]: Simplify (- 0) into 0 2.518 * [backup-simplify]: Simplify (+ 0 0) into 0 2.518 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.519 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.519 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.521 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.521 * [taylor]: Taking taylor expansion of 0 in k 2.521 * [backup-simplify]: Simplify 0 into 0 2.521 * [backup-simplify]: Simplify 0 into 0 2.521 * [backup-simplify]: Simplify 0 into 0 2.521 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.522 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.523 * [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 2.524 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.524 * [backup-simplify]: Simplify (- 0) into 0 2.524 * [backup-simplify]: Simplify (+ 0 0) into 0 2.525 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.525 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.526 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.528 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.528 * [taylor]: Taking taylor expansion of 0 in k 2.528 * [backup-simplify]: Simplify 0 into 0 2.528 * [backup-simplify]: Simplify 0 into 0 2.528 * [backup-simplify]: Simplify 0 into 0 2.528 * [backup-simplify]: Simplify 0 into 0 2.529 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.529 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.539 * [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 2.539 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.539 * [backup-simplify]: Simplify (- 0) into 0 2.540 * [backup-simplify]: Simplify (+ 0 0) into 0 2.540 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.541 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.542 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.544 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.544 * [taylor]: Taking taylor expansion of 0 in k 2.544 * [backup-simplify]: Simplify 0 into 0 2.544 * [backup-simplify]: Simplify 0 into 0 2.545 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.545 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2.545 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.545 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.545 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.546 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.546 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.546 * [taylor]: Taking taylor expansion of 0.25 in k 2.546 * [backup-simplify]: Simplify 0.25 into 0.25 2.546 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.546 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.546 * [taylor]: Taking taylor expansion of k in k 2.546 * [backup-simplify]: Simplify 0 into 0 2.546 * [backup-simplify]: Simplify 1 into 1 2.546 * [backup-simplify]: Simplify (/ 1 1) into 1 2.546 * [taylor]: Taking taylor expansion of 1.0 in k 2.546 * [backup-simplify]: Simplify 1.0 into 1.0 2.546 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.546 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.546 * [taylor]: Taking taylor expansion of -2.0 in k 2.546 * [backup-simplify]: Simplify -2.0 into -2.0 2.546 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.546 * [taylor]: Taking taylor expansion of PI in k 2.546 * [backup-simplify]: Simplify PI into PI 2.546 * [taylor]: Taking taylor expansion of n in k 2.546 * [backup-simplify]: Simplify n into n 2.546 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.546 * [backup-simplify]: Simplify (* -2.0 (/ 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 2.547 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.547 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.547 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.547 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.547 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.547 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.547 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.547 * [taylor]: Taking taylor expansion of 0.25 in n 2.547 * [backup-simplify]: Simplify 0.25 into 0.25 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 2.547 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.547 * [taylor]: Taking taylor expansion of 1.0 in n 2.547 * [backup-simplify]: Simplify 1.0 into 1.0 2.547 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.547 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.547 * [taylor]: Taking taylor expansion of -2.0 in n 2.547 * [backup-simplify]: Simplify -2.0 into -2.0 2.547 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.547 * [taylor]: Taking taylor expansion of PI in n 2.547 * [backup-simplify]: Simplify PI into PI 2.547 * [taylor]: Taking taylor expansion of n in n 2.547 * [backup-simplify]: Simplify 0 into 0 2.547 * [backup-simplify]: Simplify 1 into 1 2.548 * [backup-simplify]: Simplify (/ PI 1) into PI 2.548 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.549 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.549 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.549 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.550 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.550 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.551 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.551 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.551 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.551 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.551 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.551 * [taylor]: Taking taylor expansion of 0.25 in n 2.551 * [backup-simplify]: Simplify 0.25 into 0.25 2.551 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.551 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.551 * [taylor]: Taking taylor expansion of k in n 2.551 * [backup-simplify]: Simplify k into k 2.551 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.551 * [taylor]: Taking taylor expansion of 1.0 in n 2.551 * [backup-simplify]: Simplify 1.0 into 1.0 2.551 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.551 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.551 * [taylor]: Taking taylor expansion of -2.0 in n 2.551 * [backup-simplify]: Simplify -2.0 into -2.0 2.551 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.551 * [taylor]: Taking taylor expansion of PI in n 2.551 * [backup-simplify]: Simplify PI into PI 2.551 * [taylor]: Taking taylor expansion of n in n 2.551 * [backup-simplify]: Simplify 0 into 0 2.551 * [backup-simplify]: Simplify 1 into 1 2.552 * [backup-simplify]: Simplify (/ PI 1) into PI 2.552 * [backup-simplify]: Simplify (* -2.0 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) 2.553 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.554 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.554 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.555 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.555 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.555 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.555 * [taylor]: Taking taylor expansion of 0.25 in k 2.555 * [backup-simplify]: Simplify 0.25 into 0.25 2.555 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.555 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.555 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.555 * [taylor]: Taking taylor expansion of k in k 2.555 * [backup-simplify]: Simplify 0 into 0 2.555 * [backup-simplify]: Simplify 1 into 1 2.556 * [backup-simplify]: Simplify (/ 1 1) into 1 2.556 * [taylor]: Taking taylor expansion of 1.0 in k 2.556 * [backup-simplify]: Simplify 1.0 into 1.0 2.556 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.556 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.556 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.556 * [taylor]: Taking taylor expansion of -2.0 in k 2.556 * [backup-simplify]: Simplify -2.0 into -2.0 2.556 * [taylor]: Taking taylor expansion of PI in k 2.556 * [backup-simplify]: Simplify PI into PI 2.556 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.557 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.557 * [taylor]: Taking taylor expansion of (log n) in k 2.557 * [taylor]: Taking taylor expansion of n in k 2.557 * [backup-simplify]: Simplify n into n 2.557 * [backup-simplify]: Simplify (log n) into (log n) 2.557 * [backup-simplify]: Simplify (+ 1 0) into 1 2.557 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.558 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.559 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.559 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.560 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.561 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.561 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.562 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.563 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.563 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.563 * [backup-simplify]: Simplify (+ 0 0) into 0 2.563 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.564 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.565 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.566 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.566 * [taylor]: Taking taylor expansion of 0 in k 2.566 * [backup-simplify]: Simplify 0 into 0 2.566 * [backup-simplify]: Simplify 0 into 0 2.566 * [backup-simplify]: Simplify 0 into 0 2.567 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.567 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.569 * [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 2.569 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.569 * [backup-simplify]: Simplify (+ 0 0) into 0 2.570 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.571 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.571 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.573 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.573 * [taylor]: Taking taylor expansion of 0 in k 2.573 * [backup-simplify]: Simplify 0 into 0 2.573 * [backup-simplify]: Simplify 0 into 0 2.573 * [backup-simplify]: Simplify 0 into 0 2.573 * [backup-simplify]: Simplify 0 into 0 2.574 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.574 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.577 * [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 2.577 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.577 * [backup-simplify]: Simplify (+ 0 0) into 0 2.578 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.579 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.580 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.582 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.582 * [taylor]: Taking taylor expansion of 0 in k 2.582 * [backup-simplify]: Simplify 0 into 0 2.582 * [backup-simplify]: Simplify 0 into 0 2.583 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.583 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 2.584 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) into (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) 2.584 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in (n k) around 0 2.584 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in k 2.584 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.584 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.584 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.584 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.584 * [taylor]: Taking taylor expansion of 0.25 in k 2.584 * [backup-simplify]: Simplify 0.25 into 0.25 2.584 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.584 * [taylor]: Taking taylor expansion of 1.0 in k 2.584 * [backup-simplify]: Simplify 1.0 into 1.0 2.584 * [taylor]: Taking taylor expansion of k in k 2.584 * [backup-simplify]: Simplify 0 into 0 2.584 * [backup-simplify]: Simplify 1 into 1 2.584 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.584 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.584 * [taylor]: Taking taylor expansion of 2.0 in k 2.584 * [backup-simplify]: Simplify 2.0 into 2.0 2.584 * [taylor]: Taking taylor expansion of (* n PI) in k 2.584 * [taylor]: Taking taylor expansion of n in k 2.584 * [backup-simplify]: Simplify n into n 2.584 * [taylor]: Taking taylor expansion of PI in k 2.584 * [backup-simplify]: Simplify PI into PI 2.584 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.584 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.584 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.584 * [backup-simplify]: Simplify (- 0) into 0 2.585 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.585 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.585 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.585 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.585 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 2.585 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.585 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.585 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.585 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.585 * [taylor]: Taking taylor expansion of 0.25 in n 2.585 * [backup-simplify]: Simplify 0.25 into 0.25 2.585 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.585 * [taylor]: Taking taylor expansion of 1.0 in n 2.585 * [backup-simplify]: Simplify 1.0 into 1.0 2.585 * [taylor]: Taking taylor expansion of k in n 2.585 * [backup-simplify]: Simplify k into k 2.585 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.585 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.585 * [taylor]: Taking taylor expansion of 2.0 in n 2.585 * [backup-simplify]: Simplify 2.0 into 2.0 2.585 * [taylor]: Taking taylor expansion of (* n PI) in n 2.585 * [taylor]: Taking taylor expansion of n in n 2.585 * [backup-simplify]: Simplify 0 into 0 2.585 * [backup-simplify]: Simplify 1 into 1 2.585 * [taylor]: Taking taylor expansion of PI in n 2.585 * [backup-simplify]: Simplify PI into PI 2.586 * [backup-simplify]: Simplify (* 0 PI) into 0 2.586 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.587 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.588 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.588 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.588 * [backup-simplify]: Simplify (- k) into (- k) 2.588 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.588 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.589 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.590 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.591 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.591 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 2.591 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.591 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.591 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.591 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.591 * [taylor]: Taking taylor expansion of 0.25 in n 2.591 * [backup-simplify]: Simplify 0.25 into 0.25 2.591 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.591 * [taylor]: Taking taylor expansion of 1.0 in n 2.591 * [backup-simplify]: Simplify 1.0 into 1.0 2.591 * [taylor]: Taking taylor expansion of k in n 2.591 * [backup-simplify]: Simplify k into k 2.591 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.591 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.591 * [taylor]: Taking taylor expansion of 2.0 in n 2.591 * [backup-simplify]: Simplify 2.0 into 2.0 2.591 * [taylor]: Taking taylor expansion of (* n PI) in n 2.591 * [taylor]: Taking taylor expansion of n in n 2.591 * [backup-simplify]: Simplify 0 into 0 2.591 * [backup-simplify]: Simplify 1 into 1 2.591 * [taylor]: Taking taylor expansion of PI in n 2.591 * [backup-simplify]: Simplify PI into PI 2.591 * [backup-simplify]: Simplify (* 0 PI) into 0 2.591 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.592 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.593 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.594 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.594 * [backup-simplify]: Simplify (- k) into (- k) 2.594 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.594 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.595 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.595 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.596 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.598 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) into (pow (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2) 2.598 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2) in k 2.598 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.598 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.598 * [taylor]: Taking taylor expansion of 0.25 in k 2.598 * [backup-simplify]: Simplify 0.25 into 0.25 2.598 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.598 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.598 * [taylor]: Taking taylor expansion of 1.0 in k 2.598 * [backup-simplify]: Simplify 1.0 into 1.0 2.598 * [taylor]: Taking taylor expansion of k in k 2.598 * [backup-simplify]: Simplify 0 into 0 2.598 * [backup-simplify]: Simplify 1 into 1 2.598 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.598 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.598 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.598 * [taylor]: Taking taylor expansion of 2.0 in k 2.598 * [backup-simplify]: Simplify 2.0 into 2.0 2.598 * [taylor]: Taking taylor expansion of PI in k 2.598 * [backup-simplify]: Simplify PI into PI 2.598 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.599 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.599 * [taylor]: Taking taylor expansion of (log n) in k 2.599 * [taylor]: Taking taylor expansion of n in k 2.599 * [backup-simplify]: Simplify n into n 2.599 * [backup-simplify]: Simplify (log n) into (log n) 2.599 * [backup-simplify]: Simplify (- 0) into 0 2.599 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.600 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.601 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.601 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.602 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.603 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) 2.604 * [backup-simplify]: Simplify (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) into (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) 2.605 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.605 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.606 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.606 * [backup-simplify]: Simplify (- 0) into 0 2.606 * [backup-simplify]: Simplify (+ 0 0) into 0 2.607 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.608 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.609 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.610 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.611 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) into 0 2.611 * [taylor]: Taking taylor expansion of 0 in k 2.611 * [backup-simplify]: Simplify 0 into 0 2.611 * [backup-simplify]: Simplify 0 into 0 2.612 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.612 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.613 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.613 * [backup-simplify]: Simplify (+ 0 0) into 0 2.613 * [backup-simplify]: Simplify (- 1) into -1 2.614 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.615 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.616 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2.618 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.623 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) 2.625 * [backup-simplify]: Simplify (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) into (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) 2.626 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.626 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.634 * [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 2.635 * [backup-simplify]: Simplify (- 0) into 0 2.635 * [backup-simplify]: Simplify (+ 0 0) into 0 2.636 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.636 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.637 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.639 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.640 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))) into 0 2.640 * [taylor]: Taking taylor expansion of 0 in k 2.640 * [backup-simplify]: Simplify 0 into 0 2.640 * [backup-simplify]: Simplify 0 into 0 2.640 * [backup-simplify]: Simplify 0 into 0 2.641 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) 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 2.644 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.644 * [backup-simplify]: Simplify (+ 0 0) into 0 2.644 * [backup-simplify]: Simplify (- 0) into 0 2.645 * [backup-simplify]: Simplify (+ 0 0) into 0 2.646 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.647 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.649 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.661 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) into (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) 2.665 * [backup-simplify]: Simplify (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) into (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) 2.673 * [backup-simplify]: Simplify (+ (* (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) (* k 1)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) into (- (+ (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))))) (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2)))) (* 0.125 (* (pow k 2) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2)))) (* 0.5 (* k (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))))) 2.674 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2))) into (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) 2.674 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in (n k) around 0 2.674 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in k 2.674 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.674 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.674 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.674 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.674 * [taylor]: Taking taylor expansion of 0.25 in k 2.674 * [backup-simplify]: Simplify 0.25 into 0.25 2.674 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.674 * [taylor]: Taking taylor expansion of 1.0 in k 2.674 * [backup-simplify]: Simplify 1.0 into 1.0 2.674 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.674 * [taylor]: Taking taylor expansion of k in k 2.674 * [backup-simplify]: Simplify 0 into 0 2.674 * [backup-simplify]: Simplify 1 into 1 2.674 * [backup-simplify]: Simplify (/ 1 1) into 1 2.675 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.675 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) 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 n) in k 2.675 * [taylor]: Taking taylor expansion of PI in k 2.675 * [backup-simplify]: Simplify PI into PI 2.675 * [taylor]: Taking taylor expansion of n in k 2.675 * [backup-simplify]: Simplify n into n 2.675 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.675 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.675 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.675 * [backup-simplify]: Simplify (- 1) into -1 2.675 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.676 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.676 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.676 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.676 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 2.676 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.676 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.676 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.676 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.676 * [taylor]: Taking taylor expansion of 0.25 in n 2.676 * [backup-simplify]: Simplify 0.25 into 0.25 2.676 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.676 * [taylor]: Taking taylor expansion of 1.0 in n 2.676 * [backup-simplify]: Simplify 1.0 into 1.0 2.676 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.676 * [taylor]: Taking taylor expansion of k in n 2.676 * [backup-simplify]: Simplify k into k 2.676 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.676 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.676 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.676 * [taylor]: Taking taylor expansion of 2.0 in n 2.676 * [backup-simplify]: Simplify 2.0 into 2.0 2.676 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.676 * [taylor]: Taking taylor expansion of PI in n 2.676 * [backup-simplify]: Simplify PI into PI 2.676 * [taylor]: Taking taylor expansion of n in n 2.676 * [backup-simplify]: Simplify 0 into 0 2.676 * [backup-simplify]: Simplify 1 into 1 2.676 * [backup-simplify]: Simplify (/ PI 1) into PI 2.677 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.677 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.677 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.677 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.678 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.678 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.679 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.680 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.680 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 2.680 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.680 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.680 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.680 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.680 * [taylor]: Taking taylor expansion of 0.25 in n 2.680 * [backup-simplify]: Simplify 0.25 into 0.25 2.680 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.680 * [taylor]: Taking taylor expansion of 1.0 in n 2.680 * [backup-simplify]: Simplify 1.0 into 1.0 2.680 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.680 * [taylor]: Taking taylor expansion of k in n 2.680 * [backup-simplify]: Simplify k into k 2.680 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.680 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.680 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.680 * [taylor]: Taking taylor expansion of 2.0 in n 2.680 * [backup-simplify]: Simplify 2.0 into 2.0 2.680 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.680 * [taylor]: Taking taylor expansion of PI in n 2.680 * [backup-simplify]: Simplify PI into PI 2.680 * [taylor]: Taking taylor expansion of n in n 2.680 * [backup-simplify]: Simplify 0 into 0 2.680 * [backup-simplify]: Simplify 1 into 1 2.681 * [backup-simplify]: Simplify (/ PI 1) into PI 2.681 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.681 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.681 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.681 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.682 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.683 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.684 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.685 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 2.685 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) in k 2.685 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.685 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.685 * [taylor]: Taking taylor expansion of 0.25 in k 2.685 * [backup-simplify]: Simplify 0.25 into 0.25 2.686 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.686 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.686 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.686 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.686 * [taylor]: Taking taylor expansion of 2.0 in k 2.686 * [backup-simplify]: Simplify 2.0 into 2.0 2.686 * [taylor]: Taking taylor expansion of PI in k 2.686 * [backup-simplify]: Simplify PI into PI 2.686 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.686 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.686 * [taylor]: Taking taylor expansion of (log n) in k 2.687 * [taylor]: Taking taylor expansion of n in k 2.687 * [backup-simplify]: Simplify n into n 2.687 * [backup-simplify]: Simplify (log n) into (log n) 2.687 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.687 * [taylor]: Taking taylor expansion of 1.0 in k 2.687 * [backup-simplify]: Simplify 1.0 into 1.0 2.687 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.687 * [taylor]: Taking taylor expansion of k in k 2.687 * [backup-simplify]: Simplify 0 into 0 2.687 * [backup-simplify]: Simplify 1 into 1 2.687 * [backup-simplify]: Simplify (/ 1 1) into 1 2.687 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.688 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.688 * [backup-simplify]: Simplify (- 1) into -1 2.688 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.689 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.689 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.690 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.691 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 2.692 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 2.693 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.693 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.694 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.694 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.694 * [backup-simplify]: Simplify (- 0) into 0 2.695 * [backup-simplify]: Simplify (+ 0 0) into 0 2.695 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.696 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.697 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.698 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.699 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 2.699 * [taylor]: Taking taylor expansion of 0 in k 2.699 * [backup-simplify]: Simplify 0 into 0 2.699 * [backup-simplify]: Simplify 0 into 0 2.701 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 2.701 * [backup-simplify]: Simplify 0 into 0 2.701 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.703 * [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 2.704 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.704 * [backup-simplify]: Simplify (- 0) into 0 2.704 * [backup-simplify]: Simplify (+ 0 0) into 0 2.704 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.705 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.706 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.708 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.709 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 2.709 * [taylor]: Taking taylor expansion of 0 in k 2.710 * [backup-simplify]: Simplify 0 into 0 2.710 * [backup-simplify]: Simplify 0 into 0 2.710 * [backup-simplify]: Simplify 0 into 0 2.711 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 2.711 * [backup-simplify]: Simplify 0 into 0 2.712 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.712 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.715 * [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 2.715 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.716 * [backup-simplify]: Simplify (- 0) into 0 2.716 * [backup-simplify]: Simplify (+ 0 0) into 0 2.717 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.717 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.718 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.720 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.722 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0 2.722 * [taylor]: Taking taylor expansion of 0 in k 2.722 * [backup-simplify]: Simplify 0 into 0 2.722 * [backup-simplify]: Simplify 0 into 0 2.729 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) 2) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2) 2.730 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2))) into (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) 2.730 * [approximate]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in (n k) around 0 2.730 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in k 2.730 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.730 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.730 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.730 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.730 * [taylor]: Taking taylor expansion of 0.25 in k 2.730 * [backup-simplify]: Simplify 0.25 into 0.25 2.730 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.730 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.730 * [taylor]: Taking taylor expansion of k in k 2.730 * [backup-simplify]: Simplify 0 into 0 2.730 * [backup-simplify]: Simplify 1 into 1 2.731 * [backup-simplify]: Simplify (/ 1 1) into 1 2.731 * [taylor]: Taking taylor expansion of 1.0 in k 2.731 * [backup-simplify]: Simplify 1.0 into 1.0 2.731 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.731 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.731 * [taylor]: Taking taylor expansion of -2.0 in k 2.731 * [backup-simplify]: Simplify -2.0 into -2.0 2.731 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.731 * [taylor]: Taking taylor expansion of PI in k 2.731 * [backup-simplify]: Simplify PI into PI 2.731 * [taylor]: Taking taylor expansion of n in k 2.731 * [backup-simplify]: Simplify n into n 2.731 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.731 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.731 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.731 * [backup-simplify]: Simplify (+ 1 0) into 1 2.732 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.732 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.732 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.732 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 2.732 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.732 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.732 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.732 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.732 * [taylor]: Taking taylor expansion of 0.25 in n 2.732 * [backup-simplify]: Simplify 0.25 into 0.25 2.732 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.732 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.732 * [taylor]: Taking taylor expansion of k in n 2.732 * [backup-simplify]: Simplify k into k 2.732 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.732 * [taylor]: Taking taylor expansion of 1.0 in n 2.732 * [backup-simplify]: Simplify 1.0 into 1.0 2.732 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.732 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.732 * [taylor]: Taking taylor expansion of -2.0 in n 2.732 * [backup-simplify]: Simplify -2.0 into -2.0 2.732 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.732 * [taylor]: Taking taylor expansion of PI in n 2.732 * [backup-simplify]: Simplify PI into PI 2.732 * [taylor]: Taking taylor expansion of n in n 2.732 * [backup-simplify]: Simplify 0 into 0 2.732 * [backup-simplify]: Simplify 1 into 1 2.732 * [backup-simplify]: Simplify (/ PI 1) into PI 2.733 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.733 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.733 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.734 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.734 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.735 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.736 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.736 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 2.736 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.736 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.736 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.736 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.736 * [taylor]: Taking taylor expansion of 0.25 in n 2.736 * [backup-simplify]: Simplify 0.25 into 0.25 2.736 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.736 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.736 * [taylor]: Taking taylor expansion of k in n 2.736 * [backup-simplify]: Simplify k into k 2.736 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.736 * [taylor]: Taking taylor expansion of 1.0 in n 2.736 * [backup-simplify]: Simplify 1.0 into 1.0 2.736 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.736 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.736 * [taylor]: Taking taylor expansion of -2.0 in n 2.736 * [backup-simplify]: Simplify -2.0 into -2.0 2.736 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.736 * [taylor]: Taking taylor expansion of PI in n 2.736 * [backup-simplify]: Simplify PI into PI 2.736 * [taylor]: Taking taylor expansion of n in n 2.736 * [backup-simplify]: Simplify 0 into 0 2.736 * [backup-simplify]: Simplify 1 into 1 2.737 * [backup-simplify]: Simplify (/ PI 1) into PI 2.737 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.737 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.737 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.738 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.738 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.739 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.740 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.741 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 2.741 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) in k 2.741 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.741 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.741 * [taylor]: Taking taylor expansion of 0.25 in k 2.741 * [backup-simplify]: Simplify 0.25 into 0.25 2.741 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.741 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.742 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.742 * [taylor]: Taking taylor expansion of k in k 2.742 * [backup-simplify]: Simplify 0 into 0 2.742 * [backup-simplify]: Simplify 1 into 1 2.742 * [backup-simplify]: Simplify (/ 1 1) into 1 2.742 * [taylor]: Taking taylor expansion of 1.0 in k 2.742 * [backup-simplify]: Simplify 1.0 into 1.0 2.742 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.742 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.742 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.742 * [taylor]: Taking taylor expansion of -2.0 in k 2.742 * [backup-simplify]: Simplify -2.0 into -2.0 2.742 * [taylor]: Taking taylor expansion of PI in k 2.742 * [backup-simplify]: Simplify PI into PI 2.742 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.743 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.743 * [taylor]: Taking taylor expansion of (log n) in k 2.743 * [taylor]: Taking taylor expansion of n in k 2.743 * [backup-simplify]: Simplify n into n 2.743 * [backup-simplify]: Simplify (log n) into (log n) 2.743 * [backup-simplify]: Simplify (+ 1 0) into 1 2.743 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.744 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.745 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.745 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.746 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.747 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 2.748 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) into (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 2.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.749 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.750 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.750 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.750 * [backup-simplify]: Simplify (+ 0 0) into 0 2.751 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.752 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.752 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.753 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.755 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 2.755 * [taylor]: Taking taylor expansion of 0 in k 2.755 * [backup-simplify]: Simplify 0 into 0 2.755 * [backup-simplify]: Simplify 0 into 0 2.756 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 2.756 * [backup-simplify]: Simplify 0 into 0 2.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.758 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.760 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 2.760 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.760 * [backup-simplify]: Simplify (+ 0 0) into 0 2.760 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.761 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.762 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.763 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.765 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into 0 2.765 * [taylor]: Taking taylor expansion of 0 in k 2.765 * [backup-simplify]: Simplify 0 into 0 2.765 * [backup-simplify]: Simplify 0 into 0 2.765 * [backup-simplify]: Simplify 0 into 0 2.767 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into 0 2.767 * [backup-simplify]: Simplify 0 into 0 2.768 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.768 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.771 * [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 2.771 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.771 * [backup-simplify]: Simplify (+ 0 0) into 0 2.772 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.773 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.774 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.776 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.777 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))) into 0 2.777 * [taylor]: Taking taylor expansion of 0 in k 2.778 * [backup-simplify]: Simplify 0 into 0 2.778 * [backup-simplify]: Simplify 0 into 0 2.778 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) 2) into (pow (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2) 2.778 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1) 2.779 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.779 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.779 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.779 * [taylor]: Taking taylor expansion of 2.0 in n 2.779 * [backup-simplify]: Simplify 2.0 into 2.0 2.779 * [taylor]: Taking taylor expansion of (* n PI) in n 2.779 * [taylor]: Taking taylor expansion of n in n 2.779 * [backup-simplify]: Simplify 0 into 0 2.779 * [backup-simplify]: Simplify 1 into 1 2.779 * [taylor]: Taking taylor expansion of PI in n 2.779 * [backup-simplify]: Simplify PI into PI 2.779 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.779 * [taylor]: Taking taylor expansion of 2.0 in n 2.779 * [backup-simplify]: Simplify 2.0 into 2.0 2.779 * [taylor]: Taking taylor expansion of (* n PI) in n 2.779 * [taylor]: Taking taylor expansion of n in n 2.779 * [backup-simplify]: Simplify 0 into 0 2.779 * [backup-simplify]: Simplify 1 into 1 2.779 * [taylor]: Taking taylor expansion of PI in n 2.779 * [backup-simplify]: Simplify PI into PI 2.779 * [backup-simplify]: Simplify (* 0 PI) into 0 2.780 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.780 * [backup-simplify]: Simplify 0 into 0 2.781 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.781 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.782 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.782 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.783 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.783 * [backup-simplify]: Simplify 0 into 0 2.783 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.784 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.784 * [backup-simplify]: Simplify 0 into 0 2.785 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.785 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.786 * [backup-simplify]: Simplify 0 into 0 2.786 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.787 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.787 * [backup-simplify]: Simplify 0 into 0 2.788 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.789 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.789 * [backup-simplify]: Simplify 0 into 0 2.790 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.791 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.791 * [backup-simplify]: Simplify 0 into 0 2.791 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.791 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.791 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.791 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.792 * [taylor]: Taking taylor expansion of 2.0 in n 2.792 * [backup-simplify]: Simplify 2.0 into 2.0 2.792 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.792 * [taylor]: Taking taylor expansion of PI in n 2.792 * [backup-simplify]: Simplify PI into PI 2.792 * [taylor]: Taking taylor expansion of n in n 2.792 * [backup-simplify]: Simplify 0 into 0 2.792 * [backup-simplify]: Simplify 1 into 1 2.792 * [backup-simplify]: Simplify (/ PI 1) into PI 2.792 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.792 * [taylor]: Taking taylor expansion of 2.0 in n 2.792 * [backup-simplify]: Simplify 2.0 into 2.0 2.792 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.792 * [taylor]: Taking taylor expansion of PI in n 2.792 * [backup-simplify]: Simplify PI into PI 2.792 * [taylor]: Taking taylor expansion of n in n 2.792 * [backup-simplify]: Simplify 0 into 0 2.792 * [backup-simplify]: Simplify 1 into 1 2.792 * [backup-simplify]: Simplify (/ PI 1) into PI 2.793 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.793 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.793 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.794 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.794 * [backup-simplify]: Simplify 0 into 0 2.794 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.795 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.795 * [backup-simplify]: Simplify 0 into 0 2.796 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.796 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.796 * [backup-simplify]: Simplify 0 into 0 2.797 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.798 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.798 * [backup-simplify]: Simplify 0 into 0 2.798 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.799 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.799 * [backup-simplify]: Simplify 0 into 0 2.800 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.800 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.800 * [backup-simplify]: Simplify 0 into 0 2.801 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.801 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.801 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.801 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.801 * [taylor]: Taking taylor expansion of -2.0 in n 2.801 * [backup-simplify]: Simplify -2.0 into -2.0 2.801 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.801 * [taylor]: Taking taylor expansion of PI in n 2.801 * [backup-simplify]: Simplify PI into PI 2.801 * [taylor]: Taking taylor expansion of n in n 2.801 * [backup-simplify]: Simplify 0 into 0 2.801 * [backup-simplify]: Simplify 1 into 1 2.802 * [backup-simplify]: Simplify (/ PI 1) into PI 2.802 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.802 * [taylor]: Taking taylor expansion of -2.0 in n 2.802 * [backup-simplify]: Simplify -2.0 into -2.0 2.802 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.802 * [taylor]: Taking taylor expansion of PI in n 2.802 * [backup-simplify]: Simplify PI into PI 2.802 * [taylor]: Taking taylor expansion of n in n 2.802 * [backup-simplify]: Simplify 0 into 0 2.802 * [backup-simplify]: Simplify 1 into 1 2.802 * [backup-simplify]: Simplify (/ PI 1) into PI 2.802 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.803 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.803 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.804 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.804 * [backup-simplify]: Simplify 0 into 0 2.804 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.805 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.805 * [backup-simplify]: Simplify 0 into 0 2.805 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.806 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.806 * [backup-simplify]: Simplify 0 into 0 2.806 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.807 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.807 * [backup-simplify]: Simplify 0 into 0 2.808 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.809 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.809 * [backup-simplify]: Simplify 0 into 0 2.809 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.810 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.810 * [backup-simplify]: Simplify 0 into 0 2.811 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.811 * * * [progress]: simplifying candidates 2.821 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 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(* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (pow (exp (* h5 (+ (log (* h0 h4)) (log h3)))) 2) (+ (* h5 (* (pow h1 2) (* (log (* h0 h4)) (* (pow (exp (* h5 (+ (log (* h0 h4)) (log h3)))) 2) (log h3))))) (+ (* h10 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (pow (exp (* h5 (+ (log (* h0 h4)) (log h3)))) 2)))) (* h10 (* (pow h1 2) (* (pow (exp (* h5 (+ (log (* h0 h4)) (log h3)))) 2) (pow (log h3) 2))))))) (+ (* h9 (* h1 (* (log (* h0 h4)) (pow (exp (* h5 (+ (log (* h0 h4)) (log h3)))) 2)))) (* h9 (* h1 (* (pow (exp (* h5 (+ (log (* h0 h4)) (log h3)))) 2) (log h3)))))) (pow (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) 2) (pow (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) 2) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) 2.834 * * [simplify]: iteration 0 : 875 enodes (cost 2384 ) 2.848 * * [simplify]: iteration 1 : 3640 enodes (cost 2189 ) 2.904 * * [simplify]: iteration 2 : 5002 enodes (cost 2154 ) 2.913 * * * [progress]: adding candidates to table 3.656 * * [progress]: iteration 4 / 4 3.656 * * * [progress]: picking best candidate 3.677 * * * * [pick]: Picked # 3.677 * * * [progress]: localizing error 3.689 * * * [progress]: generating rewritten candidates 3.689 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.710 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 3.730 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 3.736 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 3.781 * * * [progress]: generating series expansions 3.781 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.782 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 3.782 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.782 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.782 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.782 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.782 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.782 * [taylor]: Taking taylor expansion of 0.5 in k 3.782 * [backup-simplify]: Simplify 0.5 into 0.5 3.782 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.782 * [taylor]: Taking taylor expansion of 1.0 in k 3.782 * [backup-simplify]: Simplify 1.0 into 1.0 3.782 * [taylor]: Taking taylor expansion of k in k 3.782 * [backup-simplify]: Simplify 0 into 0 3.783 * [backup-simplify]: Simplify 1 into 1 3.783 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.783 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.783 * [taylor]: Taking taylor expansion of 2.0 in k 3.783 * [backup-simplify]: Simplify 2.0 into 2.0 3.783 * [taylor]: Taking taylor expansion of (* n PI) in k 3.783 * [taylor]: Taking taylor expansion of n in k 3.783 * [backup-simplify]: Simplify n into n 3.783 * [taylor]: Taking taylor expansion of PI in k 3.783 * [backup-simplify]: Simplify PI into PI 3.783 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.783 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.783 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.783 * [backup-simplify]: Simplify (- 0) into 0 3.783 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.784 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.784 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.784 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.784 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.784 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.784 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.784 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.784 * [taylor]: Taking taylor expansion of 0.5 in n 3.784 * [backup-simplify]: Simplify 0.5 into 0.5 3.784 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.784 * [taylor]: Taking taylor expansion of 1.0 in n 3.784 * [backup-simplify]: Simplify 1.0 into 1.0 3.784 * [taylor]: Taking taylor expansion of k in n 3.784 * [backup-simplify]: Simplify k into k 3.784 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.784 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.784 * [taylor]: Taking taylor expansion of 2.0 in n 3.784 * [backup-simplify]: Simplify 2.0 into 2.0 3.784 * [taylor]: Taking taylor expansion of (* n PI) in n 3.784 * [taylor]: Taking taylor expansion of n in n 3.784 * [backup-simplify]: Simplify 0 into 0 3.784 * [backup-simplify]: Simplify 1 into 1 3.784 * [taylor]: Taking taylor expansion of PI in n 3.784 * [backup-simplify]: Simplify PI into PI 3.785 * [backup-simplify]: Simplify (* 0 PI) into 0 3.785 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.786 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.787 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.787 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.787 * [backup-simplify]: Simplify (- k) into (- k) 3.787 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.787 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.788 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.789 * [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)))) 3.790 * [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))))) 3.790 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.790 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.790 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.790 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.790 * [taylor]: Taking taylor expansion of 0.5 in n 3.790 * [backup-simplify]: Simplify 0.5 into 0.5 3.790 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.790 * [taylor]: Taking taylor expansion of 1.0 in n 3.790 * [backup-simplify]: Simplify 1.0 into 1.0 3.790 * [taylor]: Taking taylor expansion of k in n 3.790 * [backup-simplify]: Simplify k into k 3.790 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.790 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.790 * [taylor]: Taking taylor expansion of 2.0 in n 3.790 * [backup-simplify]: Simplify 2.0 into 2.0 3.790 * [taylor]: Taking taylor expansion of (* n PI) in n 3.790 * [taylor]: Taking taylor expansion of n in n 3.790 * [backup-simplify]: Simplify 0 into 0 3.790 * [backup-simplify]: Simplify 1 into 1 3.790 * [taylor]: Taking taylor expansion of PI in n 3.790 * [backup-simplify]: Simplify PI into PI 3.790 * [backup-simplify]: Simplify (* 0 PI) into 0 3.790 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.791 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.792 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.793 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.793 * [backup-simplify]: Simplify (- k) into (- k) 3.793 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.793 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.794 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.794 * [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)))) 3.795 * [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))))) 3.795 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.795 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.795 * [taylor]: Taking taylor expansion of 0.5 in k 3.795 * [backup-simplify]: Simplify 0.5 into 0.5 3.795 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.795 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.795 * [taylor]: Taking taylor expansion of 1.0 in k 3.795 * [backup-simplify]: Simplify 1.0 into 1.0 3.795 * [taylor]: Taking taylor expansion of k in k 3.795 * [backup-simplify]: Simplify 0 into 0 3.795 * [backup-simplify]: Simplify 1 into 1 3.795 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.795 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.795 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.795 * [taylor]: Taking taylor expansion of 2.0 in k 3.795 * [backup-simplify]: Simplify 2.0 into 2.0 3.795 * [taylor]: Taking taylor expansion of PI in k 3.795 * [backup-simplify]: Simplify PI into PI 3.796 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.796 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.796 * [taylor]: Taking taylor expansion of (log n) in k 3.796 * [taylor]: Taking taylor expansion of n in k 3.796 * [backup-simplify]: Simplify n into n 3.796 * [backup-simplify]: Simplify (log n) into (log n) 3.797 * [backup-simplify]: Simplify (- 0) into 0 3.797 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.798 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.798 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.799 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 3.800 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.800 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.801 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.801 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.802 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.803 * [backup-simplify]: Simplify (- 0) into 0 3.803 * [backup-simplify]: Simplify (+ 0 0) into 0 3.803 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.804 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.805 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.806 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.806 * [taylor]: Taking taylor expansion of 0 in k 3.806 * [backup-simplify]: Simplify 0 into 0 3.806 * [backup-simplify]: Simplify 0 into 0 3.806 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.807 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.808 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.808 * [backup-simplify]: Simplify (+ 0 0) into 0 3.808 * [backup-simplify]: Simplify (- 1) into -1 3.809 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.810 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.811 * [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)))) 3.813 * [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)))))) 3.815 * [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)))))) 3.815 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.816 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.818 * [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 3.818 * [backup-simplify]: Simplify (- 0) into 0 3.818 * [backup-simplify]: Simplify (+ 0 0) into 0 3.819 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.820 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.820 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.822 * [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 3.822 * [taylor]: Taking taylor expansion of 0 in k 3.822 * [backup-simplify]: Simplify 0 into 0 3.822 * [backup-simplify]: Simplify 0 into 0 3.822 * [backup-simplify]: Simplify 0 into 0 3.822 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.824 * [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 3.825 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.825 * [backup-simplify]: Simplify (+ 0 0) into 0 3.826 * [backup-simplify]: Simplify (- 0) into 0 3.826 * [backup-simplify]: Simplify (+ 0 0) into 0 3.827 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.828 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 3.831 * [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)))))) 3.834 * [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)))))) 3.840 * [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)))))) 3.840 * [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)))) 3.840 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.840 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.840 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.840 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.840 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.840 * [taylor]: Taking taylor expansion of 0.5 in k 3.840 * [backup-simplify]: Simplify 0.5 into 0.5 3.840 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.840 * [taylor]: Taking taylor expansion of 1.0 in k 3.840 * [backup-simplify]: Simplify 1.0 into 1.0 3.840 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.840 * [taylor]: Taking taylor expansion of k in k 3.840 * [backup-simplify]: Simplify 0 into 0 3.841 * [backup-simplify]: Simplify 1 into 1 3.841 * [backup-simplify]: Simplify (/ 1 1) into 1 3.841 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.841 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) 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 n) in k 3.841 * [taylor]: Taking taylor expansion of PI in k 3.841 * [backup-simplify]: Simplify PI into PI 3.841 * [taylor]: Taking taylor expansion of n in k 3.841 * [backup-simplify]: Simplify n into n 3.841 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.841 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.841 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.841 * [backup-simplify]: Simplify (- 1) into -1 3.842 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.842 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.842 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.842 * [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))))) 3.842 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.842 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.842 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.842 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.842 * [taylor]: Taking taylor expansion of 0.5 in n 3.842 * [backup-simplify]: Simplify 0.5 into 0.5 3.842 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.842 * [taylor]: Taking taylor expansion of 1.0 in n 3.842 * [backup-simplify]: Simplify 1.0 into 1.0 3.842 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.842 * [taylor]: Taking taylor expansion of k in n 3.842 * [backup-simplify]: Simplify k into k 3.842 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.842 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.842 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.842 * [taylor]: Taking taylor expansion of 2.0 in n 3.842 * [backup-simplify]: Simplify 2.0 into 2.0 3.842 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.842 * [taylor]: Taking taylor expansion of PI in n 3.842 * [backup-simplify]: Simplify PI into PI 3.842 * [taylor]: Taking taylor expansion of n in n 3.842 * [backup-simplify]: Simplify 0 into 0 3.842 * [backup-simplify]: Simplify 1 into 1 3.843 * [backup-simplify]: Simplify (/ PI 1) into PI 3.843 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.844 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.844 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.844 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.844 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.845 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.845 * [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)))) 3.846 * [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))))) 3.846 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.846 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.846 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.846 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.846 * [taylor]: Taking taylor expansion of 0.5 in n 3.846 * [backup-simplify]: Simplify 0.5 into 0.5 3.846 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.846 * [taylor]: Taking taylor expansion of 1.0 in n 3.846 * [backup-simplify]: Simplify 1.0 into 1.0 3.846 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.846 * [taylor]: Taking taylor expansion of k in n 3.846 * [backup-simplify]: Simplify k into k 3.846 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.846 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.846 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.846 * [taylor]: Taking taylor expansion of 2.0 in n 3.846 * [backup-simplify]: Simplify 2.0 into 2.0 3.846 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.846 * [taylor]: Taking taylor expansion of PI in n 3.846 * [backup-simplify]: Simplify PI into PI 3.846 * [taylor]: Taking taylor expansion of n in n 3.846 * [backup-simplify]: Simplify 0 into 0 3.846 * [backup-simplify]: Simplify 1 into 1 3.847 * [backup-simplify]: Simplify (/ PI 1) into PI 3.847 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.848 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.848 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.848 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.848 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.849 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.849 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 3.850 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 3.850 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.850 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.850 * [taylor]: Taking taylor expansion of 0.5 in k 3.850 * [backup-simplify]: Simplify 0.5 into 0.5 3.850 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.850 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.850 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.850 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.850 * [taylor]: Taking taylor expansion of 2.0 in k 3.850 * [backup-simplify]: Simplify 2.0 into 2.0 3.850 * [taylor]: Taking taylor expansion of PI in k 3.850 * [backup-simplify]: Simplify PI into PI 3.851 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.851 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.851 * [taylor]: Taking taylor expansion of (log n) in k 3.851 * [taylor]: Taking taylor expansion of n in k 3.851 * [backup-simplify]: Simplify n into n 3.851 * [backup-simplify]: Simplify (log n) into (log n) 3.851 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.851 * [taylor]: Taking taylor expansion of 1.0 in k 3.851 * [backup-simplify]: Simplify 1.0 into 1.0 3.851 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.851 * [taylor]: Taking taylor expansion of k in k 3.851 * [backup-simplify]: Simplify 0 into 0 3.851 * [backup-simplify]: Simplify 1 into 1 3.852 * [backup-simplify]: Simplify (/ 1 1) into 1 3.852 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.852 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 3.852 * [backup-simplify]: Simplify (- 1) into -1 3.853 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.853 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 3.854 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 3.855 * [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))))) 3.855 * [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))))) 3.856 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.856 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.857 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.857 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.858 * [backup-simplify]: Simplify (- 0) into 0 3.858 * [backup-simplify]: Simplify (+ 0 0) into 0 3.858 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.859 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.860 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.861 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.861 * [taylor]: Taking taylor expansion of 0 in k 3.861 * [backup-simplify]: Simplify 0 into 0 3.861 * [backup-simplify]: Simplify 0 into 0 3.861 * [backup-simplify]: Simplify 0 into 0 3.862 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.862 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.864 * [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 3.864 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.864 * [backup-simplify]: Simplify (- 0) into 0 3.865 * [backup-simplify]: Simplify (+ 0 0) into 0 3.865 * [backup-simplify]: Simplify (+ (* 0.5 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 (- (log (* 2.0 PI)) (log n))))) into 0 3.874 * [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 3.875 * [taylor]: Taking taylor expansion of 0 in k 3.875 * [backup-simplify]: Simplify 0 into 0 3.875 * [backup-simplify]: Simplify 0 into 0 3.875 * [backup-simplify]: Simplify 0 into 0 3.875 * [backup-simplify]: Simplify 0 into 0 3.875 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.876 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.879 * [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 3.879 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.879 * [backup-simplify]: Simplify (- 0) into 0 3.880 * [backup-simplify]: Simplify (+ 0 0) into 0 3.880 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 3.881 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.882 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 3.884 * [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 3.884 * [taylor]: Taking taylor expansion of 0 in k 3.884 * [backup-simplify]: Simplify 0 into 0 3.884 * [backup-simplify]: Simplify 0 into 0 3.885 * [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)))) 3.885 * [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))) 3.885 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.885 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.885 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.885 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.885 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.885 * [taylor]: Taking taylor expansion of 0.5 in k 3.885 * [backup-simplify]: Simplify 0.5 into 0.5 3.885 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.885 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.885 * [taylor]: Taking taylor expansion of k in k 3.885 * [backup-simplify]: Simplify 0 into 0 3.886 * [backup-simplify]: Simplify 1 into 1 3.886 * [backup-simplify]: Simplify (/ 1 1) into 1 3.886 * [taylor]: Taking taylor expansion of 1.0 in k 3.886 * [backup-simplify]: Simplify 1.0 into 1.0 3.886 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.886 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.886 * [taylor]: Taking taylor expansion of -2.0 in k 3.886 * [backup-simplify]: Simplify -2.0 into -2.0 3.886 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.886 * [taylor]: Taking taylor expansion of PI in k 3.886 * [backup-simplify]: Simplify PI into PI 3.886 * [taylor]: Taking taylor expansion of n in k 3.886 * [backup-simplify]: Simplify n into n 3.886 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.886 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.886 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.886 * [backup-simplify]: Simplify (+ 1 0) into 1 3.887 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.887 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.887 * [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)))))) 3.887 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.887 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.887 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.887 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.887 * [taylor]: Taking taylor expansion of 0.5 in n 3.887 * [backup-simplify]: Simplify 0.5 into 0.5 3.887 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.887 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.887 * [taylor]: Taking taylor expansion of k in n 3.887 * [backup-simplify]: Simplify k into k 3.887 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.887 * [taylor]: Taking taylor expansion of 1.0 in n 3.887 * [backup-simplify]: Simplify 1.0 into 1.0 3.887 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.887 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.887 * [taylor]: Taking taylor expansion of -2.0 in n 3.887 * [backup-simplify]: Simplify -2.0 into -2.0 3.887 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.887 * [taylor]: Taking taylor expansion of PI in n 3.887 * [backup-simplify]: Simplify PI into PI 3.887 * [taylor]: Taking taylor expansion of n in n 3.887 * [backup-simplify]: Simplify 0 into 0 3.887 * [backup-simplify]: Simplify 1 into 1 3.887 * [backup-simplify]: Simplify (/ PI 1) into PI 3.888 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.888 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.888 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.888 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.889 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.890 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 3.891 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 3.891 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.891 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.891 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.891 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.891 * [taylor]: Taking taylor expansion of 0.5 in n 3.891 * [backup-simplify]: Simplify 0.5 into 0.5 3.891 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.891 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.891 * [taylor]: Taking taylor expansion of k in n 3.891 * [backup-simplify]: Simplify k into k 3.891 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.891 * [taylor]: Taking taylor expansion of 1.0 in n 3.891 * [backup-simplify]: Simplify 1.0 into 1.0 3.891 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.891 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.891 * [taylor]: Taking taylor expansion of -2.0 in n 3.891 * [backup-simplify]: Simplify -2.0 into -2.0 3.891 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.891 * [taylor]: Taking taylor expansion of PI in n 3.891 * [backup-simplify]: Simplify PI into PI 3.891 * [taylor]: Taking taylor expansion of n in n 3.891 * [backup-simplify]: Simplify 0 into 0 3.891 * [backup-simplify]: Simplify 1 into 1 3.891 * [backup-simplify]: Simplify (/ PI 1) into PI 3.892 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.892 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.892 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.892 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.893 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.894 * [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)))) 3.895 * [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))))) 3.895 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 3.895 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 3.895 * [taylor]: Taking taylor expansion of 0.5 in k 3.895 * [backup-simplify]: Simplify 0.5 into 0.5 3.895 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 3.895 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.895 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.895 * [taylor]: Taking taylor expansion of k in k 3.895 * [backup-simplify]: Simplify 0 into 0 3.895 * [backup-simplify]: Simplify 1 into 1 3.895 * [backup-simplify]: Simplify (/ 1 1) into 1 3.895 * [taylor]: Taking taylor expansion of 1.0 in k 3.895 * [backup-simplify]: Simplify 1.0 into 1.0 3.895 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.895 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.895 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.895 * [taylor]: Taking taylor expansion of -2.0 in k 3.895 * [backup-simplify]: Simplify -2.0 into -2.0 3.895 * [taylor]: Taking taylor expansion of PI in k 3.895 * [backup-simplify]: Simplify PI into PI 3.896 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.896 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.896 * [taylor]: Taking taylor expansion of (log n) in k 3.896 * [taylor]: Taking taylor expansion of n in k 3.896 * [backup-simplify]: Simplify n into n 3.896 * [backup-simplify]: Simplify (log n) into (log n) 3.897 * [backup-simplify]: Simplify (+ 1 0) into 1 3.897 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.897 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 3.898 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 3.899 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 3.899 * [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))))) 3.900 * [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))))) 3.901 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.901 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.902 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.902 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.902 * [backup-simplify]: Simplify (+ 0 0) into 0 3.902 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.903 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.904 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.905 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.905 * [taylor]: Taking taylor expansion of 0 in k 3.905 * [backup-simplify]: Simplify 0 into 0 3.905 * [backup-simplify]: Simplify 0 into 0 3.905 * [backup-simplify]: Simplify 0 into 0 3.906 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.906 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.908 * [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 3.908 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.908 * [backup-simplify]: Simplify (+ 0 0) into 0 3.909 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 3.910 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.911 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 3.912 * [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 3.912 * [taylor]: Taking taylor expansion of 0 in k 3.912 * [backup-simplify]: Simplify 0 into 0 3.912 * [backup-simplify]: Simplify 0 into 0 3.912 * [backup-simplify]: Simplify 0 into 0 3.912 * [backup-simplify]: Simplify 0 into 0 3.913 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.914 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.917 * [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 3.917 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.917 * [backup-simplify]: Simplify (+ 0 0) into 0 3.918 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 3.919 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.920 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 3.921 * [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 3.921 * [taylor]: Taking taylor expansion of 0 in k 3.921 * [backup-simplify]: Simplify 0 into 0 3.921 * [backup-simplify]: Simplify 0 into 0 3.922 * [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)))))) 3.922 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 3.922 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.922 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.922 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.922 * [taylor]: Taking taylor expansion of 2.0 in n 3.923 * [backup-simplify]: Simplify 2.0 into 2.0 3.923 * [taylor]: Taking taylor expansion of (* n PI) in n 3.923 * [taylor]: Taking taylor expansion of n in n 3.923 * [backup-simplify]: Simplify 0 into 0 3.923 * [backup-simplify]: Simplify 1 into 1 3.923 * [taylor]: Taking taylor expansion of PI in n 3.923 * [backup-simplify]: Simplify PI into PI 3.923 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.923 * [taylor]: Taking taylor expansion of 2.0 in n 3.923 * [backup-simplify]: Simplify 2.0 into 2.0 3.923 * [taylor]: Taking taylor expansion of (* n PI) in n 3.923 * [taylor]: Taking taylor expansion of n in n 3.923 * [backup-simplify]: Simplify 0 into 0 3.923 * [backup-simplify]: Simplify 1 into 1 3.923 * [taylor]: Taking taylor expansion of PI in n 3.923 * [backup-simplify]: Simplify PI into PI 3.923 * [backup-simplify]: Simplify (* 0 PI) into 0 3.923 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.923 * [backup-simplify]: Simplify 0 into 0 3.924 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.925 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.925 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.926 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.926 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.926 * [backup-simplify]: Simplify 0 into 0 3.927 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.928 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.928 * [backup-simplify]: Simplify 0 into 0 3.928 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.929 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.929 * [backup-simplify]: Simplify 0 into 0 3.930 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.931 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 3.931 * [backup-simplify]: Simplify 0 into 0 3.931 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.932 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 3.932 * [backup-simplify]: Simplify 0 into 0 3.933 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 3.934 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 3.934 * [backup-simplify]: Simplify 0 into 0 3.935 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.935 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 3.935 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.935 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.935 * [taylor]: Taking taylor expansion of 2.0 in n 3.935 * [backup-simplify]: Simplify 2.0 into 2.0 3.935 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.935 * [taylor]: Taking taylor expansion of PI in n 3.935 * [backup-simplify]: Simplify PI into PI 3.935 * [taylor]: Taking taylor expansion of n in n 3.935 * [backup-simplify]: Simplify 0 into 0 3.935 * [backup-simplify]: Simplify 1 into 1 3.935 * [backup-simplify]: Simplify (/ PI 1) into PI 3.935 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.935 * [taylor]: Taking taylor expansion of 2.0 in n 3.935 * [backup-simplify]: Simplify 2.0 into 2.0 3.935 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.936 * [taylor]: Taking taylor expansion of PI in n 3.936 * [backup-simplify]: Simplify PI into PI 3.936 * [taylor]: Taking taylor expansion of n in n 3.936 * [backup-simplify]: Simplify 0 into 0 3.936 * [backup-simplify]: Simplify 1 into 1 3.936 * [backup-simplify]: Simplify (/ PI 1) into PI 3.936 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.936 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.937 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.937 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.937 * [backup-simplify]: Simplify 0 into 0 3.938 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.938 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.938 * [backup-simplify]: Simplify 0 into 0 3.939 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.940 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.940 * [backup-simplify]: Simplify 0 into 0 3.940 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.941 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.941 * [backup-simplify]: Simplify 0 into 0 3.942 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.942 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.942 * [backup-simplify]: Simplify 0 into 0 3.943 * [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 3.944 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.944 * [backup-simplify]: Simplify 0 into 0 3.944 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 3.945 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 3.945 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.945 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.945 * [taylor]: Taking taylor expansion of -2.0 in n 3.945 * [backup-simplify]: Simplify -2.0 into -2.0 3.945 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.945 * [taylor]: Taking taylor expansion of PI in n 3.945 * [backup-simplify]: Simplify PI into PI 3.945 * [taylor]: Taking taylor expansion of n in n 3.945 * [backup-simplify]: Simplify 0 into 0 3.945 * [backup-simplify]: Simplify 1 into 1 3.945 * [backup-simplify]: Simplify (/ PI 1) into PI 3.945 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.945 * [taylor]: Taking taylor expansion of -2.0 in n 3.945 * [backup-simplify]: Simplify -2.0 into -2.0 3.945 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.945 * [taylor]: Taking taylor expansion of PI in n 3.945 * [backup-simplify]: Simplify PI into PI 3.945 * [taylor]: Taking taylor expansion of n in n 3.945 * [backup-simplify]: Simplify 0 into 0 3.945 * [backup-simplify]: Simplify 1 into 1 3.945 * [backup-simplify]: Simplify (/ PI 1) into PI 3.946 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.946 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.947 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.947 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.947 * [backup-simplify]: Simplify 0 into 0 3.947 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.948 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.948 * [backup-simplify]: Simplify 0 into 0 3.949 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.949 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.949 * [backup-simplify]: Simplify 0 into 0 3.950 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.950 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.951 * [backup-simplify]: Simplify 0 into 0 3.951 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.952 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.952 * [backup-simplify]: Simplify 0 into 0 3.953 * [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 3.953 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.953 * [backup-simplify]: Simplify 0 into 0 3.954 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 3.954 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 3.954 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 3.954 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.954 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.954 * [taylor]: Taking taylor expansion of 1.0 in k 3.954 * [backup-simplify]: Simplify 1.0 into 1.0 3.954 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.954 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.954 * [taylor]: Taking taylor expansion of k in k 3.954 * [backup-simplify]: Simplify 0 into 0 3.954 * [backup-simplify]: Simplify 1 into 1 3.954 * [backup-simplify]: Simplify (/ 1 1) into 1 3.954 * [backup-simplify]: Simplify (sqrt 0) into 0 3.955 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.955 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.955 * [taylor]: Taking taylor expansion of 1.0 in k 3.955 * [backup-simplify]: Simplify 1.0 into 1.0 3.955 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.955 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.955 * [taylor]: Taking taylor expansion of k in k 3.955 * [backup-simplify]: Simplify 0 into 0 3.955 * [backup-simplify]: Simplify 1 into 1 3.956 * [backup-simplify]: Simplify (/ 1 1) into 1 3.956 * [backup-simplify]: Simplify (sqrt 0) into 0 3.957 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.957 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.957 * [backup-simplify]: Simplify 0 into 0 3.958 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.958 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.958 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.960 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.968 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.969 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.969 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.972 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.973 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.973 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.974 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 3.974 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 3.974 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.974 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.974 * [taylor]: Taking taylor expansion of 1.0 in k 3.974 * [backup-simplify]: Simplify 1.0 into 1.0 3.974 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.974 * [taylor]: Taking taylor expansion of k in k 3.975 * [backup-simplify]: Simplify 0 into 0 3.975 * [backup-simplify]: Simplify 1 into 1 3.975 * [backup-simplify]: Simplify (sqrt 0) into 0 3.976 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.976 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.976 * [taylor]: Taking taylor expansion of 1.0 in k 3.976 * [backup-simplify]: Simplify 1.0 into 1.0 3.976 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.976 * [taylor]: Taking taylor expansion of k in k 3.976 * [backup-simplify]: Simplify 0 into 0 3.976 * [backup-simplify]: Simplify 1 into 1 3.976 * [backup-simplify]: Simplify (sqrt 0) into 0 3.977 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.977 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.977 * [backup-simplify]: Simplify 0 into 0 3.978 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.978 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.980 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.981 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.981 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.983 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.984 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.985 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.986 * [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)))))))) 3.986 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 3.986 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.986 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.986 * [taylor]: Taking taylor expansion of 1.0 in k 3.986 * [backup-simplify]: Simplify 1.0 into 1.0 3.986 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.986 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.986 * [taylor]: Taking taylor expansion of -1 in k 3.986 * [backup-simplify]: Simplify -1 into -1 3.986 * [taylor]: Taking taylor expansion of k in k 3.986 * [backup-simplify]: Simplify 0 into 0 3.986 * [backup-simplify]: Simplify 1 into 1 3.986 * [backup-simplify]: Simplify (/ -1 1) into -1 3.986 * [backup-simplify]: Simplify (sqrt 0) into 0 3.987 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.987 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.987 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.987 * [taylor]: Taking taylor expansion of 1.0 in k 3.987 * [backup-simplify]: Simplify 1.0 into 1.0 3.987 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.987 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.988 * [taylor]: Taking taylor expansion of -1 in k 3.988 * [backup-simplify]: Simplify -1 into -1 3.988 * [taylor]: Taking taylor expansion of k in k 3.988 * [backup-simplify]: Simplify 0 into 0 3.988 * [backup-simplify]: Simplify 1 into 1 3.988 * [backup-simplify]: Simplify (/ -1 1) into -1 3.988 * [backup-simplify]: Simplify (sqrt 0) into 0 3.989 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.989 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.989 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.990 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.991 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.993 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.993 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.993 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.995 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.998 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 3.998 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.999 * [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))))) 3.999 * * * * [progress]: [ 4 / 4 ] generating series at (2) 3.999 * [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))))) 3.999 * [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 3.999 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 3.999 * [taylor]: Taking taylor expansion of 1.0 in n 3.999 * [backup-simplify]: Simplify 1.0 into 1.0 3.999 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 3.999 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.999 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.999 * [taylor]: Taking taylor expansion of k in n 3.999 * [backup-simplify]: Simplify k into k 3.999 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.999 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 3.999 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.000 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 4.000 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.000 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.000 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.000 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.000 * [taylor]: Taking taylor expansion of 0.5 in n 4.000 * [backup-simplify]: Simplify 0.5 into 0.5 4.000 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.000 * [taylor]: Taking taylor expansion of 1.0 in n 4.000 * [backup-simplify]: Simplify 1.0 into 1.0 4.000 * [taylor]: Taking taylor expansion of k in n 4.000 * [backup-simplify]: Simplify k into k 4.000 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.000 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.000 * [taylor]: Taking taylor expansion of 2.0 in n 4.000 * [backup-simplify]: Simplify 2.0 into 2.0 4.000 * [taylor]: Taking taylor expansion of (* n PI) in n 4.000 * [taylor]: Taking taylor expansion of n in n 4.000 * [backup-simplify]: Simplify 0 into 0 4.000 * [backup-simplify]: Simplify 1 into 1 4.000 * [taylor]: Taking taylor expansion of PI in n 4.000 * [backup-simplify]: Simplify PI into PI 4.000 * [backup-simplify]: Simplify (* 0 PI) into 0 4.000 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.001 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.002 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.003 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.003 * [backup-simplify]: Simplify (- k) into (- k) 4.003 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.003 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.004 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.004 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.005 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.005 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.005 * [taylor]: Taking taylor expansion of 1.0 in k 4.005 * [backup-simplify]: Simplify 1.0 into 1.0 4.005 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.005 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.005 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.005 * [taylor]: Taking taylor expansion of k in k 4.005 * [backup-simplify]: Simplify 0 into 0 4.005 * [backup-simplify]: Simplify 1 into 1 4.005 * [backup-simplify]: Simplify (/ 1 1) into 1 4.006 * [backup-simplify]: Simplify (sqrt 0) into 0 4.006 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.006 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.006 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.006 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.006 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.006 * [taylor]: Taking taylor expansion of 0.5 in k 4.006 * [backup-simplify]: Simplify 0.5 into 0.5 4.007 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.007 * [taylor]: Taking taylor expansion of 1.0 in k 4.007 * [backup-simplify]: Simplify 1.0 into 1.0 4.007 * [taylor]: Taking taylor expansion of k in k 4.007 * [backup-simplify]: Simplify 0 into 0 4.007 * [backup-simplify]: Simplify 1 into 1 4.007 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.007 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.007 * [taylor]: Taking taylor expansion of 2.0 in k 4.007 * [backup-simplify]: Simplify 2.0 into 2.0 4.007 * [taylor]: Taking taylor expansion of (* n PI) in k 4.007 * [taylor]: Taking taylor expansion of n in k 4.007 * [backup-simplify]: Simplify n into n 4.007 * [taylor]: Taking taylor expansion of PI in k 4.007 * [backup-simplify]: Simplify PI into PI 4.007 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.007 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.007 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.007 * [backup-simplify]: Simplify (- 0) into 0 4.007 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.008 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.008 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.008 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.008 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.008 * [taylor]: Taking taylor expansion of 1.0 in k 4.008 * [backup-simplify]: Simplify 1.0 into 1.0 4.008 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.008 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.008 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.008 * [taylor]: Taking taylor expansion of k in k 4.008 * [backup-simplify]: Simplify 0 into 0 4.008 * [backup-simplify]: Simplify 1 into 1 4.008 * [backup-simplify]: Simplify (/ 1 1) into 1 4.008 * [backup-simplify]: Simplify (sqrt 0) into 0 4.009 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.009 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.009 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.009 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.009 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.009 * [taylor]: Taking taylor expansion of 0.5 in k 4.009 * [backup-simplify]: Simplify 0.5 into 0.5 4.009 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.009 * [taylor]: Taking taylor expansion of 1.0 in k 4.009 * [backup-simplify]: Simplify 1.0 into 1.0 4.009 * [taylor]: Taking taylor expansion of k in k 4.009 * [backup-simplify]: Simplify 0 into 0 4.009 * [backup-simplify]: Simplify 1 into 1 4.009 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.009 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.009 * [taylor]: Taking taylor expansion of 2.0 in k 4.009 * [backup-simplify]: Simplify 2.0 into 2.0 4.009 * [taylor]: Taking taylor expansion of (* n PI) in k 4.009 * [taylor]: Taking taylor expansion of n in k 4.009 * [backup-simplify]: Simplify n into n 4.009 * [taylor]: Taking taylor expansion of PI in k 4.009 * [backup-simplify]: Simplify PI into PI 4.009 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.009 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.010 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.010 * [backup-simplify]: Simplify (- 0) into 0 4.010 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.011 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.011 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.011 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.011 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 4.011 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.011 * [taylor]: Taking taylor expansion of 0 in n 4.011 * [backup-simplify]: Simplify 0 into 0 4.011 * [backup-simplify]: Simplify 0 into 0 4.012 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 4.012 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 4.012 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 4.013 * [backup-simplify]: Simplify (- 1) into -1 4.013 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.014 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 4.014 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 4.015 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.016 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 4.017 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.017 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 4.017 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 4.017 * [taylor]: Taking taylor expansion of +nan.0 in n 4.017 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.017 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.017 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.017 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.017 * [taylor]: Taking taylor expansion of 0.5 in n 4.017 * [backup-simplify]: Simplify 0.5 into 0.5 4.017 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.017 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.017 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.017 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.017 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.017 * [taylor]: Taking taylor expansion of 1.0 in n 4.017 * [backup-simplify]: Simplify 1.0 into 1.0 4.017 * [taylor]: Taking taylor expansion of (log PI) in n 4.017 * [taylor]: Taking taylor expansion of PI in n 4.017 * [backup-simplify]: Simplify PI into PI 4.017 * [backup-simplify]: Simplify (log PI) into (log PI) 4.018 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.019 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.019 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.019 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.019 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.019 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.019 * [taylor]: Taking taylor expansion of 1.0 in n 4.019 * [backup-simplify]: Simplify 1.0 into 1.0 4.019 * [taylor]: Taking taylor expansion of (log n) in n 4.019 * [taylor]: Taking taylor expansion of n in n 4.019 * [backup-simplify]: Simplify 0 into 0 4.019 * [backup-simplify]: Simplify 1 into 1 4.019 * [backup-simplify]: Simplify (log 1) into 0 4.019 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.020 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.020 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.020 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.020 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.020 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.020 * [taylor]: Taking taylor expansion of 1.0 in n 4.020 * [backup-simplify]: Simplify 1.0 into 1.0 4.020 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.020 * [taylor]: Taking taylor expansion of 2.0 in n 4.020 * [backup-simplify]: Simplify 2.0 into 2.0 4.020 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.020 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.021 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.022 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 4.023 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 4.023 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 4.024 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 4.025 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.026 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 4.027 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 4.028 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.028 * [backup-simplify]: Simplify 0 into 0 4.028 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 4.029 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 4.030 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 4.030 * [backup-simplify]: Simplify (- 0) into 0 4.030 * [backup-simplify]: Simplify (+ 0 0) into 0 4.031 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 4.031 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 4.032 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.032 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.034 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.036 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 4.039 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 4.039 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 4.039 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 4.039 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 4.039 * [taylor]: Taking taylor expansion of +nan.0 in n 4.039 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.039 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.039 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.039 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.039 * [taylor]: Taking taylor expansion of 0.5 in n 4.039 * [backup-simplify]: Simplify 0.5 into 0.5 4.039 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.039 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.040 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.040 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.040 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.040 * [taylor]: Taking taylor expansion of 1.0 in n 4.040 * [backup-simplify]: Simplify 1.0 into 1.0 4.040 * [taylor]: Taking taylor expansion of (log PI) in n 4.040 * [taylor]: Taking taylor expansion of PI in n 4.040 * [backup-simplify]: Simplify PI into PI 4.040 * [backup-simplify]: Simplify (log PI) into (log PI) 4.040 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.041 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.041 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.041 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.041 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.041 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.042 * [taylor]: Taking taylor expansion of 1.0 in n 4.042 * [backup-simplify]: Simplify 1.0 into 1.0 4.042 * [taylor]: Taking taylor expansion of (log n) in n 4.042 * [taylor]: Taking taylor expansion of n in n 4.042 * [backup-simplify]: Simplify 0 into 0 4.042 * [backup-simplify]: Simplify 1 into 1 4.042 * [backup-simplify]: Simplify (log 1) into 0 4.042 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.042 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.042 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.042 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.042 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.042 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.042 * [taylor]: Taking taylor expansion of 1.0 in n 4.042 * [backup-simplify]: Simplify 1.0 into 1.0 4.042 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.042 * [taylor]: Taking taylor expansion of 2.0 in n 4.042 * [backup-simplify]: Simplify 2.0 into 2.0 4.043 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.043 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.044 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.044 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 4.045 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 4.046 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 4.047 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 4.048 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.048 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 4.048 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 4.048 * [taylor]: Taking taylor expansion of +nan.0 in n 4.048 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.048 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 4.048 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.048 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.048 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.048 * [taylor]: Taking taylor expansion of 0.5 in n 4.048 * [backup-simplify]: Simplify 0.5 into 0.5 4.048 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.048 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.048 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.048 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.048 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.048 * [taylor]: Taking taylor expansion of 1.0 in n 4.048 * [backup-simplify]: Simplify 1.0 into 1.0 4.048 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.048 * [taylor]: Taking taylor expansion of 2.0 in n 4.048 * [backup-simplify]: Simplify 2.0 into 2.0 4.048 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.049 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.050 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.050 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.050 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.050 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.050 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.050 * [taylor]: Taking taylor expansion of 1.0 in n 4.050 * [backup-simplify]: Simplify 1.0 into 1.0 4.050 * [taylor]: Taking taylor expansion of (log PI) in n 4.050 * [taylor]: Taking taylor expansion of PI in n 4.050 * [backup-simplify]: Simplify PI into PI 4.050 * [backup-simplify]: Simplify (log PI) into (log PI) 4.051 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.052 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.052 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.052 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.052 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.052 * [taylor]: Taking taylor expansion of 1.0 in n 4.052 * [backup-simplify]: Simplify 1.0 into 1.0 4.052 * [taylor]: Taking taylor expansion of (log n) in n 4.052 * [taylor]: Taking taylor expansion of n in n 4.052 * [backup-simplify]: Simplify 0 into 0 4.052 * [backup-simplify]: Simplify 1 into 1 4.052 * [backup-simplify]: Simplify (log 1) into 0 4.052 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.052 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.052 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.053 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.054 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 4.054 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 4.055 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 4.056 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.056 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.056 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.056 * [taylor]: Taking taylor expansion of 2.0 in n 4.056 * [backup-simplify]: Simplify 2.0 into 2.0 4.056 * [taylor]: Taking taylor expansion of (* n PI) in n 4.056 * [taylor]: Taking taylor expansion of n in n 4.056 * [backup-simplify]: Simplify 0 into 0 4.056 * [backup-simplify]: Simplify 1 into 1 4.056 * [taylor]: Taking taylor expansion of PI in n 4.056 * [backup-simplify]: Simplify PI into PI 4.056 * [backup-simplify]: Simplify (* 0 PI) into 0 4.057 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.058 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.058 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.059 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.060 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 4.061 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.070 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 4.072 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.073 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))) 4.077 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.080 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.084 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.085 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 4.085 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 4.086 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 4.087 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 4.087 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.088 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 4.088 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 4.089 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 4.090 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 4.090 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 4.091 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 4.092 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 4.093 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 4.094 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 4.095 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.097 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 4.097 * [backup-simplify]: Simplify (- 0) into 0 4.097 * [backup-simplify]: Simplify 0 into 0 4.097 * [backup-simplify]: Simplify 0 into 0 4.097 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.098 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 4.100 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 4.100 * [backup-simplify]: Simplify (- 0) into 0 4.100 * [backup-simplify]: Simplify (+ 0 0) into 0 4.101 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 4.102 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 4.103 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.103 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.105 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.109 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 4.115 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 4.115 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 4.115 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 4.115 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 4.115 * [taylor]: Taking taylor expansion of +nan.0 in n 4.115 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.115 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 4.115 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 4.115 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 4.115 * [taylor]: Taking taylor expansion of 0.5 in n 4.115 * [backup-simplify]: Simplify 0.5 into 0.5 4.115 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 4.116 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 4.116 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.116 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.116 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.116 * [taylor]: Taking taylor expansion of 1.0 in n 4.116 * [backup-simplify]: Simplify 1.0 into 1.0 4.116 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.116 * [taylor]: Taking taylor expansion of 2.0 in n 4.116 * [backup-simplify]: Simplify 2.0 into 2.0 4.116 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.116 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.117 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.117 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 4.117 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.117 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.117 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.117 * [taylor]: Taking taylor expansion of 1.0 in n 4.117 * [backup-simplify]: Simplify 1.0 into 1.0 4.117 * [taylor]: Taking taylor expansion of (log n) in n 4.117 * [taylor]: Taking taylor expansion of n in n 4.117 * [backup-simplify]: Simplify 0 into 0 4.117 * [backup-simplify]: Simplify 1 into 1 4.118 * [backup-simplify]: Simplify (log 1) into 0 4.118 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.118 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.118 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.118 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.118 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.118 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.118 * [taylor]: Taking taylor expansion of 1.0 in n 4.118 * [backup-simplify]: Simplify 1.0 into 1.0 4.118 * [taylor]: Taking taylor expansion of (log PI) in n 4.118 * [taylor]: Taking taylor expansion of PI in n 4.118 * [backup-simplify]: Simplify PI into PI 4.118 * [backup-simplify]: Simplify (log PI) into (log PI) 4.119 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.120 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.120 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.121 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 4.122 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 4.123 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 4.124 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.124 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 4.124 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 4.124 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 4.124 * [taylor]: Taking taylor expansion of +nan.0 in n 4.124 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.124 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 4.124 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.124 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.124 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.124 * [taylor]: Taking taylor expansion of 0.5 in n 4.124 * [backup-simplify]: Simplify 0.5 into 0.5 4.124 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.124 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.124 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.124 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.124 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.124 * [taylor]: Taking taylor expansion of 1.0 in n 4.124 * [backup-simplify]: Simplify 1.0 into 1.0 4.124 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.124 * [taylor]: Taking taylor expansion of 2.0 in n 4.124 * [backup-simplify]: Simplify 2.0 into 2.0 4.124 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.125 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.126 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.126 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.126 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.126 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.126 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.126 * [taylor]: Taking taylor expansion of 1.0 in n 4.126 * [backup-simplify]: Simplify 1.0 into 1.0 4.126 * [taylor]: Taking taylor expansion of (log PI) in n 4.126 * [taylor]: Taking taylor expansion of PI in n 4.126 * [backup-simplify]: Simplify PI into PI 4.126 * [backup-simplify]: Simplify (log PI) into (log PI) 4.127 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.128 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.128 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.128 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.128 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.128 * [taylor]: Taking taylor expansion of 1.0 in n 4.128 * [backup-simplify]: Simplify 1.0 into 1.0 4.128 * [taylor]: Taking taylor expansion of (log n) in n 4.128 * [taylor]: Taking taylor expansion of n in n 4.128 * [backup-simplify]: Simplify 0 into 0 4.128 * [backup-simplify]: Simplify 1 into 1 4.128 * [backup-simplify]: Simplify (log 1) into 0 4.128 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.128 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.128 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.129 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.129 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 4.131 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 4.131 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 4.132 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.132 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.132 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.132 * [taylor]: Taking taylor expansion of 2.0 in n 4.132 * [backup-simplify]: Simplify 2.0 into 2.0 4.132 * [taylor]: Taking taylor expansion of (* n PI) in n 4.132 * [taylor]: Taking taylor expansion of n in n 4.132 * [backup-simplify]: Simplify 0 into 0 4.132 * [backup-simplify]: Simplify 1 into 1 4.132 * [taylor]: Taking taylor expansion of PI in n 4.132 * [backup-simplify]: Simplify PI into PI 4.133 * [backup-simplify]: Simplify (* 0 PI) into 0 4.133 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.134 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.135 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.135 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.135 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 4.135 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 4.135 * [taylor]: Taking taylor expansion of +nan.0 in n 4.135 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.135 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 4.135 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.136 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.136 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.136 * [taylor]: Taking taylor expansion of 0.5 in n 4.136 * [backup-simplify]: Simplify 0.5 into 0.5 4.136 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.136 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.136 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.136 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.136 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.136 * [taylor]: Taking taylor expansion of 1.0 in n 4.136 * [backup-simplify]: Simplify 1.0 into 1.0 4.136 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.136 * [taylor]: Taking taylor expansion of 2.0 in n 4.136 * [backup-simplify]: Simplify 2.0 into 2.0 4.136 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.136 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.137 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.137 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.137 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.137 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.137 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.137 * [taylor]: Taking taylor expansion of 1.0 in n 4.137 * [backup-simplify]: Simplify 1.0 into 1.0 4.137 * [taylor]: Taking taylor expansion of (log PI) in n 4.137 * [taylor]: Taking taylor expansion of PI in n 4.138 * [backup-simplify]: Simplify PI into PI 4.138 * [backup-simplify]: Simplify (log PI) into (log PI) 4.138 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.139 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.139 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.139 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.139 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.139 * [taylor]: Taking taylor expansion of 1.0 in n 4.139 * [backup-simplify]: Simplify 1.0 into 1.0 4.139 * [taylor]: Taking taylor expansion of (log n) in n 4.139 * [taylor]: Taking taylor expansion of n in n 4.139 * [backup-simplify]: Simplify 0 into 0 4.139 * [backup-simplify]: Simplify 1 into 1 4.140 * [backup-simplify]: Simplify (log 1) into 0 4.140 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.140 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.140 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.140 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.141 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 4.142 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 4.143 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 4.144 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.144 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 4.144 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.144 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.144 * [taylor]: Taking taylor expansion of 2.0 in n 4.144 * [backup-simplify]: Simplify 2.0 into 2.0 4.144 * [taylor]: Taking taylor expansion of (* n PI) in n 4.144 * [taylor]: Taking taylor expansion of n in n 4.144 * [backup-simplify]: Simplify 0 into 0 4.144 * [backup-simplify]: Simplify 1 into 1 4.144 * [taylor]: Taking taylor expansion of PI in n 4.144 * [backup-simplify]: Simplify PI into PI 4.144 * [backup-simplify]: Simplify (* 0 PI) into 0 4.144 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.145 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.146 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.147 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.147 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.148 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 4.149 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.151 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 4.152 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.153 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.154 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.155 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 4.157 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 4.158 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.160 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.172 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))))))))))) 4.184 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))) 4.193 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 4.202 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 4.212 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 4.227 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) 4.228 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 4.228 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 4.228 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 4.228 * [taylor]: Taking taylor expansion of 1.0 in n 4.228 * [backup-simplify]: Simplify 1.0 into 1.0 4.228 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 4.228 * [taylor]: Taking taylor expansion of (sqrt k) in n 4.228 * [taylor]: Taking taylor expansion of k in n 4.228 * [backup-simplify]: Simplify k into k 4.228 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 4.228 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 4.228 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.228 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.228 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.228 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.228 * [taylor]: Taking taylor expansion of 0.5 in n 4.228 * [backup-simplify]: Simplify 0.5 into 0.5 4.228 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.228 * [taylor]: Taking taylor expansion of 1.0 in n 4.228 * [backup-simplify]: Simplify 1.0 into 1.0 4.228 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.228 * [taylor]: Taking taylor expansion of k in n 4.228 * [backup-simplify]: Simplify k into k 4.228 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.228 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.228 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.228 * [taylor]: Taking taylor expansion of 2.0 in n 4.228 * [backup-simplify]: Simplify 2.0 into 2.0 4.228 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.228 * [taylor]: Taking taylor expansion of PI in n 4.228 * [backup-simplify]: Simplify PI into PI 4.228 * [taylor]: Taking taylor expansion of n in n 4.228 * [backup-simplify]: Simplify 0 into 0 4.228 * [backup-simplify]: Simplify 1 into 1 4.228 * [backup-simplify]: Simplify (/ PI 1) into PI 4.229 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.229 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.229 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.229 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.230 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.230 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.231 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.232 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.232 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.232 * [taylor]: Taking taylor expansion of 1.0 in k 4.232 * [backup-simplify]: Simplify 1.0 into 1.0 4.232 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.232 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.232 * [taylor]: Taking taylor expansion of k in k 4.232 * [backup-simplify]: Simplify 0 into 0 4.232 * [backup-simplify]: Simplify 1 into 1 4.232 * [backup-simplify]: Simplify (sqrt 0) into 0 4.233 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.233 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.233 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.233 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.233 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.233 * [taylor]: Taking taylor expansion of 0.5 in k 4.233 * [backup-simplify]: Simplify 0.5 into 0.5 4.233 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.233 * [taylor]: Taking taylor expansion of 1.0 in k 4.233 * [backup-simplify]: Simplify 1.0 into 1.0 4.233 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.233 * [taylor]: Taking taylor expansion of k in k 4.233 * [backup-simplify]: Simplify 0 into 0 4.233 * [backup-simplify]: Simplify 1 into 1 4.233 * [backup-simplify]: Simplify (/ 1 1) into 1 4.233 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.233 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.233 * [taylor]: Taking taylor expansion of 2.0 in k 4.233 * [backup-simplify]: Simplify 2.0 into 2.0 4.233 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.233 * [taylor]: Taking taylor expansion of PI in k 4.234 * [backup-simplify]: Simplify PI into PI 4.234 * [taylor]: Taking taylor expansion of n in k 4.234 * [backup-simplify]: Simplify n into n 4.234 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.234 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.234 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.234 * [backup-simplify]: Simplify (- 1) into -1 4.234 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.234 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.235 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.235 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.235 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.235 * [taylor]: Taking taylor expansion of 1.0 in k 4.235 * [backup-simplify]: Simplify 1.0 into 1.0 4.235 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.235 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.235 * [taylor]: Taking taylor expansion of k in k 4.235 * [backup-simplify]: Simplify 0 into 0 4.235 * [backup-simplify]: Simplify 1 into 1 4.235 * [backup-simplify]: Simplify (sqrt 0) into 0 4.236 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.236 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.236 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.236 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.236 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.236 * [taylor]: Taking taylor expansion of 0.5 in k 4.236 * [backup-simplify]: Simplify 0.5 into 0.5 4.236 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.236 * [taylor]: Taking taylor expansion of 1.0 in k 4.236 * [backup-simplify]: Simplify 1.0 into 1.0 4.236 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.236 * [taylor]: Taking taylor expansion of k in k 4.236 * [backup-simplify]: Simplify 0 into 0 4.236 * [backup-simplify]: Simplify 1 into 1 4.236 * [backup-simplify]: Simplify (/ 1 1) into 1 4.236 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.236 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.236 * [taylor]: Taking taylor expansion of 2.0 in k 4.236 * [backup-simplify]: Simplify 2.0 into 2.0 4.236 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.236 * [taylor]: Taking taylor expansion of PI in k 4.236 * [backup-simplify]: Simplify PI into PI 4.236 * [taylor]: Taking taylor expansion of n in k 4.236 * [backup-simplify]: Simplify n into n 4.236 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.236 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.236 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.237 * [backup-simplify]: Simplify (- 1) into -1 4.237 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.237 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.237 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.237 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.238 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 4.238 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.238 * [taylor]: Taking taylor expansion of 0 in n 4.238 * [backup-simplify]: Simplify 0 into 0 4.238 * [backup-simplify]: Simplify 0 into 0 4.238 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.239 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.239 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.239 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.239 * [taylor]: Taking taylor expansion of +nan.0 in n 4.239 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.239 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.239 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.239 * [taylor]: Taking taylor expansion of 0.5 in n 4.239 * [backup-simplify]: Simplify 0.5 into 0.5 4.239 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.239 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.239 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.239 * [taylor]: Taking taylor expansion of 2.0 in n 4.239 * [backup-simplify]: Simplify 2.0 into 2.0 4.239 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.239 * [taylor]: Taking taylor expansion of PI in n 4.239 * [backup-simplify]: Simplify PI into PI 4.239 * [taylor]: Taking taylor expansion of n in n 4.239 * [backup-simplify]: Simplify 0 into 0 4.239 * [backup-simplify]: Simplify 1 into 1 4.239 * [backup-simplify]: Simplify (/ PI 1) into PI 4.240 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.240 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.240 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.240 * [taylor]: Taking taylor expansion of 1.0 in n 4.240 * [backup-simplify]: Simplify 1.0 into 1.0 4.240 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.240 * [taylor]: Taking taylor expansion of k in n 4.240 * [backup-simplify]: Simplify k into k 4.240 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.241 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.241 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.241 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.242 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.243 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.244 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.244 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 4.245 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 4.246 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 4.246 * [backup-simplify]: Simplify 0 into 0 4.247 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.248 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.249 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.249 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.249 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.249 * [taylor]: Taking taylor expansion of +nan.0 in n 4.249 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.249 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.249 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.249 * [taylor]: Taking taylor expansion of 0.5 in n 4.249 * [backup-simplify]: Simplify 0.5 into 0.5 4.249 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.249 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.249 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.249 * [taylor]: Taking taylor expansion of 2.0 in n 4.249 * [backup-simplify]: Simplify 2.0 into 2.0 4.249 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.249 * [taylor]: Taking taylor expansion of PI in n 4.249 * [backup-simplify]: Simplify PI into PI 4.249 * [taylor]: Taking taylor expansion of n in n 4.249 * [backup-simplify]: Simplify 0 into 0 4.249 * [backup-simplify]: Simplify 1 into 1 4.249 * [backup-simplify]: Simplify (/ PI 1) into PI 4.250 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.250 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.250 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.250 * [taylor]: Taking taylor expansion of 1.0 in n 4.250 * [backup-simplify]: Simplify 1.0 into 1.0 4.250 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.250 * [taylor]: Taking taylor expansion of k in n 4.250 * [backup-simplify]: Simplify k into k 4.250 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.251 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.251 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.251 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.252 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.253 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.253 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.254 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 4.255 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 4.256 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 4.257 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.257 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.257 * [backup-simplify]: Simplify (- 0) into 0 4.257 * [backup-simplify]: Simplify (+ 0 0) into 0 4.258 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.258 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.259 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.259 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.267 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 4.268 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.269 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 4.269 * [backup-simplify]: Simplify (- 0) into 0 4.270 * [backup-simplify]: Simplify 0 into 0 4.270 * [backup-simplify]: Simplify 0 into 0 4.272 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.273 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.273 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.273 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.273 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.273 * [taylor]: Taking taylor expansion of +nan.0 in n 4.273 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.273 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.273 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.274 * [taylor]: Taking taylor expansion of 0.5 in n 4.274 * [backup-simplify]: Simplify 0.5 into 0.5 4.274 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.274 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.274 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.274 * [taylor]: Taking taylor expansion of 2.0 in n 4.274 * [backup-simplify]: Simplify 2.0 into 2.0 4.274 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.274 * [taylor]: Taking taylor expansion of PI in n 4.274 * [backup-simplify]: Simplify PI into PI 4.274 * [taylor]: Taking taylor expansion of n in n 4.274 * [backup-simplify]: Simplify 0 into 0 4.274 * [backup-simplify]: Simplify 1 into 1 4.274 * [backup-simplify]: Simplify (/ PI 1) into PI 4.274 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.275 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.275 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.275 * [taylor]: Taking taylor expansion of 1.0 in n 4.275 * [backup-simplify]: Simplify 1.0 into 1.0 4.275 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.275 * [taylor]: Taking taylor expansion of k in n 4.275 * [backup-simplify]: Simplify k into k 4.275 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.276 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.276 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.276 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.277 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.277 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.278 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.279 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 4.280 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 4.280 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 4.283 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 4.284 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 4.284 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 4.284 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 4.284 * [taylor]: Taking taylor expansion of 1.0 in n 4.284 * [backup-simplify]: Simplify 1.0 into 1.0 4.284 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 4.284 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.284 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.284 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.284 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.284 * [taylor]: Taking taylor expansion of 0.5 in n 4.284 * [backup-simplify]: Simplify 0.5 into 0.5 4.284 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.284 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.284 * [taylor]: Taking taylor expansion of k in n 4.284 * [backup-simplify]: Simplify k into k 4.284 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.284 * [taylor]: Taking taylor expansion of 1.0 in n 4.284 * [backup-simplify]: Simplify 1.0 into 1.0 4.284 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.284 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.284 * [taylor]: Taking taylor expansion of -2.0 in n 4.284 * [backup-simplify]: Simplify -2.0 into -2.0 4.284 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.284 * [taylor]: Taking taylor expansion of PI in n 4.284 * [backup-simplify]: Simplify PI into PI 4.284 * [taylor]: Taking taylor expansion of n in n 4.284 * [backup-simplify]: Simplify 0 into 0 4.284 * [backup-simplify]: Simplify 1 into 1 4.285 * [backup-simplify]: Simplify (/ PI 1) into PI 4.285 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.285 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.285 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.286 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.286 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.287 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.288 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.288 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 4.288 * [taylor]: Taking taylor expansion of (/ -1 k) in n 4.288 * [taylor]: Taking taylor expansion of -1 in n 4.288 * [backup-simplify]: Simplify -1 into -1 4.288 * [taylor]: Taking taylor expansion of k in n 4.288 * [backup-simplify]: Simplify k into k 4.288 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 4.288 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 4.288 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 4.288 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 4.289 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 4.289 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.289 * [taylor]: Taking taylor expansion of 1.0 in k 4.289 * [backup-simplify]: Simplify 1.0 into 1.0 4.289 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.289 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.289 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.289 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.289 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.289 * [taylor]: Taking taylor expansion of 0.5 in k 4.289 * [backup-simplify]: Simplify 0.5 into 0.5 4.289 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.289 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.289 * [taylor]: Taking taylor expansion of k in k 4.289 * [backup-simplify]: Simplify 0 into 0 4.289 * [backup-simplify]: Simplify 1 into 1 4.289 * [backup-simplify]: Simplify (/ 1 1) into 1 4.289 * [taylor]: Taking taylor expansion of 1.0 in k 4.289 * [backup-simplify]: Simplify 1.0 into 1.0 4.289 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.289 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.289 * [taylor]: Taking taylor expansion of -2.0 in k 4.289 * [backup-simplify]: Simplify -2.0 into -2.0 4.289 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.290 * [taylor]: Taking taylor expansion of PI in k 4.290 * [backup-simplify]: Simplify PI into PI 4.290 * [taylor]: Taking taylor expansion of n in k 4.290 * [backup-simplify]: Simplify n into n 4.290 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.290 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.290 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.290 * [backup-simplify]: Simplify (+ 1 0) into 1 4.290 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.290 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.290 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.290 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.290 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.291 * [taylor]: Taking taylor expansion of -1 in k 4.291 * [backup-simplify]: Simplify -1 into -1 4.291 * [taylor]: Taking taylor expansion of k in k 4.291 * [backup-simplify]: Simplify 0 into 0 4.291 * [backup-simplify]: Simplify 1 into 1 4.291 * [backup-simplify]: Simplify (/ -1 1) into -1 4.291 * [backup-simplify]: Simplify (sqrt 0) into 0 4.292 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.292 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 4.292 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.292 * [taylor]: Taking taylor expansion of 1.0 in k 4.292 * [backup-simplify]: Simplify 1.0 into 1.0 4.292 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.292 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.292 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.292 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.292 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.292 * [taylor]: Taking taylor expansion of 0.5 in k 4.292 * [backup-simplify]: Simplify 0.5 into 0.5 4.292 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.292 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.292 * [taylor]: Taking taylor expansion of k in k 4.292 * [backup-simplify]: Simplify 0 into 0 4.292 * [backup-simplify]: Simplify 1 into 1 4.292 * [backup-simplify]: Simplify (/ 1 1) into 1 4.293 * [taylor]: Taking taylor expansion of 1.0 in k 4.293 * [backup-simplify]: Simplify 1.0 into 1.0 4.293 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.293 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.293 * [taylor]: Taking taylor expansion of -2.0 in k 4.293 * [backup-simplify]: Simplify -2.0 into -2.0 4.293 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.293 * [taylor]: Taking taylor expansion of PI in k 4.293 * [backup-simplify]: Simplify PI into PI 4.293 * [taylor]: Taking taylor expansion of n in k 4.293 * [backup-simplify]: Simplify n into n 4.293 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.293 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.293 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.293 * [backup-simplify]: Simplify (+ 1 0) into 1 4.293 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.293 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.294 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.294 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.294 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.294 * [taylor]: Taking taylor expansion of -1 in k 4.294 * [backup-simplify]: Simplify -1 into -1 4.294 * [taylor]: Taking taylor expansion of k in k 4.294 * [backup-simplify]: Simplify 0 into 0 4.294 * [backup-simplify]: Simplify 1 into 1 4.294 * [backup-simplify]: Simplify (/ -1 1) into -1 4.294 * [backup-simplify]: Simplify (sqrt 0) into 0 4.295 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.295 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 4.295 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 4.295 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.295 * [taylor]: Taking taylor expansion of +nan.0 in n 4.295 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.295 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.296 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.296 * [taylor]: Taking taylor expansion of 0.5 in n 4.296 * [backup-simplify]: Simplify 0.5 into 0.5 4.296 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.296 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.296 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.296 * [taylor]: Taking taylor expansion of k in n 4.296 * [backup-simplify]: Simplify k into k 4.296 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.296 * [taylor]: Taking taylor expansion of 1.0 in n 4.296 * [backup-simplify]: Simplify 1.0 into 1.0 4.296 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.296 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.296 * [taylor]: Taking taylor expansion of -2.0 in n 4.296 * [backup-simplify]: Simplify -2.0 into -2.0 4.296 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.296 * [taylor]: Taking taylor expansion of PI in n 4.296 * [backup-simplify]: Simplify PI into PI 4.296 * [taylor]: Taking taylor expansion of n in n 4.296 * [backup-simplify]: Simplify 0 into 0 4.296 * [backup-simplify]: Simplify 1 into 1 4.296 * [backup-simplify]: Simplify (/ PI 1) into PI 4.296 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.297 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.297 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.298 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.299 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.300 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.300 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.301 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 4.302 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 4.302 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.304 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.305 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 4.305 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 4.305 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 4.305 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.305 * [taylor]: Taking taylor expansion of +nan.0 in n 4.305 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.305 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.305 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.305 * [taylor]: Taking taylor expansion of 0.5 in n 4.305 * [backup-simplify]: Simplify 0.5 into 0.5 4.305 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.305 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.305 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.305 * [taylor]: Taking taylor expansion of k in n 4.305 * [backup-simplify]: Simplify k into k 4.305 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.305 * [taylor]: Taking taylor expansion of 1.0 in n 4.305 * [backup-simplify]: Simplify 1.0 into 1.0 4.305 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.305 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.305 * [taylor]: Taking taylor expansion of -2.0 in n 4.305 * [backup-simplify]: Simplify -2.0 into -2.0 4.305 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.306 * [taylor]: Taking taylor expansion of PI in n 4.306 * [backup-simplify]: Simplify PI into PI 4.306 * [taylor]: Taking taylor expansion of n in n 4.306 * [backup-simplify]: Simplify 0 into 0 4.306 * [backup-simplify]: Simplify 1 into 1 4.306 * [backup-simplify]: Simplify (/ PI 1) into PI 4.306 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.307 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.307 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.308 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.308 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.309 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.310 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.311 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 4.311 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 4.313 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 4.313 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.314 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.315 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.315 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.315 * [backup-simplify]: Simplify (+ 0 0) into 0 4.316 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.316 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.317 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 4.319 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.319 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 4.319 * [backup-simplify]: Simplify 0 into 0 4.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.322 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.323 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 4.324 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 4.324 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 4.324 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.324 * [taylor]: Taking taylor expansion of +nan.0 in n 4.324 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.324 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.324 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.324 * [taylor]: Taking taylor expansion of 0.5 in n 4.324 * [backup-simplify]: Simplify 0.5 into 0.5 4.324 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.324 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.324 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.324 * [taylor]: Taking taylor expansion of k in n 4.324 * [backup-simplify]: Simplify k into k 4.324 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.324 * [taylor]: Taking taylor expansion of 1.0 in n 4.324 * [backup-simplify]: Simplify 1.0 into 1.0 4.324 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.324 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.324 * [taylor]: Taking taylor expansion of -2.0 in n 4.324 * [backup-simplify]: Simplify -2.0 into -2.0 4.324 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.324 * [taylor]: Taking taylor expansion of PI in n 4.324 * [backup-simplify]: Simplify PI into PI 4.324 * [taylor]: Taking taylor expansion of n in n 4.324 * [backup-simplify]: Simplify 0 into 0 4.324 * [backup-simplify]: Simplify 1 into 1 4.325 * [backup-simplify]: Simplify (/ PI 1) into PI 4.325 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.325 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.325 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.327 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.328 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.328 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.329 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 4.330 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 4.331 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 4.333 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 4.333 * * * [progress]: simplifying candidates 4.336 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt 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(cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 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(sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 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 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h4)) 2)) (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log (* h0 h4))) (pow (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (* (log (* h0 h4)) (log h3))) (pow (* (pow h4 h2) (* (pow h0 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log h3)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* h1 (log (* h0 h4))) (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (pow (log h3) 2)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* h1 (log h3)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5)) (- (+ (* h9 (* (pow h1 2) (pow (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2))) h5))) (- (* h9 (* h1 (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5)))))))))))))))))))))) (- (+ (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (pow h1 3))) (- (+ (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) h1)) (- (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (pow h1 2)))))))) (- (+ (* h9 (/ (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) h1)) (- (+ (* h9 (/ (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (pow h1 2))) (- (* h9 (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))))))))) 4.345 * * [simplify]: iteration 0 : 950 enodes (cost 1461 ) 4.361 * * [simplify]: iteration 1 : 3924 enodes (cost 1358 ) 4.421 * * [simplify]: iteration 2 : 5002 enodes (cost 1344 ) 4.427 * * * [progress]: adding candidates to table 4.969 * [progress]: [Phase 3 of 3] Extracting. 4.969 * * [regime]: Finding splitpoints for: (# # # # # # #) 4.972 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2.0 PI) n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) n k) 4.972 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 5.006 * * * * [regimes]: Trying to branch on (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) from (# # # # # # #) 5.048 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 5.079 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 5.113 * * * [regime]: Found split indices: #