20.021 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.088 * * * [progress]: [2/2] Setting up program. 0.091 * [progress]: [Phase 2 of 3] Improving. 0.091 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.091 * [simplify]: Sending expressions to egg_math: (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) 0.093 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.095 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.097 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.099 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.106 * * [simplify]: iteration 4 : 1044 enodes (cost 8 ) 0.129 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.130 * * [progress]: iteration 1 / 4 0.130 * * * [progress]: picking best candidate 0.132 * * * * [pick]: Picked # 0.133 * * * [progress]: localizing error 0.145 * * * [progress]: generating rewritten candidates 0.145 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.170 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.187 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.193 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.238 * * * [progress]: generating series expansions 0.238 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.239 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 0.239 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.239 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.239 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.239 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.239 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.239 * [taylor]: Taking taylor expansion of 0.5 in k 0.239 * [backup-simplify]: Simplify 0.5 into 0.5 0.239 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.239 * [taylor]: Taking taylor expansion of 1.0 in k 0.239 * [backup-simplify]: Simplify 1.0 into 1.0 0.239 * [taylor]: Taking taylor expansion of k in k 0.239 * [backup-simplify]: Simplify 0 into 0 0.239 * [backup-simplify]: Simplify 1 into 1 0.239 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.239 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.239 * [taylor]: Taking taylor expansion of 2.0 in k 0.239 * [backup-simplify]: Simplify 2.0 into 2.0 0.239 * [taylor]: Taking taylor expansion of (* n PI) in k 0.239 * [taylor]: Taking taylor expansion of n in k 0.239 * [backup-simplify]: Simplify n into n 0.239 * [taylor]: Taking taylor expansion of PI in k 0.239 * [backup-simplify]: Simplify PI into PI 0.239 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.239 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.239 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.240 * [backup-simplify]: Simplify (- 0) into 0 0.240 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.240 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.240 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.241 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.241 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.241 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.241 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.241 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.241 * [taylor]: Taking taylor expansion of 0.5 in n 0.241 * [backup-simplify]: Simplify 0.5 into 0.5 0.241 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.241 * [taylor]: Taking taylor expansion of 1.0 in n 0.241 * [backup-simplify]: Simplify 1.0 into 1.0 0.241 * [taylor]: Taking taylor expansion of k in n 0.241 * [backup-simplify]: Simplify k into k 0.241 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.241 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.241 * [taylor]: Taking taylor expansion of 2.0 in n 0.241 * [backup-simplify]: Simplify 2.0 into 2.0 0.241 * [taylor]: Taking taylor expansion of (* n PI) in n 0.241 * [taylor]: Taking taylor expansion of n in n 0.241 * [backup-simplify]: Simplify 0 into 0 0.241 * [backup-simplify]: Simplify 1 into 1 0.241 * [taylor]: Taking taylor expansion of PI in n 0.241 * [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) 0.244 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.244 * [backup-simplify]: Simplify (- k) into (- k) 0.244 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.244 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.245 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.246 * [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 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.246 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.246 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.246 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.246 * [taylor]: Taking taylor expansion of 0.5 in n 0.246 * [backup-simplify]: Simplify 0.5 into 0.5 0.246 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.246 * [taylor]: Taking taylor expansion of 1.0 in n 0.246 * [backup-simplify]: Simplify 1.0 into 1.0 0.246 * [taylor]: Taking taylor expansion of k in n 0.246 * [backup-simplify]: Simplify k into k 0.246 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.246 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.247 * [taylor]: Taking taylor expansion of 2.0 in n 0.247 * [backup-simplify]: Simplify 2.0 into 2.0 0.247 * [taylor]: Taking taylor expansion of (* n PI) in n 0.247 * [taylor]: Taking taylor expansion of n in n 0.247 * [backup-simplify]: Simplify 0 into 0 0.247 * [backup-simplify]: Simplify 1 into 1 0.247 * [taylor]: Taking taylor expansion of PI in n 0.247 * [backup-simplify]: Simplify PI into PI 0.247 * [backup-simplify]: Simplify (* 0 PI) into 0 0.247 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.248 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.249 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.249 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.249 * [backup-simplify]: Simplify (- k) into (- k) 0.250 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.250 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.250 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.251 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.252 * [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))))) 0.252 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.252 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.252 * [taylor]: Taking taylor expansion of 0.5 in k 0.252 * [backup-simplify]: Simplify 0.5 into 0.5 0.252 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.252 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.252 * [taylor]: Taking taylor expansion of 1.0 in k 0.252 * [backup-simplify]: Simplify 1.0 into 1.0 0.252 * [taylor]: Taking taylor expansion of k in k 0.252 * [backup-simplify]: Simplify 0 into 0 0.252 * [backup-simplify]: Simplify 1 into 1 0.252 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.252 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.252 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.252 * [taylor]: Taking taylor expansion of 2.0 in k 0.252 * [backup-simplify]: Simplify 2.0 into 2.0 0.252 * [taylor]: Taking taylor expansion of PI in k 0.252 * [backup-simplify]: Simplify PI into PI 0.252 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.253 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.253 * [taylor]: Taking taylor expansion of (log n) in k 0.253 * [taylor]: Taking taylor expansion of n in k 0.253 * [backup-simplify]: Simplify n into n 0.253 * [backup-simplify]: Simplify (log n) into (log n) 0.253 * [backup-simplify]: Simplify (- 0) into 0 0.254 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.254 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.255 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.255 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.256 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.257 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.257 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.258 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.259 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.259 * [backup-simplify]: Simplify (- 0) into 0 0.259 * [backup-simplify]: Simplify (+ 0 0) into 0 0.260 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 0.260 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.261 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.262 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.262 * [taylor]: Taking taylor expansion of 0 in k 0.262 * [backup-simplify]: Simplify 0 into 0 0.262 * [backup-simplify]: Simplify 0 into 0 0.263 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.264 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.264 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.264 * [backup-simplify]: Simplify (+ 0 0) into 0 0.265 * [backup-simplify]: Simplify (- 1) into -1 0.265 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.266 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.267 * [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)))) 0.269 * [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)))))) 0.271 * [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)))))) 0.271 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.272 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.274 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.274 * [backup-simplify]: Simplify (- 0) into 0 0.274 * [backup-simplify]: Simplify (+ 0 0) into 0 0.275 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 0.275 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.276 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.278 * [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 0.278 * [taylor]: Taking taylor expansion of 0 in k 0.278 * [backup-simplify]: Simplify 0 into 0 0.278 * [backup-simplify]: Simplify 0 into 0 0.278 * [backup-simplify]: Simplify 0 into 0 0.278 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.280 * [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 0.281 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 0.281 * [backup-simplify]: Simplify (+ 0 0) into 0 0.281 * [backup-simplify]: Simplify (- 0) into 0 0.282 * [backup-simplify]: Simplify (+ 0 0) into 0 0.283 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.284 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 0.287 * [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)))))) 0.290 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 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)))))) 0.299 * [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)))))) 0.300 * [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)))) 0.300 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.300 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.300 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.300 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.300 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.300 * [taylor]: Taking taylor expansion of 0.5 in k 0.300 * [backup-simplify]: Simplify 0.5 into 0.5 0.300 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.300 * [taylor]: Taking taylor expansion of 1.0 in k 0.300 * [backup-simplify]: Simplify 1.0 into 1.0 0.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.300 * [taylor]: Taking taylor expansion of k in k 0.300 * [backup-simplify]: Simplify 0 into 0 0.300 * [backup-simplify]: Simplify 1 into 1 0.301 * [backup-simplify]: Simplify (/ 1 1) into 1 0.301 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.301 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.301 * [taylor]: Taking taylor expansion of 2.0 in k 0.301 * [backup-simplify]: Simplify 2.0 into 2.0 0.301 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.301 * [taylor]: Taking taylor expansion of PI in k 0.301 * [backup-simplify]: Simplify PI into PI 0.301 * [taylor]: Taking taylor expansion of n in k 0.301 * [backup-simplify]: Simplify n into n 0.301 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.301 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.301 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.301 * [backup-simplify]: Simplify (- 1) into -1 0.301 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.302 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.302 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.302 * [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))))) 0.302 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.302 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.302 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.302 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.302 * [taylor]: Taking taylor expansion of 0.5 in n 0.302 * [backup-simplify]: Simplify 0.5 into 0.5 0.302 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.302 * [taylor]: Taking taylor expansion of 1.0 in n 0.302 * [backup-simplify]: Simplify 1.0 into 1.0 0.302 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.302 * [taylor]: Taking taylor expansion of k in n 0.302 * [backup-simplify]: Simplify k into k 0.302 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.302 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.302 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.302 * [taylor]: Taking taylor expansion of 2.0 in n 0.302 * [backup-simplify]: Simplify 2.0 into 2.0 0.302 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.302 * [taylor]: Taking taylor expansion of PI in n 0.302 * [backup-simplify]: Simplify PI into PI 0.302 * [taylor]: Taking taylor expansion of n in n 0.302 * [backup-simplify]: Simplify 0 into 0 0.302 * [backup-simplify]: Simplify 1 into 1 0.303 * [backup-simplify]: Simplify (/ PI 1) into PI 0.303 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.304 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.304 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.304 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.304 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.305 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.305 * [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)))) 0.306 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.306 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.306 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.306 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.306 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.306 * [taylor]: Taking taylor expansion of 0.5 in n 0.306 * [backup-simplify]: Simplify 0.5 into 0.5 0.306 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.306 * [taylor]: Taking taylor expansion of 1.0 in n 0.306 * [backup-simplify]: Simplify 1.0 into 1.0 0.306 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.306 * [taylor]: Taking taylor expansion of k in n 0.306 * [backup-simplify]: Simplify k into k 0.306 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.306 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.306 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.306 * [taylor]: Taking taylor expansion of 2.0 in n 0.306 * [backup-simplify]: Simplify 2.0 into 2.0 0.306 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.306 * [taylor]: Taking taylor expansion of PI in n 0.306 * [backup-simplify]: Simplify PI into PI 0.306 * [taylor]: Taking taylor expansion of n in n 0.306 * [backup-simplify]: Simplify 0 into 0 0.306 * [backup-simplify]: Simplify 1 into 1 0.307 * [backup-simplify]: Simplify (/ PI 1) into PI 0.307 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.308 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.308 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.308 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.308 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.309 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.309 * [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)))) 0.310 * [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))))) 0.311 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.311 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.311 * [taylor]: Taking taylor expansion of 0.5 in k 0.311 * [backup-simplify]: Simplify 0.5 into 0.5 0.311 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.311 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.311 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.311 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.311 * [taylor]: Taking taylor expansion of 2.0 in k 0.311 * [backup-simplify]: Simplify 2.0 into 2.0 0.311 * [taylor]: Taking taylor expansion of PI in k 0.311 * [backup-simplify]: Simplify PI into PI 0.311 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.312 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.312 * [taylor]: Taking taylor expansion of (log n) in k 0.312 * [taylor]: Taking taylor expansion of n in k 0.312 * [backup-simplify]: Simplify n into n 0.312 * [backup-simplify]: Simplify (log n) into (log n) 0.312 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.312 * [taylor]: Taking taylor expansion of 1.0 in k 0.312 * [backup-simplify]: Simplify 1.0 into 1.0 0.312 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.312 * [taylor]: Taking taylor expansion of k in k 0.312 * [backup-simplify]: Simplify 0 into 0 0.312 * [backup-simplify]: Simplify 1 into 1 0.312 * [backup-simplify]: Simplify (/ 1 1) into 1 0.312 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.313 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.313 * [backup-simplify]: Simplify (- 1) into -1 0.313 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.314 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.315 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 0.315 * [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))))) 0.316 * [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))))) 0.317 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.317 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.318 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.318 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.318 * [backup-simplify]: Simplify (- 0) into 0 0.318 * [backup-simplify]: Simplify (+ 0 0) into 0 0.319 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.320 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.320 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.321 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.321 * [taylor]: Taking taylor expansion of 0 in k 0.322 * [backup-simplify]: Simplify 0 into 0 0.322 * [backup-simplify]: Simplify 0 into 0 0.322 * [backup-simplify]: Simplify 0 into 0 0.322 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.323 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.324 * [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 0.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.325 * [backup-simplify]: Simplify (- 0) into 0 0.325 * [backup-simplify]: Simplify (+ 0 0) into 0 0.325 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 0.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.327 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 0.329 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.329 * [taylor]: Taking taylor expansion of 0 in k 0.329 * [backup-simplify]: Simplify 0 into 0 0.329 * [backup-simplify]: Simplify 0 into 0 0.329 * [backup-simplify]: Simplify 0 into 0 0.329 * [backup-simplify]: Simplify 0 into 0 0.329 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.330 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.333 * [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 0.333 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.333 * [backup-simplify]: Simplify (- 0) into 0 0.333 * [backup-simplify]: Simplify (+ 0 0) into 0 0.334 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 0.335 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.336 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 0.338 * [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 0.338 * [taylor]: Taking taylor expansion of 0 in k 0.338 * [backup-simplify]: Simplify 0 into 0 0.338 * [backup-simplify]: Simplify 0 into 0 0.338 * [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)))) 0.339 * [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))) 0.339 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.339 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.339 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.339 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.339 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.339 * [taylor]: Taking taylor expansion of 0.5 in k 0.339 * [backup-simplify]: Simplify 0.5 into 0.5 0.339 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.339 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.339 * [taylor]: Taking taylor expansion of k in k 0.339 * [backup-simplify]: Simplify 0 into 0 0.339 * [backup-simplify]: Simplify 1 into 1 0.339 * [backup-simplify]: Simplify (/ 1 1) into 1 0.339 * [taylor]: Taking taylor expansion of 1.0 in k 0.339 * [backup-simplify]: Simplify 1.0 into 1.0 0.339 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.339 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.339 * [taylor]: Taking taylor expansion of -2.0 in k 0.340 * [backup-simplify]: Simplify -2.0 into -2.0 0.340 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.340 * [taylor]: Taking taylor expansion of PI in k 0.340 * [backup-simplify]: Simplify PI into PI 0.340 * [taylor]: Taking taylor expansion of n in k 0.340 * [backup-simplify]: Simplify n into n 0.340 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.340 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.340 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.340 * [backup-simplify]: Simplify (+ 1 0) into 1 0.340 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.340 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.340 * [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)))))) 0.340 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.340 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.341 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.341 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.341 * [taylor]: Taking taylor expansion of 0.5 in n 0.341 * [backup-simplify]: Simplify 0.5 into 0.5 0.341 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.341 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.341 * [taylor]: Taking taylor expansion of k in n 0.341 * [backup-simplify]: Simplify k into k 0.341 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.341 * [taylor]: Taking taylor expansion of 1.0 in n 0.341 * [backup-simplify]: Simplify 1.0 into 1.0 0.341 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.341 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.341 * [taylor]: Taking taylor expansion of -2.0 in n 0.341 * [backup-simplify]: Simplify -2.0 into -2.0 0.341 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.341 * [taylor]: Taking taylor expansion of PI in n 0.341 * [backup-simplify]: Simplify PI into PI 0.341 * [taylor]: Taking taylor expansion of n in n 0.341 * [backup-simplify]: Simplify 0 into 0 0.341 * [backup-simplify]: Simplify 1 into 1 0.341 * [backup-simplify]: Simplify (/ PI 1) into PI 0.342 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.342 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.342 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.342 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.343 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.344 * [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)))) 0.345 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.345 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.345 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.345 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.345 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.345 * [taylor]: Taking taylor expansion of 0.5 in n 0.345 * [backup-simplify]: Simplify 0.5 into 0.5 0.345 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.345 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.345 * [taylor]: Taking taylor expansion of k in n 0.345 * [backup-simplify]: Simplify k into k 0.345 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.345 * [taylor]: Taking taylor expansion of 1.0 in n 0.345 * [backup-simplify]: Simplify 1.0 into 1.0 0.345 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.345 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.345 * [taylor]: Taking taylor expansion of -2.0 in n 0.345 * [backup-simplify]: Simplify -2.0 into -2.0 0.345 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.345 * [taylor]: Taking taylor expansion of PI in n 0.345 * [backup-simplify]: Simplify PI into PI 0.345 * [taylor]: Taking taylor expansion of n in n 0.345 * [backup-simplify]: Simplify 0 into 0 0.345 * [backup-simplify]: Simplify 1 into 1 0.345 * [backup-simplify]: Simplify (/ PI 1) into PI 0.346 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.346 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.346 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.346 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.347 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.348 * [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)))) 0.349 * [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))))) 0.349 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.349 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.349 * [taylor]: Taking taylor expansion of 0.5 in k 0.349 * [backup-simplify]: Simplify 0.5 into 0.5 0.349 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.349 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.349 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.349 * [taylor]: Taking taylor expansion of k in k 0.349 * [backup-simplify]: Simplify 0 into 0 0.349 * [backup-simplify]: Simplify 1 into 1 0.349 * [backup-simplify]: Simplify (/ 1 1) into 1 0.349 * [taylor]: Taking taylor expansion of 1.0 in k 0.349 * [backup-simplify]: Simplify 1.0 into 1.0 0.349 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.349 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.349 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.349 * [taylor]: Taking taylor expansion of -2.0 in k 0.349 * [backup-simplify]: Simplify -2.0 into -2.0 0.349 * [taylor]: Taking taylor expansion of PI in k 0.349 * [backup-simplify]: Simplify PI into PI 0.350 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.350 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.350 * [taylor]: Taking taylor expansion of (log n) in k 0.350 * [taylor]: Taking taylor expansion of n in k 0.350 * [backup-simplify]: Simplify n into n 0.350 * [backup-simplify]: Simplify (log n) into (log n) 0.351 * [backup-simplify]: Simplify (+ 1 0) into 1 0.351 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.351 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 0.352 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 0.352 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 0.353 * [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))))) 0.354 * [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))))) 0.355 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.355 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.356 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.356 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.356 * [backup-simplify]: Simplify (+ 0 0) into 0 0.356 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 0.357 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.358 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.359 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.359 * [taylor]: Taking taylor expansion of 0 in k 0.359 * [backup-simplify]: Simplify 0 into 0 0.359 * [backup-simplify]: Simplify 0 into 0 0.359 * [backup-simplify]: Simplify 0 into 0 0.360 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.360 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.362 * [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 0.362 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.362 * [backup-simplify]: Simplify (+ 0 0) into 0 0.363 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 0.364 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.365 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 0.366 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.366 * [taylor]: Taking taylor expansion of 0 in k 0.366 * [backup-simplify]: Simplify 0 into 0 0.366 * [backup-simplify]: Simplify 0 into 0 0.366 * [backup-simplify]: Simplify 0 into 0 0.366 * [backup-simplify]: Simplify 0 into 0 0.367 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.367 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.370 * [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 0.370 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.371 * [backup-simplify]: Simplify (+ 0 0) into 0 0.371 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.372 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.374 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 0.375 * [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 0.375 * [taylor]: Taking taylor expansion of 0 in k 0.375 * [backup-simplify]: Simplify 0 into 0 0.375 * [backup-simplify]: Simplify 0 into 0 0.376 * [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)))))) 0.376 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.376 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.376 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.376 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.376 * [taylor]: Taking taylor expansion of 2.0 in n 0.376 * [backup-simplify]: Simplify 2.0 into 2.0 0.376 * [taylor]: Taking taylor expansion of (* n PI) in n 0.376 * [taylor]: Taking taylor expansion of n in n 0.376 * [backup-simplify]: Simplify 0 into 0 0.376 * [backup-simplify]: Simplify 1 into 1 0.376 * [taylor]: Taking taylor expansion of PI in n 0.376 * [backup-simplify]: Simplify PI into PI 0.376 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.376 * [taylor]: Taking taylor expansion of 2.0 in n 0.376 * [backup-simplify]: Simplify 2.0 into 2.0 0.377 * [taylor]: Taking taylor expansion of (* n PI) in n 0.377 * [taylor]: Taking taylor expansion of n in n 0.377 * [backup-simplify]: Simplify 0 into 0 0.377 * [backup-simplify]: Simplify 1 into 1 0.377 * [taylor]: Taking taylor expansion of PI in n 0.377 * [backup-simplify]: Simplify PI into PI 0.377 * [backup-simplify]: Simplify (* 0 PI) into 0 0.377 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.377 * [backup-simplify]: Simplify 0 into 0 0.378 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.379 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.379 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.380 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.380 * [backup-simplify]: Simplify (+ (* 2.0 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 PI)))) into 0 0.382 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.382 * [backup-simplify]: Simplify 0 into 0 0.382 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.383 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.383 * [backup-simplify]: Simplify 0 into 0 0.384 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.385 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 0.385 * [backup-simplify]: Simplify 0 into 0 0.385 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.386 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.386 * [backup-simplify]: Simplify 0 into 0 0.391 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.392 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.392 * [backup-simplify]: Simplify 0 into 0 0.392 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.393 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 0.393 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.393 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.393 * [taylor]: Taking taylor expansion of 2.0 in n 0.393 * [backup-simplify]: Simplify 2.0 into 2.0 0.393 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.393 * [taylor]: Taking taylor expansion of PI in n 0.393 * [backup-simplify]: Simplify PI into PI 0.393 * [taylor]: Taking taylor expansion of n in n 0.393 * [backup-simplify]: Simplify 0 into 0 0.393 * [backup-simplify]: Simplify 1 into 1 0.393 * [backup-simplify]: Simplify (/ PI 1) into PI 0.393 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.393 * [taylor]: Taking taylor expansion of 2.0 in n 0.393 * [backup-simplify]: Simplify 2.0 into 2.0 0.393 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.393 * [taylor]: Taking taylor expansion of PI in n 0.393 * [backup-simplify]: Simplify PI into PI 0.393 * [taylor]: Taking taylor expansion of n in n 0.393 * [backup-simplify]: Simplify 0 into 0 0.393 * [backup-simplify]: Simplify 1 into 1 0.394 * [backup-simplify]: Simplify (/ PI 1) into PI 0.394 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.394 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.395 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.395 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.395 * [backup-simplify]: Simplify 0 into 0 0.396 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.396 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.396 * [backup-simplify]: Simplify 0 into 0 0.397 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.398 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 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)) (* 0 (/ 0 1)))) into 0 0.399 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.399 * [backup-simplify]: Simplify 0 into 0 0.400 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 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 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)) (* 0 (/ 0 1)))) into 0 0.402 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.402 * [backup-simplify]: Simplify 0 into 0 0.402 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.403 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.403 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.403 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.403 * [taylor]: Taking taylor expansion of -2.0 in n 0.403 * [backup-simplify]: Simplify -2.0 into -2.0 0.403 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.403 * [taylor]: Taking taylor expansion of PI in n 0.403 * [backup-simplify]: Simplify PI into PI 0.403 * [taylor]: Taking taylor expansion of n in n 0.403 * [backup-simplify]: Simplify 0 into 0 0.403 * [backup-simplify]: Simplify 1 into 1 0.403 * [backup-simplify]: Simplify (/ PI 1) into PI 0.403 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.403 * [taylor]: Taking taylor expansion of -2.0 in n 0.403 * [backup-simplify]: Simplify -2.0 into -2.0 0.403 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.403 * [taylor]: Taking taylor expansion of PI in n 0.403 * [backup-simplify]: Simplify PI into PI 0.403 * [taylor]: Taking taylor expansion of n in n 0.403 * [backup-simplify]: Simplify 0 into 0 0.403 * [backup-simplify]: Simplify 1 into 1 0.403 * [backup-simplify]: Simplify (/ PI 1) into PI 0.404 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.404 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.405 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.405 * [backup-simplify]: Simplify 0 into 0 0.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.406 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 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)) (* 0 (/ 0 1)))) into 0 0.407 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 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)) (* 0 (/ 0 1)))) into 0 0.409 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.409 * [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)) (* 0 (/ 0 1)))) into 0 0.410 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.410 * [backup-simplify]: Simplify 0 into 0 0.411 * [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 0.411 * [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 0.412 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.412 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.412 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.412 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.412 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.412 * [taylor]: Taking taylor expansion of 1.0 in k 0.412 * [backup-simplify]: Simplify 1.0 into 1.0 0.412 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.412 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.412 * [taylor]: Taking taylor expansion of k in k 0.412 * [backup-simplify]: Simplify 0 into 0 0.412 * [backup-simplify]: Simplify 1 into 1 0.412 * [backup-simplify]: Simplify (/ 1 1) into 1 0.413 * [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 0.414 * [backup-simplify]: Simplify (/ 1 1) into 1 0.414 * [backup-simplify]: Simplify (sqrt 0) into 0 0.415 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.415 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.415 * [backup-simplify]: Simplify 0 into 0 0.416 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.416 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.417 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.418 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.419 * [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) 0.420 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.422 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.423 * [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 0.425 * [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 0.426 * [backup-simplify]: Simplify (sqrt 0) into 0 0.427 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.427 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.427 * [backup-simplify]: Simplify 0 into 0 0.428 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.428 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.430 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.431 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.431 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.433 * [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)))))))) 0.436 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.436 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.436 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.436 * [taylor]: Taking taylor expansion of 1.0 in k 0.436 * [backup-simplify]: Simplify 1.0 into 1.0 0.436 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.436 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.436 * [taylor]: Taking taylor expansion of -1 in k 0.436 * [backup-simplify]: Simplify -1 into -1 0.436 * [taylor]: Taking taylor expansion of k in k 0.436 * [backup-simplify]: Simplify 0 into 0 0.436 * [backup-simplify]: Simplify 1 into 1 0.436 * [backup-simplify]: Simplify (/ -1 1) into -1 0.437 * [backup-simplify]: Simplify (sqrt 0) into 0 0.437 * [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 0.438 * [backup-simplify]: Simplify (/ -1 1) into -1 0.438 * [backup-simplify]: Simplify (sqrt 0) into 0 0.439 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.439 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.439 * [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) 0.449 * [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 0.451 * [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) 0.454 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.454 * [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)))) 0.456 * [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)) 0.458 * [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 0.459 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.459 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.459 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.459 * [taylor]: Taking taylor expansion of k in k 0.459 * [backup-simplify]: Simplify 0 into 0 0.459 * [backup-simplify]: Simplify 1 into 1 0.459 * [backup-simplify]: Simplify (/ 1 1) into 1 0.459 * [backup-simplify]: Simplify (sqrt 0) into 0 0.460 * [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 0.461 * [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 0.462 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.462 * [taylor]: Taking taylor expansion of 0 in n 0.462 * [backup-simplify]: Simplify 0 into 0 0.462 * [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 0.463 * [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) 0.465 * [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 0.468 * [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 0.470 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.470 * [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) 0.471 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.472 * [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) 0.473 * [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) 0.474 * [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 0.480 * [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 0.480 * [backup-simplify]: Simplify (- 0) into 0 0.480 * [backup-simplify]: Simplify (+ 0 0) into 0 0.481 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.487 * [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 0.490 * [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)) 0.499 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.499 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.499 * [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) 0.510 * [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 0.514 * [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)))))) 0.524 * [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)))))))) 0.528 * [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)))))))) 0.531 * [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)))))))) 0.532 * [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 0.534 * [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) 0.535 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.535 * [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 0.537 * [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 0.541 * [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 0.545 * [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 0.547 * [backup-simplify]: Simplify (- 0) into 0 0.547 * [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 0.562 * [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 0.562 * [taylor]: Taking taylor expansion of +nan.0 in n 0.562 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.562 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.562 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.562 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.562 * [taylor]: Taking taylor expansion of 0.5 in n 0.562 * [backup-simplify]: Simplify 0.5 into 0.5 0.562 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.562 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.562 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.562 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.562 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.562 * [taylor]: Taking taylor expansion of 1.0 in n 0.562 * [backup-simplify]: Simplify 1.0 into 1.0 0.562 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.562 * [taylor]: Taking taylor expansion of 2.0 in n 0.562 * [backup-simplify]: Simplify 2.0 into 2.0 0.563 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.563 * [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 0.564 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.564 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.564 * [taylor]: Taking taylor expansion of 1.0 in n 0.564 * [backup-simplify]: Simplify 1.0 into 1.0 0.564 * [taylor]: Taking taylor expansion of (log n) in n 0.564 * [taylor]: Taking taylor expansion of n in n 0.564 * [backup-simplify]: Simplify 0 into 0 0.564 * [backup-simplify]: Simplify 1 into 1 0.564 * [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 0.565 * [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) 0.567 * [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)) 0.569 * [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))) 0.570 * [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) 0.570 * [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 0.570 * [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 0.570 * [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 0.570 * [taylor]: Taking taylor expansion of +nan.0 in n 0.570 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.570 * [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 0.570 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.570 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.570 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.570 * [taylor]: Taking taylor expansion of 0.5 in n 0.570 * [backup-simplify]: Simplify 0.5 into 0.5 0.570 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.570 * [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) 0.571 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.572 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.572 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.572 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.572 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.572 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.572 * [taylor]: Taking taylor expansion of 1.0 in n 0.572 * [backup-simplify]: Simplify 1.0 into 1.0 0.572 * [taylor]: Taking taylor expansion of (log PI) in n 0.572 * [taylor]: Taking taylor expansion of PI in n 0.572 * [backup-simplify]: Simplify PI into PI 0.573 * [backup-simplify]: Simplify (log PI) into (log PI) 0.573 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.574 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.574 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.574 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.574 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.574 * [taylor]: Taking taylor expansion of 1.0 in n 0.574 * [backup-simplify]: Simplify 1.0 into 1.0 0.574 * [taylor]: Taking taylor expansion of (log n) in n 0.574 * [taylor]: Taking taylor expansion of n in n 0.574 * [backup-simplify]: Simplify 0 into 0 0.574 * [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) 0.575 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.575 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.575 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.576 * [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) 0.577 * [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)) 0.578 * [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))) 0.578 * [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) 0.578 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.578 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.578 * [taylor]: Taking taylor expansion of 2.0 in n 0.578 * [backup-simplify]: Simplify 2.0 into 2.0 0.578 * [taylor]: Taking taylor expansion of (* n PI) in n 0.579 * [taylor]: Taking taylor expansion of n in n 0.579 * [backup-simplify]: Simplify 0 into 0 0.579 * [backup-simplify]: Simplify 1 into 1 0.579 * [taylor]: Taking taylor expansion of PI in n 0.579 * [backup-simplify]: Simplify PI into PI 0.579 * [backup-simplify]: Simplify (* 0 PI) into 0 0.579 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.580 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.587 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.587 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.587 * [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 0.587 * [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 0.587 * [taylor]: Taking taylor expansion of +nan.0 in n 0.587 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.587 * [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 0.587 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.587 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.587 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.587 * [taylor]: Taking taylor expansion of 0.5 in n 0.587 * [backup-simplify]: Simplify 0.5 into 0.5 0.587 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.587 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.588 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.588 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.588 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.588 * [taylor]: Taking taylor expansion of 1.0 in n 0.588 * [backup-simplify]: Simplify 1.0 into 1.0 0.588 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.588 * [taylor]: Taking taylor expansion of 2.0 in n 0.588 * [backup-simplify]: Simplify 2.0 into 2.0 0.588 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.588 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.589 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.589 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.589 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.589 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.589 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) 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 PI) in n 0.589 * [taylor]: Taking taylor expansion of PI in n 0.589 * [backup-simplify]: Simplify PI into PI 0.590 * [backup-simplify]: Simplify (log PI) into (log PI) 0.590 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.591 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.591 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.591 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.591 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) 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 n) in n 0.591 * [taylor]: Taking taylor expansion of n in n 0.591 * [backup-simplify]: Simplify 0 into 0 0.591 * [backup-simplify]: Simplify 1 into 1 0.592 * [backup-simplify]: Simplify (log 1) into 0 0.592 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.592 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.592 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.593 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.593 * [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) 0.594 * [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)) 0.595 * [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))) 0.596 * [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) 0.596 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.596 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.596 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.596 * [taylor]: Taking taylor expansion of 2.0 in n 0.596 * [backup-simplify]: Simplify 2.0 into 2.0 0.596 * [taylor]: Taking taylor expansion of (* n PI) in n 0.596 * [taylor]: Taking taylor expansion of n in n 0.596 * [backup-simplify]: Simplify 0 into 0 0.596 * [backup-simplify]: Simplify 1 into 1 0.596 * [taylor]: Taking taylor expansion of PI in n 0.596 * [backup-simplify]: Simplify PI into PI 0.596 * [backup-simplify]: Simplify (* 0 PI) into 0 0.597 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.598 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.598 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.599 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.600 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.601 * [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)) 0.602 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.603 * [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)) 0.605 * [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))) 0.605 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.606 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.607 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 0.609 * [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)) 0.610 * [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))) 0.612 * [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)))))))) 0.618 * [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)))))))))))) 0.626 * [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)))))))))))) 0.635 * [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)))))))))))))) 0.645 * [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)))))))))))))) 0.654 * [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)))))))))))))) 0.668 * [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)))))))))))))))))))))) 0.669 * [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)))))) 0.669 * [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 0.669 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.669 * [taylor]: Taking taylor expansion of 1.0 in n 0.669 * [backup-simplify]: Simplify 1.0 into 1.0 0.669 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.669 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.669 * [taylor]: Taking taylor expansion of k in n 0.669 * [backup-simplify]: Simplify k into k 0.669 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 0.669 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 0.669 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.669 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.669 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.669 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.669 * [taylor]: Taking taylor expansion of 0.5 in n 0.669 * [backup-simplify]: Simplify 0.5 into 0.5 0.669 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.669 * [taylor]: Taking taylor expansion of 1.0 in n 0.669 * [backup-simplify]: Simplify 1.0 into 1.0 0.669 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.669 * [taylor]: Taking taylor expansion of k in n 0.669 * [backup-simplify]: Simplify k into k 0.669 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.669 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.669 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.669 * [taylor]: Taking taylor expansion of 2.0 in n 0.669 * [backup-simplify]: Simplify 2.0 into 2.0 0.669 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.669 * [taylor]: Taking taylor expansion of PI in n 0.669 * [backup-simplify]: Simplify PI into PI 0.669 * [taylor]: Taking taylor expansion of n in n 0.669 * [backup-simplify]: Simplify 0 into 0 0.669 * [backup-simplify]: Simplify 1 into 1 0.670 * [backup-simplify]: Simplify (/ PI 1) into PI 0.670 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.671 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.671 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.671 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.671 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.672 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.677 * [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)))) 0.678 * [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))))) 0.678 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.678 * [taylor]: Taking taylor expansion of 1.0 in k 0.678 * [backup-simplify]: Simplify 1.0 into 1.0 0.678 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.678 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.678 * [taylor]: Taking taylor expansion of k in k 0.678 * [backup-simplify]: Simplify 0 into 0 0.678 * [backup-simplify]: Simplify 1 into 1 0.679 * [backup-simplify]: Simplify (sqrt 0) into 0 0.680 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.680 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.680 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.680 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.680 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.680 * [taylor]: Taking taylor expansion of 0.5 in k 0.680 * [backup-simplify]: Simplify 0.5 into 0.5 0.680 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.680 * [taylor]: Taking taylor expansion of 1.0 in k 0.680 * [backup-simplify]: Simplify 1.0 into 1.0 0.680 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.680 * [taylor]: Taking taylor expansion of k in k 0.680 * [backup-simplify]: Simplify 0 into 0 0.680 * [backup-simplify]: Simplify 1 into 1 0.680 * [backup-simplify]: Simplify (/ 1 1) into 1 0.680 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.680 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.680 * [taylor]: Taking taylor expansion of 2.0 in k 0.680 * [backup-simplify]: Simplify 2.0 into 2.0 0.680 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.680 * [taylor]: Taking taylor expansion of PI in k 0.680 * [backup-simplify]: Simplify PI into PI 0.680 * [taylor]: Taking taylor expansion of n in k 0.680 * [backup-simplify]: Simplify n into n 0.680 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.680 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.680 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.681 * [backup-simplify]: Simplify (- 1) into -1 0.681 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.681 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.681 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.681 * [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))))) 0.681 * [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 0.682 * [taylor]: Taking taylor expansion of (sqrt 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 (sqrt 0) into 0 0.683 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.683 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.683 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.683 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.683 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.683 * [taylor]: Taking taylor expansion of 0.5 in k 0.683 * [backup-simplify]: Simplify 0.5 into 0.5 0.683 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.683 * [taylor]: Taking taylor expansion of 1.0 in k 0.683 * [backup-simplify]: Simplify 1.0 into 1.0 0.683 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.683 * [taylor]: Taking taylor expansion of k in k 0.683 * [backup-simplify]: Simplify 0 into 0 0.683 * [backup-simplify]: Simplify 1 into 1 0.683 * [backup-simplify]: Simplify (/ 1 1) into 1 0.683 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.683 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.683 * [taylor]: Taking taylor expansion of 2.0 in k 0.683 * [backup-simplify]: Simplify 2.0 into 2.0 0.683 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.683 * [taylor]: Taking taylor expansion of PI in k 0.683 * [backup-simplify]: Simplify PI into PI 0.683 * [taylor]: Taking taylor expansion of n in k 0.683 * [backup-simplify]: Simplify n into n 0.683 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.683 * [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 0.684 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.684 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.684 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.684 * [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 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 0.685 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.685 * [taylor]: Taking taylor expansion of 0 in n 0.685 * [backup-simplify]: Simplify 0 into 0 0.685 * [backup-simplify]: Simplify 0 into 0 0.685 * [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))))))) 0.686 * [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))))))) 0.686 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.686 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.686 * [taylor]: Taking taylor expansion of +nan.0 in n 0.686 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.686 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.686 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.686 * [taylor]: Taking taylor expansion of 0.5 in n 0.686 * [backup-simplify]: Simplify 0.5 into 0.5 0.686 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.686 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.686 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.686 * [taylor]: Taking taylor expansion of 2.0 in n 0.686 * [backup-simplify]: Simplify 2.0 into 2.0 0.686 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.686 * [taylor]: Taking taylor expansion of PI in n 0.686 * [backup-simplify]: Simplify PI into PI 0.686 * [taylor]: Taking taylor expansion of n in n 0.686 * [backup-simplify]: Simplify 0 into 0 0.686 * [backup-simplify]: Simplify 1 into 1 0.686 * [backup-simplify]: Simplify (/ PI 1) into PI 0.686 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.687 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.687 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.687 * [taylor]: Taking taylor expansion of 1.0 in n 0.687 * [backup-simplify]: Simplify 1.0 into 1.0 0.687 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.687 * [taylor]: Taking taylor expansion of k in n 0.687 * [backup-simplify]: Simplify k into k 0.687 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.688 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.688 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.688 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.689 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.690 * [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)))) 0.690 * [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))))) 0.691 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 0.692 * [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))))))) 0.692 * [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))))))) 0.692 * [backup-simplify]: Simplify 0 into 0 0.695 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.695 * [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))))))) 0.696 * [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))))))) 0.696 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.696 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.696 * [taylor]: Taking taylor expansion of +nan.0 in n 0.696 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.696 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.696 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.696 * [taylor]: Taking taylor expansion of 0.5 in n 0.696 * [backup-simplify]: Simplify 0.5 into 0.5 0.696 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.696 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.696 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.696 * [taylor]: Taking taylor expansion of 2.0 in n 0.696 * [backup-simplify]: Simplify 2.0 into 2.0 0.696 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.696 * [taylor]: Taking taylor expansion of PI in n 0.696 * [backup-simplify]: Simplify PI into PI 0.696 * [taylor]: Taking taylor expansion of n in n 0.696 * [backup-simplify]: Simplify 0 into 0 0.696 * [backup-simplify]: Simplify 1 into 1 0.697 * [backup-simplify]: Simplify (/ PI 1) into PI 0.697 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.697 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.697 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.697 * [taylor]: Taking taylor expansion of 1.0 in n 0.697 * [backup-simplify]: Simplify 1.0 into 1.0 0.697 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.697 * [taylor]: Taking taylor expansion of k in n 0.698 * [backup-simplify]: Simplify k into k 0.698 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.698 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.698 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.699 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.699 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.700 * [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)))) 0.701 * [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))))) 0.701 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 0.702 * [backup-simplify]: Simplify (- (* +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))))))) 0.703 * [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 (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.704 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.704 * [backup-simplify]: Simplify (- 0) into 0 0.704 * [backup-simplify]: Simplify (+ 0 0) into 0 0.705 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.705 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.706 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.707 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.708 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 0.709 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.710 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 0.710 * [backup-simplify]: Simplify (- 0) into 0 0.710 * [backup-simplify]: Simplify 0 into 0 0.710 * [backup-simplify]: Simplify 0 into 0 0.712 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.713 * [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))))))) 0.714 * [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))))))) 0.714 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.714 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.714 * [taylor]: Taking taylor expansion of +nan.0 in n 0.714 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.714 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.714 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.714 * [taylor]: Taking taylor expansion of 0.5 in n 0.714 * [backup-simplify]: Simplify 0.5 into 0.5 0.714 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.714 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.714 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.714 * [taylor]: Taking taylor expansion of 2.0 in n 0.714 * [backup-simplify]: Simplify 2.0 into 2.0 0.714 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.714 * [taylor]: Taking taylor expansion of PI in n 0.714 * [backup-simplify]: Simplify PI into PI 0.714 * [taylor]: Taking taylor expansion of n in n 0.714 * [backup-simplify]: Simplify 0 into 0 0.714 * [backup-simplify]: Simplify 1 into 1 0.714 * [backup-simplify]: Simplify (/ PI 1) into PI 0.715 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.715 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.715 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.715 * [taylor]: Taking taylor expansion of 1.0 in n 0.715 * [backup-simplify]: Simplify 1.0 into 1.0 0.715 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.715 * [taylor]: Taking taylor expansion of k in n 0.715 * [backup-simplify]: Simplify k into k 0.715 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.716 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.716 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.716 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.717 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.718 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.718 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.719 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 0.720 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.721 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.723 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 0.724 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 0.724 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 0.724 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.724 * [taylor]: Taking taylor expansion of 1.0 in n 0.724 * [backup-simplify]: Simplify 1.0 into 1.0 0.724 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.724 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.724 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.724 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.724 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.724 * [taylor]: Taking taylor expansion of 0.5 in n 0.724 * [backup-simplify]: Simplify 0.5 into 0.5 0.724 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.724 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.724 * [taylor]: Taking taylor expansion of k in n 0.724 * [backup-simplify]: Simplify k into k 0.724 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.724 * [taylor]: Taking taylor expansion of 1.0 in n 0.724 * [backup-simplify]: Simplify 1.0 into 1.0 0.724 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.724 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.724 * [taylor]: Taking taylor expansion of -2.0 in n 0.724 * [backup-simplify]: Simplify -2.0 into -2.0 0.724 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.724 * [taylor]: Taking taylor expansion of PI in n 0.724 * [backup-simplify]: Simplify PI into PI 0.724 * [taylor]: Taking taylor expansion of n in n 0.724 * [backup-simplify]: Simplify 0 into 0 0.724 * [backup-simplify]: Simplify 1 into 1 0.725 * [backup-simplify]: Simplify (/ PI 1) into PI 0.725 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.726 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.726 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.726 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.727 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.727 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.728 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.728 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.728 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.728 * [taylor]: Taking taylor expansion of -1 in n 0.728 * [backup-simplify]: Simplify -1 into -1 0.728 * [taylor]: Taking taylor expansion of k in n 0.728 * [backup-simplify]: Simplify k into k 0.728 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 0.728 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 0.728 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 0.728 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 0.729 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 0.729 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.729 * [taylor]: Taking taylor expansion of 1.0 in k 0.729 * [backup-simplify]: Simplify 1.0 into 1.0 0.729 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.729 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.729 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.729 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.729 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.729 * [taylor]: Taking taylor expansion of 0.5 in k 0.729 * [backup-simplify]: Simplify 0.5 into 0.5 0.729 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.729 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.729 * [taylor]: Taking taylor expansion of k in k 0.730 * [backup-simplify]: Simplify 0 into 0 0.730 * [backup-simplify]: Simplify 1 into 1 0.730 * [backup-simplify]: Simplify (/ 1 1) into 1 0.730 * [taylor]: Taking taylor expansion of 1.0 in k 0.730 * [backup-simplify]: Simplify 1.0 into 1.0 0.730 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.730 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.730 * [taylor]: Taking taylor expansion of -2.0 in k 0.730 * [backup-simplify]: Simplify -2.0 into -2.0 0.730 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.730 * [taylor]: Taking taylor expansion of PI in k 0.730 * [backup-simplify]: Simplify PI into PI 0.730 * [taylor]: Taking taylor expansion of n in k 0.730 * [backup-simplify]: Simplify n into n 0.730 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.730 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.730 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.730 * [backup-simplify]: Simplify (+ 1 0) into 1 0.731 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.731 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.731 * [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)))))) 0.731 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.731 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.731 * [taylor]: Taking taylor expansion of -1 in k 0.731 * [backup-simplify]: Simplify -1 into -1 0.731 * [taylor]: Taking taylor expansion of k in k 0.731 * [backup-simplify]: Simplify 0 into 0 0.731 * [backup-simplify]: Simplify 1 into 1 0.731 * [backup-simplify]: Simplify (/ -1 1) into -1 0.731 * [backup-simplify]: Simplify (sqrt 0) into 0 0.732 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.732 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 0.732 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.732 * [taylor]: Taking taylor expansion of 1.0 in k 0.732 * [backup-simplify]: Simplify 1.0 into 1.0 0.732 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.732 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.732 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.732 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.732 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.732 * [taylor]: Taking taylor expansion of 0.5 in k 0.732 * [backup-simplify]: Simplify 0.5 into 0.5 0.732 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.732 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.733 * [taylor]: Taking taylor expansion of k in k 0.733 * [backup-simplify]: Simplify 0 into 0 0.733 * [backup-simplify]: Simplify 1 into 1 0.733 * [backup-simplify]: Simplify (/ 1 1) into 1 0.733 * [taylor]: Taking taylor expansion of 1.0 in k 0.733 * [backup-simplify]: Simplify 1.0 into 1.0 0.733 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.733 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.733 * [taylor]: Taking taylor expansion of -2.0 in k 0.733 * [backup-simplify]: Simplify -2.0 into -2.0 0.733 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.733 * [taylor]: Taking taylor expansion of PI in k 0.733 * [backup-simplify]: Simplify PI into PI 0.733 * [taylor]: Taking taylor expansion of n in k 0.733 * [backup-simplify]: Simplify n into n 0.733 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.733 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.733 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.733 * [backup-simplify]: Simplify (+ 1 0) into 1 0.734 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.734 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.734 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 0.734 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.734 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.734 * [taylor]: Taking taylor expansion of -1 in k 0.734 * [backup-simplify]: Simplify -1 into -1 0.734 * [taylor]: Taking taylor expansion of k in k 0.734 * [backup-simplify]: Simplify 0 into 0 0.734 * [backup-simplify]: Simplify 1 into 1 0.734 * [backup-simplify]: Simplify (/ -1 1) into -1 0.734 * [backup-simplify]: Simplify (sqrt 0) into 0 0.735 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.735 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 0.736 * [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))))))) 0.736 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.736 * [taylor]: Taking taylor expansion of +nan.0 in n 0.736 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.736 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.736 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.736 * [taylor]: Taking taylor expansion of 0.5 in n 0.736 * [backup-simplify]: Simplify 0.5 into 0.5 0.736 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.736 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.736 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.736 * [taylor]: Taking taylor expansion of k in n 0.736 * [backup-simplify]: Simplify k into k 0.736 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.736 * [taylor]: Taking taylor expansion of 1.0 in n 0.736 * [backup-simplify]: Simplify 1.0 into 1.0 0.736 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.736 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.736 * [taylor]: Taking taylor expansion of -2.0 in n 0.736 * [backup-simplify]: Simplify -2.0 into -2.0 0.736 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.736 * [taylor]: Taking taylor expansion of PI in n 0.736 * [backup-simplify]: Simplify PI into PI 0.736 * [taylor]: Taking taylor expansion of n in n 0.736 * [backup-simplify]: Simplify 0 into 0 0.736 * [backup-simplify]: Simplify 1 into 1 0.736 * [backup-simplify]: Simplify (/ PI 1) into PI 0.737 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.737 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.737 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.738 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.739 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.739 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.740 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.741 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.742 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.744 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.745 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 0.745 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 0.745 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.745 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.745 * [taylor]: Taking taylor expansion of +nan.0 in n 0.745 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.745 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.745 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.745 * [taylor]: Taking taylor expansion of 0.5 in n 0.745 * [backup-simplify]: Simplify 0.5 into 0.5 0.745 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.745 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.745 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.745 * [taylor]: Taking taylor expansion of k in n 0.745 * [backup-simplify]: Simplify k into k 0.745 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.745 * [taylor]: Taking taylor expansion of 1.0 in n 0.745 * [backup-simplify]: Simplify 1.0 into 1.0 0.745 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.745 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.745 * [taylor]: Taking taylor expansion of -2.0 in n 0.745 * [backup-simplify]: Simplify -2.0 into -2.0 0.745 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.745 * [taylor]: Taking taylor expansion of PI in n 0.745 * [backup-simplify]: Simplify PI into PI 0.745 * [taylor]: Taking taylor expansion of n in n 0.745 * [backup-simplify]: Simplify 0 into 0 0.745 * [backup-simplify]: Simplify 1 into 1 0.746 * [backup-simplify]: Simplify (/ PI 1) into PI 0.746 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.747 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.747 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.748 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.748 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.749 * [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)))) 0.750 * [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))))) 0.750 * [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)))))) 0.751 * [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))))))) 0.752 * [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))))))) 0.752 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.753 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.754 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.754 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.754 * [backup-simplify]: Simplify (+ 0 0) into 0 0.755 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.756 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.756 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 0.758 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.759 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 0.759 * [backup-simplify]: Simplify 0 into 0 0.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.761 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.762 * [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)))))))) 0.763 * [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)))))))) 0.763 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.763 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.763 * [taylor]: Taking taylor expansion of +nan.0 in n 0.763 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.763 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.763 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.763 * [taylor]: Taking taylor expansion of 0.5 in n 0.763 * [backup-simplify]: Simplify 0.5 into 0.5 0.763 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.763 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.763 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.763 * [taylor]: Taking taylor expansion of k in n 0.763 * [backup-simplify]: Simplify k into k 0.763 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.763 * [taylor]: Taking taylor expansion of 1.0 in n 0.763 * [backup-simplify]: Simplify 1.0 into 1.0 0.763 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.763 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.763 * [taylor]: Taking taylor expansion of -2.0 in n 0.763 * [backup-simplify]: Simplify -2.0 into -2.0 0.763 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.763 * [taylor]: Taking taylor expansion of PI in n 0.763 * [backup-simplify]: Simplify PI into PI 0.763 * [taylor]: Taking taylor expansion of n in n 0.763 * [backup-simplify]: Simplify 0 into 0 0.763 * [backup-simplify]: Simplify 1 into 1 0.764 * [backup-simplify]: Simplify (/ PI 1) into PI 0.764 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.764 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.764 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.765 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.766 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.767 * [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)))) 0.767 * [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))))) 0.768 * [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)))))) 0.769 * [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))))))) 0.770 * [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))))))) 0.778 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 0.778 * * * [progress]: simplifying candidates 0.781 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 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2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- 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(sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (cbrt (sqrt h1))) (/ 1 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (cbrt h1))) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 (sqrt 1)) (/ h2 (sqrt h1)) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 1) (/ h2 (sqrt h1)) (/ 1 (sqrt h1)) (/ (sqrt h1) h2) (/ h2 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (sqrt h1))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h1))) (/ h2 1) (/ (sqrt h1) (cbrt h2)) (/ (sqrt h1) (sqrt h2)) (/ (sqrt h1) h2) (expm1 (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (log1p (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (+ (- (log h2) (log (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (+ (log (/ h2 (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (log (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (exp (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (* (* (/ h2 (sqrt h1)) (/ h2 (sqrt h1))) (/ h2 (sqrt h1))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (* (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (sqrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (sqrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* h2 (pow (* (* h0 h4) h3) (/ h2 h0))) (* (sqrt h1) (pow (* (* h0 h4) h3) (/ h1 h0))) (* (sqrt (/ h2 (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (sqrt (/ h2 (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ h2 (sqrt h1)) (pow (* h0 h4) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (* (/ h2 (sqrt h1)) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ h2 (sqrt h1)) 1) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ 1 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ h2 h0))) (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (- (+ (* h7 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h7 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (+ (* h6 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (- (+ (* h9 h1) (- (+ (* h9 (pow h1 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- (* h9 (/ 1 (pow h1 3)))))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- h9))))) (- (+ (* h9 (* (* (pow h1 2) (pow (log (* h0 h4)) 2)) (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log (* h0 h4))) (pow (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (* (log (* h0 h4)) (log h3))) (pow (* (pow h4 h2) (* (pow h0 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log h3)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* h1 (log (* h0 h4))) (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (pow (log h3) 2)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* h1 (log h3)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5)) (- (+ (* h9 (* (pow h1 2) (pow (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2))) h5))) (- (* h9 (* h1 (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5)))))))))))))))))))))) (- (+ (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (pow h1 3))) (- (+ (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) h1)) (- (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (pow h1 2)))))))) (- (+ (* h9 (/ (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) h1)) (- (+ (* h9 (/ (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (pow h1 2))) (- (* h9 (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))))))))) 0.791 * * [simplify]: iteration 0 : 981 enodes (cost 1502 ) 0.809 * * [simplify]: iteration 1 : 4021 enodes (cost 1398 ) 0.875 * * [simplify]: iteration 2 : 5003 enodes (cost 1383 ) 0.882 * * * [progress]: adding candidates to table 1.327 * * [progress]: iteration 2 / 4 1.327 * * * [progress]: picking best candidate 1.344 * * * * [pick]: Picked # 1.344 * * * [progress]: localizing error 1.358 * * * [progress]: generating rewritten candidates 1.358 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 1.379 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 1.399 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 1.405 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 1.415 * * * [progress]: generating series expansions 1.415 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 1.416 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.416 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.416 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.416 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.416 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.416 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.416 * [taylor]: Taking taylor expansion of 0.5 in k 1.416 * [backup-simplify]: Simplify 0.5 into 0.5 1.416 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.416 * [taylor]: Taking taylor expansion of 1.0 in k 1.416 * [backup-simplify]: Simplify 1.0 into 1.0 1.416 * [taylor]: Taking taylor expansion of k in k 1.416 * [backup-simplify]: Simplify 0 into 0 1.416 * [backup-simplify]: Simplify 1 into 1 1.416 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.416 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.416 * [taylor]: Taking taylor expansion of 2.0 in k 1.417 * [backup-simplify]: Simplify 2.0 into 2.0 1.417 * [taylor]: Taking taylor expansion of (* n PI) in k 1.417 * [taylor]: Taking taylor expansion of n in k 1.417 * [backup-simplify]: Simplify n into n 1.417 * [taylor]: Taking taylor expansion of PI in k 1.417 * [backup-simplify]: Simplify PI into PI 1.417 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.417 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.417 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.417 * [backup-simplify]: Simplify (- 0) into 0 1.417 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.418 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.418 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.418 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.418 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.418 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.418 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.418 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.418 * [taylor]: Taking taylor expansion of 0.5 in n 1.418 * [backup-simplify]: Simplify 0.5 into 0.5 1.418 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.418 * [taylor]: Taking taylor expansion of 1.0 in n 1.418 * [backup-simplify]: Simplify 1.0 into 1.0 1.418 * [taylor]: Taking taylor expansion of k in n 1.418 * [backup-simplify]: Simplify k into k 1.418 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.418 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.418 * [taylor]: Taking taylor expansion of 2.0 in n 1.418 * [backup-simplify]: Simplify 2.0 into 2.0 1.418 * [taylor]: Taking taylor expansion of (* n PI) in n 1.418 * [taylor]: Taking taylor expansion of n in n 1.418 * [backup-simplify]: Simplify 0 into 0 1.418 * [backup-simplify]: Simplify 1 into 1 1.418 * [taylor]: Taking taylor expansion of PI in n 1.418 * [backup-simplify]: Simplify PI into PI 1.419 * [backup-simplify]: Simplify (* 0 PI) into 0 1.419 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.420 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.421 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.422 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.422 * [backup-simplify]: Simplify (- k) into (- k) 1.422 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.422 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.423 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.423 * [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)))) 1.424 * [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))))) 1.424 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.424 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.424 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.424 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.424 * [taylor]: Taking taylor expansion of 0.5 in n 1.424 * [backup-simplify]: Simplify 0.5 into 0.5 1.424 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.424 * [taylor]: Taking taylor expansion of 1.0 in n 1.424 * [backup-simplify]: Simplify 1.0 into 1.0 1.424 * [taylor]: Taking taylor expansion of k in n 1.424 * [backup-simplify]: Simplify k into k 1.424 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.424 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.424 * [taylor]: Taking taylor expansion of 2.0 in n 1.424 * [backup-simplify]: Simplify 2.0 into 2.0 1.424 * [taylor]: Taking taylor expansion of (* n PI) in n 1.424 * [taylor]: Taking taylor expansion of n in n 1.424 * [backup-simplify]: Simplify 0 into 0 1.424 * [backup-simplify]: Simplify 1 into 1 1.424 * [taylor]: Taking taylor expansion of PI in n 1.424 * [backup-simplify]: Simplify PI into PI 1.425 * [backup-simplify]: Simplify (* 0 PI) into 0 1.425 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.426 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.427 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.427 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.427 * [backup-simplify]: Simplify (- k) into (- k) 1.427 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.427 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.428 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.429 * [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)))) 1.429 * [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))))) 1.430 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.430 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.430 * [taylor]: Taking taylor expansion of 0.5 in k 1.430 * [backup-simplify]: Simplify 0.5 into 0.5 1.430 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.430 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.430 * [taylor]: Taking taylor expansion of 1.0 in k 1.430 * [backup-simplify]: Simplify 1.0 into 1.0 1.430 * [taylor]: Taking taylor expansion of k in k 1.430 * [backup-simplify]: Simplify 0 into 0 1.430 * [backup-simplify]: Simplify 1 into 1 1.430 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.430 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.430 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.430 * [taylor]: Taking taylor expansion of 2.0 in k 1.430 * [backup-simplify]: Simplify 2.0 into 2.0 1.430 * [taylor]: Taking taylor expansion of PI in k 1.430 * [backup-simplify]: Simplify PI into PI 1.430 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.431 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.431 * [taylor]: Taking taylor expansion of (log n) in k 1.431 * [taylor]: Taking taylor expansion of n in k 1.431 * [backup-simplify]: Simplify n into n 1.431 * [backup-simplify]: Simplify (log n) into (log n) 1.431 * [backup-simplify]: Simplify (- 0) into 0 1.431 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.432 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.433 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.433 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.434 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.434 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.435 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.436 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.436 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.437 * [backup-simplify]: Simplify (- 0) into 0 1.437 * [backup-simplify]: Simplify (+ 0 0) into 0 1.437 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.438 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.439 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.440 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.440 * [taylor]: Taking taylor expansion of 0 in k 1.440 * [backup-simplify]: Simplify 0 into 0 1.440 * [backup-simplify]: Simplify 0 into 0 1.440 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.441 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.442 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.442 * [backup-simplify]: Simplify (+ 0 0) into 0 1.442 * [backup-simplify]: Simplify (- 1) into -1 1.442 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.443 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.445 * [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)))) 1.446 * [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)))))) 1.448 * [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)))))) 1.449 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.450 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.451 * [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 1.452 * [backup-simplify]: Simplify (- 0) into 0 1.452 * [backup-simplify]: Simplify (+ 0 0) into 0 1.452 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.453 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.454 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.456 * [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 1.456 * [taylor]: Taking taylor expansion of 0 in k 1.456 * [backup-simplify]: Simplify 0 into 0 1.456 * [backup-simplify]: Simplify 0 into 0 1.456 * [backup-simplify]: Simplify 0 into 0 1.456 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.458 * [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 1.459 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.459 * [backup-simplify]: Simplify (+ 0 0) into 0 1.460 * [backup-simplify]: Simplify (- 0) into 0 1.460 * [backup-simplify]: Simplify (+ 0 0) into 0 1.461 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.462 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.465 * [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)))))) 1.474 * [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)))))) 1.479 * [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)))))) 1.480 * [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)))) 1.480 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.480 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.480 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.480 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.480 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.480 * [taylor]: Taking taylor expansion of 0.5 in k 1.480 * [backup-simplify]: Simplify 0.5 into 0.5 1.480 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.480 * [taylor]: Taking taylor expansion of 1.0 in k 1.480 * [backup-simplify]: Simplify 1.0 into 1.0 1.480 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.480 * [taylor]: Taking taylor expansion of k in k 1.480 * [backup-simplify]: Simplify 0 into 0 1.480 * [backup-simplify]: Simplify 1 into 1 1.481 * [backup-simplify]: Simplify (/ 1 1) into 1 1.481 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.481 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.481 * [taylor]: Taking taylor expansion of 2.0 in k 1.481 * [backup-simplify]: Simplify 2.0 into 2.0 1.481 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.481 * [taylor]: Taking taylor expansion of PI in k 1.481 * [backup-simplify]: Simplify PI into PI 1.481 * [taylor]: Taking taylor expansion of n in k 1.481 * [backup-simplify]: Simplify n into n 1.481 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.481 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.481 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.481 * [backup-simplify]: Simplify (- 1) into -1 1.481 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.482 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.482 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.482 * [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))))) 1.482 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.482 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.482 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.482 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.482 * [taylor]: Taking taylor expansion of 0.5 in n 1.482 * [backup-simplify]: Simplify 0.5 into 0.5 1.482 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.482 * [taylor]: Taking taylor expansion of 1.0 in n 1.482 * [backup-simplify]: Simplify 1.0 into 1.0 1.482 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.482 * [taylor]: Taking taylor expansion of k in n 1.482 * [backup-simplify]: Simplify k into k 1.482 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.482 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.482 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.482 * [taylor]: Taking taylor expansion of 2.0 in n 1.482 * [backup-simplify]: Simplify 2.0 into 2.0 1.482 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.482 * [taylor]: Taking taylor expansion of PI in n 1.482 * [backup-simplify]: Simplify PI into PI 1.482 * [taylor]: Taking taylor expansion of n in n 1.482 * [backup-simplify]: Simplify 0 into 0 1.482 * [backup-simplify]: Simplify 1 into 1 1.483 * [backup-simplify]: Simplify (/ PI 1) into PI 1.483 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.483 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.484 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.484 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.484 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.485 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.485 * [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)))) 1.486 * [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))))) 1.486 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.486 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.486 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.486 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.486 * [taylor]: Taking taylor expansion of 0.5 in n 1.486 * [backup-simplify]: Simplify 0.5 into 0.5 1.486 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.486 * [taylor]: Taking taylor expansion of 1.0 in n 1.486 * [backup-simplify]: Simplify 1.0 into 1.0 1.486 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.486 * [taylor]: Taking taylor expansion of k in n 1.486 * [backup-simplify]: Simplify k into k 1.486 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.486 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.486 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.486 * [taylor]: Taking taylor expansion of 2.0 in n 1.486 * [backup-simplify]: Simplify 2.0 into 2.0 1.486 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.486 * [taylor]: Taking taylor expansion of PI in n 1.486 * [backup-simplify]: Simplify PI into PI 1.486 * [taylor]: Taking taylor expansion of n in n 1.486 * [backup-simplify]: Simplify 0 into 0 1.486 * [backup-simplify]: Simplify 1 into 1 1.487 * [backup-simplify]: Simplify (/ PI 1) into PI 1.487 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.488 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.488 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.488 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.488 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.489 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.489 * [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)))) 1.490 * [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))))) 1.490 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.490 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.490 * [taylor]: Taking taylor expansion of 0.5 in k 1.490 * [backup-simplify]: Simplify 0.5 into 0.5 1.490 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.490 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.490 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.490 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.490 * [taylor]: Taking taylor expansion of 2.0 in k 1.490 * [backup-simplify]: Simplify 2.0 into 2.0 1.490 * [taylor]: Taking taylor expansion of PI in k 1.490 * [backup-simplify]: Simplify PI into PI 1.491 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.491 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.491 * [taylor]: Taking taylor expansion of (log n) in k 1.491 * [taylor]: Taking taylor expansion of n in k 1.491 * [backup-simplify]: Simplify n into n 1.491 * [backup-simplify]: Simplify (log n) into (log n) 1.491 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.491 * [taylor]: Taking taylor expansion of 1.0 in k 1.491 * [backup-simplify]: Simplify 1.0 into 1.0 1.491 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.491 * [taylor]: Taking taylor expansion of k in k 1.491 * [backup-simplify]: Simplify 0 into 0 1.491 * [backup-simplify]: Simplify 1 into 1 1.492 * [backup-simplify]: Simplify (/ 1 1) into 1 1.492 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.492 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.492 * [backup-simplify]: Simplify (- 1) into -1 1.493 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.493 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.494 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.495 * [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))))) 1.495 * [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))))) 1.496 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.496 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.497 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.497 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.498 * [backup-simplify]: Simplify (- 0) into 0 1.498 * [backup-simplify]: Simplify (+ 0 0) into 0 1.498 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.499 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.500 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.501 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.501 * [taylor]: Taking taylor expansion of 0 in k 1.501 * [backup-simplify]: Simplify 0 into 0 1.501 * [backup-simplify]: Simplify 0 into 0 1.501 * [backup-simplify]: Simplify 0 into 0 1.502 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.502 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.504 * [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 1.504 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.504 * [backup-simplify]: Simplify (- 0) into 0 1.505 * [backup-simplify]: Simplify (+ 0 0) into 0 1.505 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.506 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.507 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.508 * [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 1.508 * [taylor]: Taking taylor expansion of 0 in k 1.508 * [backup-simplify]: Simplify 0 into 0 1.508 * [backup-simplify]: Simplify 0 into 0 1.508 * [backup-simplify]: Simplify 0 into 0 1.508 * [backup-simplify]: Simplify 0 into 0 1.509 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.509 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.512 * [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 1.512 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.513 * [backup-simplify]: Simplify (- 0) into 0 1.513 * [backup-simplify]: Simplify (+ 0 0) into 0 1.513 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) 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 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.517 * [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 1.517 * [taylor]: Taking taylor expansion of 0 in k 1.517 * [backup-simplify]: Simplify 0 into 0 1.517 * [backup-simplify]: Simplify 0 into 0 1.518 * [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)))) 1.518 * [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))) 1.518 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.518 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.518 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.518 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.518 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.518 * [taylor]: Taking taylor expansion of 0.5 in k 1.518 * [backup-simplify]: Simplify 0.5 into 0.5 1.518 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.518 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.518 * [taylor]: Taking taylor expansion of k in k 1.518 * [backup-simplify]: Simplify 0 into 0 1.518 * [backup-simplify]: Simplify 1 into 1 1.519 * [backup-simplify]: Simplify (/ 1 1) into 1 1.519 * [taylor]: Taking taylor expansion of 1.0 in k 1.519 * [backup-simplify]: Simplify 1.0 into 1.0 1.519 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.519 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.519 * [taylor]: Taking taylor expansion of -2.0 in k 1.519 * [backup-simplify]: Simplify -2.0 into -2.0 1.519 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.519 * [taylor]: Taking taylor expansion of PI in k 1.519 * [backup-simplify]: Simplify PI into PI 1.519 * [taylor]: Taking taylor expansion of n in k 1.519 * [backup-simplify]: Simplify n into n 1.519 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.519 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.519 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.519 * [backup-simplify]: Simplify (+ 1 0) into 1 1.520 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.520 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.520 * [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)))))) 1.520 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.520 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.520 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.520 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.520 * [taylor]: Taking taylor expansion of 0.5 in n 1.520 * [backup-simplify]: Simplify 0.5 into 0.5 1.520 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.520 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.520 * [taylor]: Taking taylor expansion of k in n 1.520 * [backup-simplify]: Simplify k into k 1.520 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.520 * [taylor]: Taking taylor expansion of 1.0 in n 1.520 * [backup-simplify]: Simplify 1.0 into 1.0 1.520 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.520 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.520 * [taylor]: Taking taylor expansion of -2.0 in n 1.520 * [backup-simplify]: Simplify -2.0 into -2.0 1.520 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.520 * [taylor]: Taking taylor expansion of PI in n 1.520 * [backup-simplify]: Simplify PI into PI 1.520 * [taylor]: Taking taylor expansion of n in n 1.520 * [backup-simplify]: Simplify 0 into 0 1.520 * [backup-simplify]: Simplify 1 into 1 1.520 * [backup-simplify]: Simplify (/ PI 1) into PI 1.521 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.521 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.521 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.521 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.522 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.523 * [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)))) 1.524 * [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))))) 1.524 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.524 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.524 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.524 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.524 * [taylor]: Taking taylor expansion of 0.5 in n 1.524 * [backup-simplify]: Simplify 0.5 into 0.5 1.524 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.524 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.524 * [taylor]: Taking taylor expansion of k in n 1.524 * [backup-simplify]: Simplify k into k 1.524 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.524 * [taylor]: Taking taylor expansion of 1.0 in n 1.524 * [backup-simplify]: Simplify 1.0 into 1.0 1.524 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.524 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.524 * [taylor]: Taking taylor expansion of -2.0 in n 1.524 * [backup-simplify]: Simplify -2.0 into -2.0 1.524 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.524 * [taylor]: Taking taylor expansion of PI in n 1.524 * [backup-simplify]: Simplify PI into PI 1.524 * [taylor]: Taking taylor expansion of n in n 1.524 * [backup-simplify]: Simplify 0 into 0 1.524 * [backup-simplify]: Simplify 1 into 1 1.524 * [backup-simplify]: Simplify (/ PI 1) into PI 1.525 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.525 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.525 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.525 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.526 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.527 * [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)))) 1.528 * [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))))) 1.528 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.528 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.528 * [taylor]: Taking taylor expansion of 0.5 in k 1.528 * [backup-simplify]: Simplify 0.5 into 0.5 1.528 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.528 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.528 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.528 * [taylor]: Taking taylor expansion of k in k 1.528 * [backup-simplify]: Simplify 0 into 0 1.528 * [backup-simplify]: Simplify 1 into 1 1.528 * [backup-simplify]: Simplify (/ 1 1) into 1 1.528 * [taylor]: Taking taylor expansion of 1.0 in k 1.528 * [backup-simplify]: Simplify 1.0 into 1.0 1.528 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.528 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.528 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.528 * [taylor]: Taking taylor expansion of -2.0 in k 1.528 * [backup-simplify]: Simplify -2.0 into -2.0 1.528 * [taylor]: Taking taylor expansion of PI in k 1.528 * [backup-simplify]: Simplify PI into PI 1.529 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.529 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.529 * [taylor]: Taking taylor expansion of (log n) in k 1.529 * [taylor]: Taking taylor expansion of n in k 1.529 * [backup-simplify]: Simplify n into n 1.529 * [backup-simplify]: Simplify (log n) into (log n) 1.529 * [backup-simplify]: Simplify (+ 1 0) into 1 1.530 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.530 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.531 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.531 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.532 * [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))))) 1.533 * [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))))) 1.534 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.534 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.535 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.535 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.535 * [backup-simplify]: Simplify (+ 0 0) into 0 1.536 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.536 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.537 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.538 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.538 * [taylor]: Taking taylor expansion of 0 in k 1.538 * [backup-simplify]: Simplify 0 into 0 1.538 * [backup-simplify]: Simplify 0 into 0 1.538 * [backup-simplify]: Simplify 0 into 0 1.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.539 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.541 * [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 1.541 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.541 * [backup-simplify]: Simplify (+ 0 0) into 0 1.542 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.543 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.544 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.545 * [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 1.545 * [taylor]: Taking taylor expansion of 0 in k 1.545 * [backup-simplify]: Simplify 0 into 0 1.545 * [backup-simplify]: Simplify 0 into 0 1.545 * [backup-simplify]: Simplify 0 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)))) into 0 1.546 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.549 * [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 1.550 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.550 * [backup-simplify]: Simplify (+ 0 0) into 0 1.550 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.551 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.552 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.554 * [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 1.554 * [taylor]: Taking taylor expansion of 0 in k 1.554 * [backup-simplify]: Simplify 0 into 0 1.554 * [backup-simplify]: Simplify 0 into 0 1.555 * [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)))))) 1.555 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 1.555 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.555 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.555 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.555 * [taylor]: Taking taylor expansion of 2.0 in n 1.555 * [backup-simplify]: Simplify 2.0 into 2.0 1.555 * [taylor]: Taking taylor expansion of (* n PI) in n 1.555 * [taylor]: Taking taylor expansion of n in n 1.555 * [backup-simplify]: Simplify 0 into 0 1.555 * [backup-simplify]: Simplify 1 into 1 1.555 * [taylor]: Taking taylor expansion of PI in n 1.555 * [backup-simplify]: Simplify PI into PI 1.555 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.555 * [taylor]: Taking taylor expansion of 2.0 in n 1.555 * [backup-simplify]: Simplify 2.0 into 2.0 1.555 * [taylor]: Taking taylor expansion of (* n PI) in n 1.555 * [taylor]: Taking taylor expansion of n in n 1.555 * [backup-simplify]: Simplify 0 into 0 1.555 * [backup-simplify]: Simplify 1 into 1 1.555 * [taylor]: Taking taylor expansion of PI in n 1.555 * [backup-simplify]: Simplify PI into PI 1.556 * [backup-simplify]: Simplify (* 0 PI) into 0 1.556 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.556 * [backup-simplify]: Simplify 0 into 0 1.557 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.558 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.558 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.559 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.559 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.559 * [backup-simplify]: Simplify 0 into 0 1.560 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.566 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.566 * [backup-simplify]: Simplify 0 into 0 1.567 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.568 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.568 * [backup-simplify]: Simplify 0 into 0 1.569 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.570 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.570 * [backup-simplify]: Simplify 0 into 0 1.570 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.571 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.571 * [backup-simplify]: Simplify 0 into 0 1.572 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.573 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.573 * [backup-simplify]: Simplify 0 into 0 1.574 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.574 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.574 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.574 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.574 * [taylor]: Taking taylor expansion of 2.0 in n 1.574 * [backup-simplify]: Simplify 2.0 into 2.0 1.574 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.574 * [taylor]: Taking taylor expansion of PI in n 1.574 * [backup-simplify]: Simplify PI into PI 1.574 * [taylor]: Taking taylor expansion of n in n 1.574 * [backup-simplify]: Simplify 0 into 0 1.574 * [backup-simplify]: Simplify 1 into 1 1.574 * [backup-simplify]: Simplify (/ PI 1) into PI 1.574 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.575 * [taylor]: Taking taylor expansion of 2.0 in n 1.575 * [backup-simplify]: Simplify 2.0 into 2.0 1.575 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.575 * [taylor]: Taking taylor expansion of PI in n 1.575 * [backup-simplify]: Simplify PI into PI 1.575 * [taylor]: Taking taylor expansion of n in n 1.575 * [backup-simplify]: Simplify 0 into 0 1.575 * [backup-simplify]: Simplify 1 into 1 1.575 * [backup-simplify]: Simplify (/ PI 1) into PI 1.575 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.576 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.576 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.576 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.576 * [backup-simplify]: Simplify 0 into 0 1.577 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.578 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.578 * [backup-simplify]: Simplify 0 into 0 1.578 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.579 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.579 * [backup-simplify]: Simplify 0 into 0 1.579 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.580 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.580 * [backup-simplify]: Simplify 0 into 0 1.581 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.581 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.581 * [backup-simplify]: Simplify 0 into 0 1.582 * [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 1.583 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.583 * [backup-simplify]: Simplify 0 into 0 1.583 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.584 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.584 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.584 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.584 * [taylor]: Taking taylor expansion of -2.0 in n 1.584 * [backup-simplify]: Simplify -2.0 into -2.0 1.584 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.584 * [taylor]: Taking taylor expansion of PI in n 1.584 * [backup-simplify]: Simplify PI into PI 1.584 * [taylor]: Taking taylor expansion of n in n 1.584 * [backup-simplify]: Simplify 0 into 0 1.584 * [backup-simplify]: Simplify 1 into 1 1.584 * [backup-simplify]: Simplify (/ PI 1) into PI 1.584 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.584 * [taylor]: Taking taylor expansion of -2.0 in n 1.584 * [backup-simplify]: Simplify -2.0 into -2.0 1.584 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.584 * [taylor]: Taking taylor expansion of PI in n 1.584 * [backup-simplify]: Simplify PI into PI 1.584 * [taylor]: Taking taylor expansion of n in n 1.584 * [backup-simplify]: Simplify 0 into 0 1.584 * [backup-simplify]: Simplify 1 into 1 1.584 * [backup-simplify]: Simplify (/ PI 1) into PI 1.585 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.585 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.586 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.586 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.586 * [backup-simplify]: Simplify 0 into 0 1.587 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.587 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.587 * [backup-simplify]: Simplify 0 into 0 1.588 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.588 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.588 * [backup-simplify]: Simplify 0 into 0 1.589 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.590 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.590 * [backup-simplify]: Simplify 0 into 0 1.590 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.591 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.591 * [backup-simplify]: Simplify 0 into 0 1.592 * [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 1.593 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.593 * [backup-simplify]: Simplify 0 into 0 1.593 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.593 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 1.593 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 1.593 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.593 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.593 * [taylor]: Taking taylor expansion of 1.0 in k 1.593 * [backup-simplify]: Simplify 1.0 into 1.0 1.593 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.593 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.593 * [taylor]: Taking taylor expansion of k in k 1.593 * [backup-simplify]: Simplify 0 into 0 1.593 * [backup-simplify]: Simplify 1 into 1 1.593 * [backup-simplify]: Simplify (/ 1 1) into 1 1.594 * [backup-simplify]: Simplify (sqrt 0) into 0 1.594 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.595 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.595 * [taylor]: Taking taylor expansion of 1.0 in k 1.595 * [backup-simplify]: Simplify 1.0 into 1.0 1.595 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.595 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.595 * [taylor]: Taking taylor expansion of k in k 1.595 * [backup-simplify]: Simplify 0 into 0 1.595 * [backup-simplify]: Simplify 1 into 1 1.595 * [backup-simplify]: Simplify (/ 1 1) into 1 1.595 * [backup-simplify]: Simplify (sqrt 0) into 0 1.596 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.596 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.596 * [backup-simplify]: Simplify 0 into 0 1.597 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.597 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.598 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.599 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.600 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.601 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.601 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.603 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.604 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.605 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.605 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 1.606 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 1.606 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.606 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.606 * [taylor]: Taking taylor expansion of 1.0 in k 1.606 * [backup-simplify]: Simplify 1.0 into 1.0 1.606 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.606 * [taylor]: Taking taylor expansion of k in k 1.606 * [backup-simplify]: Simplify 0 into 0 1.606 * [backup-simplify]: Simplify 1 into 1 1.606 * [backup-simplify]: Simplify (sqrt 0) into 0 1.607 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.607 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.607 * [taylor]: Taking taylor expansion of 1.0 in k 1.607 * [backup-simplify]: Simplify 1.0 into 1.0 1.607 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.607 * [taylor]: Taking taylor expansion of k in k 1.607 * [backup-simplify]: Simplify 0 into 0 1.607 * [backup-simplify]: Simplify 1 into 1 1.607 * [backup-simplify]: Simplify (sqrt 0) into 0 1.608 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.608 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.608 * [backup-simplify]: Simplify 0 into 0 1.609 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.609 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.611 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.612 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.612 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.614 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.615 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.615 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.616 * [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)))))))) 1.617 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 1.617 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.617 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.617 * [taylor]: Taking taylor expansion of 1.0 in k 1.617 * [backup-simplify]: Simplify 1.0 into 1.0 1.617 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.617 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.617 * [taylor]: Taking taylor expansion of -1 in k 1.617 * [backup-simplify]: Simplify -1 into -1 1.617 * [taylor]: Taking taylor expansion of k in k 1.617 * [backup-simplify]: Simplify 0 into 0 1.617 * [backup-simplify]: Simplify 1 into 1 1.617 * [backup-simplify]: Simplify (/ -1 1) into -1 1.617 * [backup-simplify]: Simplify (sqrt 0) into 0 1.618 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.618 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.618 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.618 * [taylor]: Taking taylor expansion of 1.0 in k 1.618 * [backup-simplify]: Simplify 1.0 into 1.0 1.618 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.618 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.618 * [taylor]: Taking taylor expansion of -1 in k 1.618 * [backup-simplify]: Simplify -1 into -1 1.618 * [taylor]: Taking taylor expansion of k in k 1.618 * [backup-simplify]: Simplify 0 into 0 1.618 * [backup-simplify]: Simplify 1 into 1 1.619 * [backup-simplify]: Simplify (/ -1 1) into -1 1.619 * [backup-simplify]: Simplify (sqrt 0) into 0 1.620 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.620 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.620 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.620 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.622 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.623 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1.624 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.624 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.626 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.629 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1.629 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.629 * [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))))) 1.630 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 1.630 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 1.630 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.630 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.630 * [taylor]: Taking taylor expansion of 1.0 in k 1.630 * [backup-simplify]: Simplify 1.0 into 1.0 1.630 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.630 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.630 * [taylor]: Taking taylor expansion of k in k 1.630 * [backup-simplify]: Simplify 0 into 0 1.630 * [backup-simplify]: Simplify 1 into 1 1.630 * [backup-simplify]: Simplify (/ 1 1) into 1 1.630 * [backup-simplify]: Simplify (sqrt 0) into 0 1.631 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.631 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.631 * [taylor]: Taking taylor expansion of 1.0 in k 1.631 * [backup-simplify]: Simplify 1.0 into 1.0 1.631 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.631 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.631 * [taylor]: Taking taylor expansion of k in k 1.631 * [backup-simplify]: Simplify 0 into 0 1.631 * [backup-simplify]: Simplify 1 into 1 1.631 * [backup-simplify]: Simplify (/ 1 1) into 1 1.632 * [backup-simplify]: Simplify (sqrt 0) into 0 1.632 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.633 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.633 * [backup-simplify]: Simplify 0 into 0 1.633 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.634 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.634 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.636 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.637 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.637 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.637 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.640 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.641 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.641 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.642 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 1.642 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 1.642 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.642 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.642 * [taylor]: Taking taylor expansion of 1.0 in k 1.642 * [backup-simplify]: Simplify 1.0 into 1.0 1.642 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.642 * [taylor]: Taking taylor expansion of k in k 1.642 * [backup-simplify]: Simplify 0 into 0 1.642 * [backup-simplify]: Simplify 1 into 1 1.642 * [backup-simplify]: Simplify (sqrt 0) into 0 1.643 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.643 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.643 * [taylor]: Taking taylor expansion of 1.0 in k 1.643 * [backup-simplify]: Simplify 1.0 into 1.0 1.643 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.643 * [taylor]: Taking taylor expansion of k in k 1.643 * [backup-simplify]: Simplify 0 into 0 1.643 * [backup-simplify]: Simplify 1 into 1 1.643 * [backup-simplify]: Simplify (sqrt 0) into 0 1.644 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.644 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.644 * [backup-simplify]: Simplify 0 into 0 1.645 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.645 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.647 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.648 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.648 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.651 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.658 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.659 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.660 * [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)))))))) 1.660 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 1.660 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.660 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.660 * [taylor]: Taking taylor expansion of 1.0 in k 1.660 * [backup-simplify]: Simplify 1.0 into 1.0 1.660 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.660 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.660 * [taylor]: Taking taylor expansion of -1 in k 1.660 * [backup-simplify]: Simplify -1 into -1 1.660 * [taylor]: Taking taylor expansion of k in k 1.660 * [backup-simplify]: Simplify 0 into 0 1.660 * [backup-simplify]: Simplify 1 into 1 1.660 * [backup-simplify]: Simplify (/ -1 1) into -1 1.661 * [backup-simplify]: Simplify (sqrt 0) into 0 1.661 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.662 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.662 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.662 * [taylor]: Taking taylor expansion of 1.0 in k 1.662 * [backup-simplify]: Simplify 1.0 into 1.0 1.662 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.662 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.662 * [taylor]: Taking taylor expansion of -1 in k 1.662 * [backup-simplify]: Simplify -1 into -1 1.662 * [taylor]: Taking taylor expansion of k in k 1.662 * [backup-simplify]: Simplify 0 into 0 1.662 * [backup-simplify]: Simplify 1 into 1 1.662 * [backup-simplify]: Simplify (/ -1 1) into -1 1.662 * [backup-simplify]: Simplify (sqrt 0) into 0 1.663 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.663 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.663 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.664 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.665 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.667 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1.667 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.667 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.669 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.672 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1.672 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.673 * [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))))) 1.673 * * * [progress]: simplifying candidates 1.675 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (+ (* 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))))) 1.676 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (log1p (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (+ (+ (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)) (expm1 (* (* h0 h4) h3)) (log1p (* (* h0 h4) h3)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (expm1 (/ h2 (sqrt h1))) (log1p (/ h2 (sqrt h1))) (- (log h2) (log (sqrt h1))) (log (/ h2 (sqrt h1))) (exp (/ h2 (sqrt h1))) (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (cbrt (/ h2 (sqrt h1))) (cbrt (/ h2 (sqrt h1)))) (cbrt (/ h2 (sqrt h1))) (* (* (/ h2 (sqrt h1)) (/ h2 (sqrt h1))) (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (- h2) (- (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (cbrt h2) (cbrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (cbrt h2) (sqrt (cbrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt 1)) (/ (cbrt h2) (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) 1) (/ (cbrt h2) (sqrt h1)) (/ (sqrt h2) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (sqrt h2) (cbrt (sqrt h1))) (/ (sqrt h2) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (sqrt h2) (sqrt (cbrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt 1)) (/ (sqrt h2) (sqrt h1)) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) 1) (/ (sqrt h2) (sqrt h1)) (/ 1 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (cbrt (sqrt h1))) (/ 1 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (cbrt h1))) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 (sqrt 1)) (/ h2 (sqrt h1)) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 1) (/ h2 (sqrt h1)) (/ 1 (sqrt h1)) (/ (sqrt h1) h2) (/ h2 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (sqrt h1))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h1))) (/ h2 1) (/ (sqrt h1) (cbrt h2)) (/ (sqrt h1) (sqrt h2)) (/ (sqrt h1) h2) (expm1 (/ h2 (sqrt h1))) (log1p (/ h2 (sqrt h1))) (- (log h2) (log (sqrt h1))) (log (/ h2 (sqrt h1))) (exp (/ h2 (sqrt h1))) (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (cbrt (/ h2 (sqrt h1))) (cbrt (/ h2 (sqrt h1)))) (cbrt (/ h2 (sqrt h1))) (* (* (/ h2 (sqrt h1)) (/ h2 (sqrt h1))) (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (- h2) (- (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (cbrt h2) (cbrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (cbrt h2) (sqrt (cbrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt 1)) (/ (cbrt h2) (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) 1) (/ (cbrt h2) (sqrt h1)) (/ (sqrt h2) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (sqrt h2) (cbrt (sqrt h1))) (/ (sqrt h2) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (sqrt h2) (sqrt (cbrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt 1)) (/ (sqrt h2) (sqrt h1)) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) 1) (/ (sqrt h2) (sqrt h1)) (/ 1 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (cbrt (sqrt h1))) (/ 1 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (cbrt h1))) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 (sqrt 1)) (/ h2 (sqrt h1)) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 1) (/ h2 (sqrt h1)) (/ 1 (sqrt h1)) (/ (sqrt h1) h2) (/ h2 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (sqrt h1))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h1))) (/ h2 1) (/ (sqrt h1) (cbrt h2)) (/ (sqrt h1) (sqrt h2)) (/ (sqrt h1) h2) (- (+ (* 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))))) 1.682 * * [simplify]: iteration 0 : 579 enodes (cost 912 ) 1.691 * * [simplify]: iteration 1 : 2248 enodes (cost 843 ) 1.730 * * [simplify]: iteration 2 : 5001 enodes (cost 807 ) 1.734 * * * [progress]: adding candidates to table 2.176 * * [progress]: iteration 3 / 4 2.176 * * * [progress]: picking best candidate 2.194 * * * * [pick]: Picked # 2.194 * * * [progress]: localizing error 2.208 * * * [progress]: generating rewritten candidates 2.208 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 2.233 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 2.261 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 2.304 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1) 2.334 * * * [progress]: generating series expansions 2.334 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 2.335 * [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))) 2.335 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.335 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.335 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.335 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.335 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.335 * [taylor]: Taking taylor expansion of 0.25 in k 2.335 * [backup-simplify]: Simplify 0.25 into 0.25 2.335 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.335 * [taylor]: Taking taylor expansion of 1.0 in k 2.335 * [backup-simplify]: Simplify 1.0 into 1.0 2.335 * [taylor]: Taking taylor expansion of k in k 2.335 * [backup-simplify]: Simplify 0 into 0 2.335 * [backup-simplify]: Simplify 1 into 1 2.335 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.335 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.335 * [taylor]: Taking taylor expansion of 2.0 in k 2.335 * [backup-simplify]: Simplify 2.0 into 2.0 2.335 * [taylor]: Taking taylor expansion of (* n PI) in k 2.335 * [taylor]: Taking taylor expansion of n in k 2.335 * [backup-simplify]: Simplify n into n 2.335 * [taylor]: Taking taylor expansion of PI in k 2.335 * [backup-simplify]: Simplify PI into PI 2.336 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.336 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.336 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.336 * [backup-simplify]: Simplify (- 0) into 0 2.336 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.336 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.336 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.337 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.337 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.337 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.337 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.337 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.337 * [taylor]: Taking taylor expansion of 0.25 in n 2.337 * [backup-simplify]: Simplify 0.25 into 0.25 2.337 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.337 * [taylor]: Taking taylor expansion of 1.0 in n 2.337 * [backup-simplify]: Simplify 1.0 into 1.0 2.337 * [taylor]: Taking taylor expansion of k in n 2.337 * [backup-simplify]: Simplify k into k 2.337 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.337 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.337 * [taylor]: Taking taylor expansion of 2.0 in n 2.337 * [backup-simplify]: Simplify 2.0 into 2.0 2.337 * [taylor]: Taking taylor expansion of (* n PI) in n 2.337 * [taylor]: Taking taylor expansion of n in n 2.337 * [backup-simplify]: Simplify 0 into 0 2.337 * [backup-simplify]: Simplify 1 into 1 2.337 * [taylor]: Taking taylor expansion of PI in n 2.337 * [backup-simplify]: Simplify PI into PI 2.337 * [backup-simplify]: Simplify (* 0 PI) into 0 2.337 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.338 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.339 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.340 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.340 * [backup-simplify]: Simplify (- k) into (- k) 2.340 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.340 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.341 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.342 * [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)))) 2.342 * [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))))) 2.342 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.342 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.342 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.342 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.342 * [taylor]: Taking taylor expansion of 0.25 in n 2.342 * [backup-simplify]: Simplify 0.25 into 0.25 2.342 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.342 * [taylor]: Taking taylor expansion of 1.0 in n 2.342 * [backup-simplify]: Simplify 1.0 into 1.0 2.342 * [taylor]: Taking taylor expansion of k in n 2.342 * [backup-simplify]: Simplify k into k 2.343 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.343 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.343 * [taylor]: Taking taylor expansion of 2.0 in n 2.343 * [backup-simplify]: Simplify 2.0 into 2.0 2.343 * [taylor]: Taking taylor expansion of (* n PI) in n 2.343 * [taylor]: Taking taylor expansion of n in n 2.343 * [backup-simplify]: Simplify 0 into 0 2.343 * [backup-simplify]: Simplify 1 into 1 2.343 * [taylor]: Taking taylor expansion of PI in n 2.343 * [backup-simplify]: Simplify PI into PI 2.343 * [backup-simplify]: Simplify (* 0 PI) into 0 2.343 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.344 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.345 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.346 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.346 * [backup-simplify]: Simplify (- k) into (- k) 2.346 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.346 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.347 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.347 * [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)))) 2.348 * [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))))) 2.348 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.348 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.348 * [taylor]: Taking taylor expansion of 0.25 in k 2.348 * [backup-simplify]: Simplify 0.25 into 0.25 2.348 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.348 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.348 * [taylor]: Taking taylor expansion of 1.0 in k 2.348 * [backup-simplify]: Simplify 1.0 into 1.0 2.348 * [taylor]: Taking taylor expansion of k in k 2.348 * [backup-simplify]: Simplify 0 into 0 2.348 * [backup-simplify]: Simplify 1 into 1 2.348 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.348 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.348 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.348 * [taylor]: Taking taylor expansion of 2.0 in k 2.348 * [backup-simplify]: Simplify 2.0 into 2.0 2.348 * [taylor]: Taking taylor expansion of PI in k 2.348 * [backup-simplify]: Simplify PI into PI 2.349 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.349 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.349 * [taylor]: Taking taylor expansion of (log n) in k 2.349 * [taylor]: Taking taylor expansion of n in k 2.349 * [backup-simplify]: Simplify n into n 2.349 * [backup-simplify]: Simplify (log n) into (log n) 2.350 * [backup-simplify]: Simplify (- 0) into 0 2.350 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.351 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.351 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.352 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.352 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.353 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.354 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.354 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.355 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.355 * [backup-simplify]: Simplify (- 0) into 0 2.356 * [backup-simplify]: Simplify (+ 0 0) into 0 2.356 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.357 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.357 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.359 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.359 * [taylor]: Taking taylor expansion of 0 in k 2.359 * [backup-simplify]: Simplify 0 into 0 2.359 * [backup-simplify]: Simplify 0 into 0 2.359 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.360 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.360 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.361 * [backup-simplify]: Simplify (+ 0 0) into 0 2.361 * [backup-simplify]: Simplify (- 1) into -1 2.361 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.362 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.363 * [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)))) 2.365 * [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)))))) 2.367 * [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)))))) 2.368 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.368 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.370 * [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 2.370 * [backup-simplify]: Simplify (- 0) into 0 2.370 * [backup-simplify]: Simplify (+ 0 0) into 0 2.377 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.378 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.379 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.380 * [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 2.380 * [taylor]: Taking taylor expansion of 0 in k 2.380 * [backup-simplify]: Simplify 0 into 0 2.380 * [backup-simplify]: Simplify 0 into 0 2.380 * [backup-simplify]: Simplify 0 into 0 2.381 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.382 * [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 2.384 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.384 * [backup-simplify]: Simplify (+ 0 0) into 0 2.384 * [backup-simplify]: Simplify (- 0) into 0 2.384 * [backup-simplify]: Simplify (+ 0 0) into 0 2.386 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.387 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.389 * [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))))) 2.392 * [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))))) 2.398 * [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)))))) 2.398 * [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)))) 2.398 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.398 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.399 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.399 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.399 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) 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 (- 1.0 (/ 1 k)) in k 2.399 * [taylor]: Taking taylor expansion of 1.0 in k 2.399 * [backup-simplify]: Simplify 1.0 into 1.0 2.399 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.399 * [taylor]: Taking taylor expansion of k in k 2.399 * [backup-simplify]: Simplify 0 into 0 2.399 * [backup-simplify]: Simplify 1 into 1 2.399 * [backup-simplify]: Simplify (/ 1 1) into 1 2.399 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.399 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.399 * [taylor]: Taking taylor expansion of 2.0 in k 2.399 * [backup-simplify]: Simplify 2.0 into 2.0 2.399 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.399 * [taylor]: Taking taylor expansion of PI in k 2.399 * [backup-simplify]: Simplify PI into PI 2.399 * [taylor]: Taking taylor expansion of n in k 2.399 * [backup-simplify]: Simplify n into n 2.399 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.399 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.399 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.399 * [backup-simplify]: Simplify (- 1) into -1 2.400 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.400 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.400 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.400 * [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))))) 2.400 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.400 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.400 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.400 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.400 * [taylor]: Taking taylor expansion of 0.25 in n 2.400 * [backup-simplify]: Simplify 0.25 into 0.25 2.400 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.400 * [taylor]: Taking taylor expansion of 1.0 in n 2.400 * [backup-simplify]: Simplify 1.0 into 1.0 2.400 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.400 * [taylor]: Taking taylor expansion of k in n 2.400 * [backup-simplify]: Simplify k into k 2.400 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.400 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.400 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.400 * [taylor]: Taking taylor expansion of 2.0 in n 2.400 * [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 2.401 * [backup-simplify]: Simplify (/ PI 1) into PI 2.401 * [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)) into (- (/ 1 k)) 2.402 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.402 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.403 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.403 * [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)))) 2.404 * [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))))) 2.404 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.404 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.404 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.404 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.404 * [taylor]: Taking taylor expansion of 0.25 in n 2.404 * [backup-simplify]: Simplify 0.25 into 0.25 2.404 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.404 * [taylor]: Taking taylor expansion of 1.0 in n 2.404 * [backup-simplify]: Simplify 1.0 into 1.0 2.404 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.404 * [taylor]: Taking taylor expansion of k in n 2.404 * [backup-simplify]: Simplify k into k 2.404 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.404 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.404 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.404 * [taylor]: Taking taylor expansion of 2.0 in n 2.404 * [backup-simplify]: Simplify 2.0 into 2.0 2.404 * [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 2.405 * [backup-simplify]: Simplify (/ PI 1) into PI 2.405 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.406 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.406 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.406 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.406 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.407 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.407 * [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)))) 2.408 * [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))))) 2.408 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.408 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.408 * [taylor]: Taking taylor expansion of 0.25 in k 2.408 * [backup-simplify]: Simplify 0.25 into 0.25 2.408 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.408 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.408 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.408 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.408 * [taylor]: Taking taylor expansion of 2.0 in k 2.409 * [backup-simplify]: Simplify 2.0 into 2.0 2.409 * [taylor]: Taking taylor expansion of PI in k 2.409 * [backup-simplify]: Simplify PI into PI 2.409 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.409 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.409 * [taylor]: Taking taylor expansion of (log n) in k 2.409 * [taylor]: Taking taylor expansion of n in k 2.409 * [backup-simplify]: Simplify n into n 2.410 * [backup-simplify]: Simplify (log n) into (log n) 2.410 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.410 * [taylor]: Taking taylor expansion of 1.0 in k 2.410 * [backup-simplify]: Simplify 1.0 into 1.0 2.410 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.410 * [taylor]: Taking taylor expansion of k in k 2.410 * [backup-simplify]: Simplify 0 into 0 2.410 * [backup-simplify]: Simplify 1 into 1 2.410 * [backup-simplify]: Simplify (/ 1 1) into 1 2.410 * [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)) 2.411 * [backup-simplify]: Simplify (- 1) into -1 2.411 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.412 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.412 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.413 * [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))))) 2.414 * [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))))) 2.414 * [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) into 0 2.416 * [backup-simplify]: Simplify (+ 0 0) into 0 2.416 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.417 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.418 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.419 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (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 2.420 * [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) into 0 2.423 * [backup-simplify]: Simplify (+ 0 0) into 0 2.423 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) 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 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.427 * [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 2.427 * [taylor]: Taking taylor expansion of 0 in k 2.427 * [backup-simplify]: Simplify 0 into 0 2.427 * [backup-simplify]: Simplify 0 into 0 2.427 * [backup-simplify]: Simplify 0 into 0 2.427 * [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 2.431 * [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 2.431 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.431 * [backup-simplify]: Simplify (- 0) into 0 2.431 * [backup-simplify]: Simplify (+ 0 0) into 0 2.432 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.433 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.435 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.436 * [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 2.436 * [taylor]: Taking taylor expansion of 0 in k 2.436 * [backup-simplify]: Simplify 0 into 0 2.436 * [backup-simplify]: Simplify 0 into 0 2.437 * [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)))) 2.438 * [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))) 2.438 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.438 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.438 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.438 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.438 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.438 * [taylor]: Taking taylor expansion of 0.25 in k 2.438 * [backup-simplify]: Simplify 0.25 into 0.25 2.438 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.438 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.438 * [taylor]: Taking taylor expansion of k in k 2.438 * [backup-simplify]: Simplify 0 into 0 2.438 * [backup-simplify]: Simplify 1 into 1 2.438 * [backup-simplify]: Simplify (/ 1 1) into 1 2.438 * [taylor]: Taking taylor expansion of 1.0 in k 2.438 * [backup-simplify]: Simplify 1.0 into 1.0 2.438 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.438 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.438 * [taylor]: Taking taylor expansion of -2.0 in k 2.438 * [backup-simplify]: Simplify -2.0 into -2.0 2.438 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.438 * [taylor]: Taking taylor expansion of PI in k 2.438 * [backup-simplify]: Simplify PI into PI 2.438 * [taylor]: Taking taylor expansion of n in k 2.438 * [backup-simplify]: Simplify n into n 2.438 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.438 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.438 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.439 * [backup-simplify]: Simplify (+ 1 0) into 1 2.439 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.439 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.439 * [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)))))) 2.439 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.439 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.439 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.439 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.439 * [taylor]: Taking taylor expansion of 0.25 in n 2.439 * [backup-simplify]: Simplify 0.25 into 0.25 2.439 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.439 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.439 * [taylor]: Taking taylor expansion of k in n 2.439 * [backup-simplify]: Simplify k into k 2.439 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.439 * [taylor]: Taking taylor expansion of 1.0 in n 2.439 * [backup-simplify]: Simplify 1.0 into 1.0 2.439 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.439 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.439 * [taylor]: Taking taylor expansion of -2.0 in n 2.440 * [backup-simplify]: Simplify -2.0 into -2.0 2.440 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.440 * [taylor]: Taking taylor expansion of PI in n 2.440 * [backup-simplify]: Simplify PI into PI 2.440 * [taylor]: Taking taylor expansion of n in n 2.440 * [backup-simplify]: Simplify 0 into 0 2.440 * [backup-simplify]: Simplify 1 into 1 2.440 * [backup-simplify]: Simplify (/ PI 1) into PI 2.440 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.441 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.441 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.441 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.442 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.442 * [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)))) 2.443 * [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))))) 2.443 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.443 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.443 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.443 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.443 * [taylor]: Taking taylor expansion of 0.25 in n 2.443 * [backup-simplify]: Simplify 0.25 into 0.25 2.443 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.443 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.443 * [taylor]: Taking taylor expansion of k in n 2.443 * [backup-simplify]: Simplify k into k 2.443 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.443 * [taylor]: Taking taylor expansion of 1.0 in n 2.443 * [backup-simplify]: Simplify 1.0 into 1.0 2.443 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.443 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.444 * [taylor]: Taking taylor expansion of -2.0 in n 2.444 * [backup-simplify]: Simplify -2.0 into -2.0 2.444 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.444 * [taylor]: Taking taylor expansion of PI in n 2.444 * [backup-simplify]: Simplify PI into PI 2.444 * [taylor]: Taking taylor expansion of n in n 2.444 * [backup-simplify]: Simplify 0 into 0 2.444 * [backup-simplify]: Simplify 1 into 1 2.444 * [backup-simplify]: Simplify (/ PI 1) into PI 2.444 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.445 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.445 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.445 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.446 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.447 * [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)))) 2.447 * [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))))) 2.447 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.447 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.447 * [taylor]: Taking taylor expansion of 0.25 in k 2.447 * [backup-simplify]: Simplify 0.25 into 0.25 2.447 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.447 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.447 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.447 * [taylor]: Taking taylor expansion of k in k 2.447 * [backup-simplify]: Simplify 0 into 0 2.447 * [backup-simplify]: Simplify 1 into 1 2.448 * [backup-simplify]: Simplify (/ 1 1) into 1 2.448 * [taylor]: Taking taylor expansion of 1.0 in k 2.448 * [backup-simplify]: Simplify 1.0 into 1.0 2.448 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.448 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.448 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.448 * [taylor]: Taking taylor expansion of -2.0 in k 2.448 * [backup-simplify]: Simplify -2.0 into -2.0 2.448 * [taylor]: Taking taylor expansion of PI in k 2.448 * [backup-simplify]: Simplify PI into PI 2.448 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.449 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.449 * [taylor]: Taking taylor expansion of (log n) in k 2.449 * [taylor]: Taking taylor expansion of n in k 2.449 * [backup-simplify]: Simplify n into n 2.449 * [backup-simplify]: Simplify (log n) into (log n) 2.449 * [backup-simplify]: Simplify (+ 1 0) into 1 2.449 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.450 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.450 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.451 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.452 * [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))))) 2.452 * [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))))) 2.453 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.453 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.454 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.454 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.455 * [backup-simplify]: Simplify (+ 0 0) into 0 2.455 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.456 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.457 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.458 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.458 * [taylor]: Taking taylor expansion of 0 in k 2.458 * [backup-simplify]: Simplify 0 into 0 2.458 * [backup-simplify]: Simplify 0 into 0 2.458 * [backup-simplify]: Simplify 0 into 0 2.458 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.459 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.461 * [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 2.461 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.461 * [backup-simplify]: Simplify (+ 0 0) into 0 2.461 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.462 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.463 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.465 * [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 2.465 * [taylor]: Taking taylor expansion of 0 in k 2.465 * [backup-simplify]: Simplify 0 into 0 2.465 * [backup-simplify]: Simplify 0 into 0 2.465 * [backup-simplify]: Simplify 0 into 0 2.465 * [backup-simplify]: Simplify 0 into 0 2.465 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.466 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.475 * [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 2.475 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.476 * [backup-simplify]: Simplify (+ 0 0) into 0 2.477 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.478 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.479 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.480 * [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 2.480 * [taylor]: Taking taylor expansion of 0 in k 2.480 * [backup-simplify]: Simplify 0 into 0 2.480 * [backup-simplify]: Simplify 0 into 0 2.481 * [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)))))) 2.481 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 2.482 * [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))) 2.482 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.482 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.482 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.482 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.482 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.482 * [taylor]: Taking taylor expansion of 0.25 in k 2.482 * [backup-simplify]: Simplify 0.25 into 0.25 2.482 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.482 * [taylor]: Taking taylor expansion of 1.0 in k 2.482 * [backup-simplify]: Simplify 1.0 into 1.0 2.482 * [taylor]: Taking taylor expansion of k in k 2.482 * [backup-simplify]: Simplify 0 into 0 2.482 * [backup-simplify]: Simplify 1 into 1 2.482 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.482 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.482 * [taylor]: Taking taylor expansion of 2.0 in k 2.482 * [backup-simplify]: Simplify 2.0 into 2.0 2.482 * [taylor]: Taking taylor expansion of (* n PI) in k 2.482 * [taylor]: Taking taylor expansion of n in k 2.482 * [backup-simplify]: Simplify n into n 2.482 * [taylor]: Taking taylor expansion of PI in k 2.482 * [backup-simplify]: Simplify PI into PI 2.482 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.482 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.482 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.482 * [backup-simplify]: Simplify (- 0) into 0 2.483 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.483 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.483 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.483 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.483 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.483 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.483 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.483 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.483 * [taylor]: Taking taylor expansion of 0.25 in n 2.483 * [backup-simplify]: Simplify 0.25 into 0.25 2.483 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.483 * [taylor]: Taking taylor expansion of 1.0 in n 2.483 * [backup-simplify]: Simplify 1.0 into 1.0 2.483 * [taylor]: Taking taylor expansion of k in n 2.483 * [backup-simplify]: Simplify k into k 2.483 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.483 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.483 * [taylor]: Taking taylor expansion of 2.0 in n 2.483 * [backup-simplify]: Simplify 2.0 into 2.0 2.483 * [taylor]: Taking taylor expansion of (* n PI) in n 2.483 * [taylor]: Taking taylor expansion of n in n 2.483 * [backup-simplify]: Simplify 0 into 0 2.483 * [backup-simplify]: Simplify 1 into 1 2.483 * [taylor]: Taking taylor expansion of PI in n 2.483 * [backup-simplify]: Simplify PI into PI 2.484 * [backup-simplify]: Simplify (* 0 PI) into 0 2.484 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.485 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.486 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.487 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.487 * [backup-simplify]: Simplify (- k) into (- k) 2.487 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.487 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.487 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.488 * [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)))) 2.489 * [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))))) 2.489 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.489 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.489 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.489 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.489 * [taylor]: Taking taylor expansion of 0.25 in n 2.489 * [backup-simplify]: Simplify 0.25 into 0.25 2.489 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.489 * [taylor]: Taking taylor expansion of 1.0 in n 2.489 * [backup-simplify]: Simplify 1.0 into 1.0 2.489 * [taylor]: Taking taylor expansion of k in n 2.489 * [backup-simplify]: Simplify k into k 2.489 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.489 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.489 * [taylor]: Taking taylor expansion of 2.0 in n 2.489 * [backup-simplify]: Simplify 2.0 into 2.0 2.489 * [taylor]: Taking taylor expansion of (* n PI) in n 2.489 * [taylor]: Taking taylor expansion of n in n 2.489 * [backup-simplify]: Simplify 0 into 0 2.489 * [backup-simplify]: Simplify 1 into 1 2.489 * [taylor]: Taking taylor expansion of PI in n 2.489 * [backup-simplify]: Simplify PI into PI 2.490 * [backup-simplify]: Simplify (* 0 PI) into 0 2.490 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.491 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.492 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.493 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.493 * [backup-simplify]: Simplify (- k) into (- k) 2.493 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.493 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.494 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.495 * [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)))) 2.495 * [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))))) 2.495 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.495 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.496 * [taylor]: Taking taylor expansion of 0.25 in k 2.496 * [backup-simplify]: Simplify 0.25 into 0.25 2.496 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.496 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.496 * [taylor]: Taking taylor expansion of 1.0 in k 2.496 * [backup-simplify]: Simplify 1.0 into 1.0 2.496 * [taylor]: Taking taylor expansion of k in k 2.496 * [backup-simplify]: Simplify 0 into 0 2.496 * [backup-simplify]: Simplify 1 into 1 2.496 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.496 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.496 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.496 * [taylor]: Taking taylor expansion of 2.0 in k 2.496 * [backup-simplify]: Simplify 2.0 into 2.0 2.496 * [taylor]: Taking taylor expansion of PI in k 2.496 * [backup-simplify]: Simplify PI into PI 2.496 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.497 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.497 * [taylor]: Taking taylor expansion of (log n) in k 2.497 * [taylor]: Taking taylor expansion of n in k 2.497 * [backup-simplify]: Simplify n into n 2.497 * [backup-simplify]: Simplify (log n) into (log n) 2.497 * [backup-simplify]: Simplify (- 0) into 0 2.497 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.498 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.499 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.499 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.500 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.500 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.501 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.502 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.503 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.503 * [backup-simplify]: Simplify (- 0) into 0 2.503 * [backup-simplify]: Simplify (+ 0 0) into 0 2.503 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 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 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.506 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.506 * [taylor]: Taking taylor expansion of 0 in k 2.506 * [backup-simplify]: Simplify 0 into 0 2.506 * [backup-simplify]: Simplify 0 into 0 2.506 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.507 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.508 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.508 * [backup-simplify]: Simplify (+ 0 0) into 0 2.508 * [backup-simplify]: Simplify (- 1) into -1 2.509 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.509 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.511 * [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)))) 2.513 * [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)))))) 2.514 * [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)))))) 2.515 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.516 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.517 * [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 2.518 * [backup-simplify]: Simplify (- 0) into 0 2.518 * [backup-simplify]: Simplify (+ 0 0) into 0 2.518 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.519 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.520 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.521 * [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 2.521 * [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 2.522 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.524 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.525 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.525 * [backup-simplify]: Simplify (+ 0 0) into 0 2.525 * [backup-simplify]: Simplify (- 0) into 0 2.525 * [backup-simplify]: Simplify (+ 0 0) into 0 2.526 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.528 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.530 * [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))))) 2.533 * [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))))) 2.539 * [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)))))) 2.540 * [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)))) 2.540 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.540 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.540 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.540 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.540 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.540 * [taylor]: Taking taylor expansion of 0.25 in k 2.540 * [backup-simplify]: Simplify 0.25 into 0.25 2.540 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.540 * [taylor]: Taking taylor expansion of 1.0 in k 2.540 * [backup-simplify]: Simplify 1.0 into 1.0 2.540 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.540 * [taylor]: Taking taylor expansion of k in k 2.540 * [backup-simplify]: Simplify 0 into 0 2.540 * [backup-simplify]: Simplify 1 into 1 2.540 * [backup-simplify]: Simplify (/ 1 1) into 1 2.540 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.540 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.540 * [taylor]: Taking taylor expansion of 2.0 in k 2.540 * [backup-simplify]: Simplify 2.0 into 2.0 2.540 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.540 * [taylor]: Taking taylor expansion of PI in k 2.541 * [backup-simplify]: Simplify PI into PI 2.541 * [taylor]: Taking taylor expansion of n in k 2.541 * [backup-simplify]: Simplify n into n 2.541 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.541 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.541 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.541 * [backup-simplify]: Simplify (- 1) into -1 2.541 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.541 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.541 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.542 * [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))))) 2.542 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.542 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.542 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.542 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.542 * [taylor]: Taking taylor expansion of 0.25 in n 2.542 * [backup-simplify]: Simplify 0.25 into 0.25 2.542 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.542 * [taylor]: Taking taylor expansion of 1.0 in n 2.542 * [backup-simplify]: Simplify 1.0 into 1.0 2.542 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.542 * [taylor]: Taking taylor expansion of k in n 2.542 * [backup-simplify]: Simplify k into k 2.542 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.542 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.542 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.542 * [taylor]: Taking taylor expansion of 2.0 in n 2.542 * [backup-simplify]: Simplify 2.0 into 2.0 2.542 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.542 * [taylor]: Taking taylor expansion of PI in n 2.542 * [backup-simplify]: Simplify PI into PI 2.542 * [taylor]: Taking taylor expansion of n in n 2.542 * [backup-simplify]: Simplify 0 into 0 2.542 * [backup-simplify]: Simplify 1 into 1 2.542 * [backup-simplify]: Simplify (/ PI 1) into PI 2.543 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.543 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.543 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.543 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.543 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.544 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.545 * [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)))) 2.546 * [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))))) 2.546 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.546 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.546 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.546 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.546 * [taylor]: Taking taylor expansion of 0.25 in n 2.546 * [backup-simplify]: Simplify 0.25 into 0.25 2.546 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.546 * [taylor]: Taking taylor expansion of 1.0 in n 2.546 * [backup-simplify]: Simplify 1.0 into 1.0 2.546 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.546 * [taylor]: Taking taylor expansion of k in n 2.546 * [backup-simplify]: Simplify k into k 2.546 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.546 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.546 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.546 * [taylor]: Taking taylor expansion of 2.0 in n 2.546 * [backup-simplify]: Simplify 2.0 into 2.0 2.546 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.546 * [taylor]: Taking taylor expansion of PI in n 2.546 * [backup-simplify]: Simplify PI into PI 2.546 * [taylor]: Taking taylor expansion of n in n 2.546 * [backup-simplify]: Simplify 0 into 0 2.546 * [backup-simplify]: Simplify 1 into 1 2.546 * [backup-simplify]: Simplify (/ PI 1) into PI 2.547 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.547 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.547 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.547 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.547 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.549 * [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)))) 2.550 * [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))))) 2.550 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.550 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.550 * [taylor]: Taking taylor expansion of 0.25 in k 2.550 * [backup-simplify]: Simplify 0.25 into 0.25 2.550 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.550 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.550 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.550 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.550 * [taylor]: Taking taylor expansion of 2.0 in k 2.550 * [backup-simplify]: Simplify 2.0 into 2.0 2.550 * [taylor]: Taking taylor expansion of PI in k 2.550 * [backup-simplify]: Simplify PI into PI 2.550 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.551 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.551 * [taylor]: Taking taylor expansion of (log n) in k 2.551 * [taylor]: Taking taylor expansion of n in k 2.551 * [backup-simplify]: Simplify n into n 2.551 * [backup-simplify]: Simplify (log n) into (log n) 2.551 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.551 * [taylor]: Taking taylor expansion of 1.0 in k 2.551 * [backup-simplify]: Simplify 1.0 into 1.0 2.551 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.551 * [taylor]: Taking taylor expansion of k in k 2.551 * [backup-simplify]: Simplify 0 into 0 2.551 * [backup-simplify]: Simplify 1 into 1 2.551 * [backup-simplify]: Simplify (/ 1 1) into 1 2.551 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.552 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.552 * [backup-simplify]: Simplify (- 1) into -1 2.552 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.553 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.554 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.554 * [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))))) 2.555 * [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))))) 2.556 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.556 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.557 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.557 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.557 * [backup-simplify]: Simplify (- 0) into 0 2.558 * [backup-simplify]: Simplify (+ 0 0) into 0 2.558 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.559 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.561 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.561 * [taylor]: Taking taylor expansion of 0 in k 2.561 * [backup-simplify]: Simplify 0 into 0 2.561 * [backup-simplify]: Simplify 0 into 0 2.561 * [backup-simplify]: Simplify 0 into 0 2.561 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.562 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.563 * [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 2.564 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.564 * [backup-simplify]: Simplify (- 0) into 0 2.564 * [backup-simplify]: Simplify (+ 0 0) into 0 2.572 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.573 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.574 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.575 * [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 2.575 * [taylor]: Taking taylor expansion of 0 in k 2.575 * [backup-simplify]: Simplify 0 into 0 2.575 * [backup-simplify]: Simplify 0 into 0 2.575 * [backup-simplify]: Simplify 0 into 0 2.575 * [backup-simplify]: Simplify 0 into 0 2.576 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.576 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.579 * [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 2.580 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.580 * [backup-simplify]: Simplify (- 0) into 0 2.580 * [backup-simplify]: Simplify (+ 0 0) into 0 2.581 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.582 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.583 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.584 * [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 2.584 * [taylor]: Taking taylor expansion of 0 in k 2.584 * [backup-simplify]: Simplify 0 into 0 2.584 * [backup-simplify]: Simplify 0 into 0 2.586 * [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)))) 2.586 * [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))) 2.586 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.586 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.586 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.586 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.586 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.586 * [taylor]: Taking taylor expansion of 0.25 in k 2.586 * [backup-simplify]: Simplify 0.25 into 0.25 2.586 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.586 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.586 * [taylor]: Taking taylor expansion of k in k 2.586 * [backup-simplify]: Simplify 0 into 0 2.586 * [backup-simplify]: Simplify 1 into 1 2.587 * [backup-simplify]: Simplify (/ 1 1) into 1 2.587 * [taylor]: Taking taylor expansion of 1.0 in k 2.587 * [backup-simplify]: Simplify 1.0 into 1.0 2.587 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.587 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.587 * [taylor]: Taking taylor expansion of -2.0 in k 2.587 * [backup-simplify]: Simplify -2.0 into -2.0 2.587 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.587 * [taylor]: Taking taylor expansion of PI in k 2.587 * [backup-simplify]: Simplify PI into PI 2.587 * [taylor]: Taking taylor expansion of n in k 2.587 * [backup-simplify]: Simplify n into n 2.587 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.587 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.587 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.587 * [backup-simplify]: Simplify (+ 1 0) into 1 2.588 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.588 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.588 * [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)))))) 2.588 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.588 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.588 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.588 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.588 * [taylor]: Taking taylor expansion of 0.25 in n 2.588 * [backup-simplify]: Simplify 0.25 into 0.25 2.588 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.588 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.588 * [taylor]: Taking taylor expansion of k in n 2.588 * [backup-simplify]: Simplify k into k 2.588 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.588 * [taylor]: Taking taylor expansion of 1.0 in n 2.588 * [backup-simplify]: Simplify 1.0 into 1.0 2.588 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.588 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.588 * [taylor]: Taking taylor expansion of -2.0 in n 2.588 * [backup-simplify]: Simplify -2.0 into -2.0 2.588 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.588 * [taylor]: Taking taylor expansion of PI in n 2.588 * [backup-simplify]: Simplify PI into PI 2.588 * [taylor]: Taking taylor expansion of n in n 2.588 * [backup-simplify]: Simplify 0 into 0 2.588 * [backup-simplify]: Simplify 1 into 1 2.589 * [backup-simplify]: Simplify (/ PI 1) into PI 2.589 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.589 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.589 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.590 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.590 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.591 * [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)))) 2.592 * [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))))) 2.592 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.592 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.592 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.592 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.592 * [taylor]: Taking taylor expansion of 0.25 in n 2.592 * [backup-simplify]: Simplify 0.25 into 0.25 2.592 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.592 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.592 * [taylor]: Taking taylor expansion of k in n 2.592 * [backup-simplify]: Simplify k into k 2.592 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.592 * [taylor]: Taking taylor expansion of 1.0 in n 2.592 * [backup-simplify]: Simplify 1.0 into 1.0 2.592 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.592 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.592 * [taylor]: Taking taylor expansion of -2.0 in n 2.592 * [backup-simplify]: Simplify -2.0 into -2.0 2.592 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.592 * [taylor]: Taking taylor expansion of PI in n 2.592 * [backup-simplify]: Simplify PI into PI 2.592 * [taylor]: Taking taylor expansion of n in n 2.592 * [backup-simplify]: Simplify 0 into 0 2.592 * [backup-simplify]: Simplify 1 into 1 2.593 * [backup-simplify]: Simplify (/ PI 1) into PI 2.593 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.593 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.594 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.594 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 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 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.596 * [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))))) 2.596 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.596 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.596 * [taylor]: Taking taylor expansion of 0.25 in k 2.596 * [backup-simplify]: Simplify 0.25 into 0.25 2.596 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.596 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.596 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.596 * [taylor]: Taking taylor expansion of k in k 2.596 * [backup-simplify]: Simplify 0 into 0 2.596 * [backup-simplify]: Simplify 1 into 1 2.596 * [backup-simplify]: Simplify (/ 1 1) into 1 2.596 * [taylor]: Taking taylor expansion of 1.0 in k 2.597 * [backup-simplify]: Simplify 1.0 into 1.0 2.597 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.597 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.597 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.597 * [taylor]: Taking taylor expansion of -2.0 in k 2.597 * [backup-simplify]: Simplify -2.0 into -2.0 2.597 * [taylor]: Taking taylor expansion of PI in k 2.597 * [backup-simplify]: Simplify PI into PI 2.597 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.597 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.598 * [taylor]: Taking taylor expansion of (log n) in k 2.598 * [taylor]: Taking taylor expansion of n in k 2.598 * [backup-simplify]: Simplify n into n 2.598 * [backup-simplify]: Simplify (log n) into (log n) 2.598 * [backup-simplify]: Simplify (+ 1 0) into 1 2.598 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.599 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.599 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.600 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.601 * [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))))) 2.601 * [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))))) 2.602 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.602 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.603 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.603 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.603 * [backup-simplify]: Simplify (+ 0 0) into 0 2.604 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.605 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.605 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.606 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.606 * [taylor]: Taking taylor expansion of 0 in k 2.606 * [backup-simplify]: Simplify 0 into 0 2.607 * [backup-simplify]: Simplify 0 into 0 2.607 * [backup-simplify]: Simplify 0 into 0 2.607 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.608 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.609 * [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 2.609 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.610 * [backup-simplify]: Simplify (+ 0 0) into 0 2.610 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.611 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.612 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.613 * [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 2.613 * [taylor]: Taking taylor expansion of 0 in k 2.613 * [backup-simplify]: Simplify 0 into 0 2.613 * [backup-simplify]: Simplify 0 into 0 2.613 * [backup-simplify]: Simplify 0 into 0 2.613 * [backup-simplify]: Simplify 0 into 0 2.614 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.615 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.618 * [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 2.618 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.618 * [backup-simplify]: Simplify (+ 0 0) into 0 2.619 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.620 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.621 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.622 * [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 2.622 * [taylor]: Taking taylor expansion of 0 in k 2.622 * [backup-simplify]: Simplify 0 into 0 2.622 * [backup-simplify]: Simplify 0 into 0 2.623 * [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)))))) 2.623 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 2.624 * [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) 2.624 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in (n k) around 0 2.624 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in k 2.624 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.624 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.624 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.624 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.624 * [taylor]: Taking taylor expansion of 0.25 in k 2.624 * [backup-simplify]: Simplify 0.25 into 0.25 2.624 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.624 * [taylor]: Taking taylor expansion of 1.0 in k 2.624 * [backup-simplify]: Simplify 1.0 into 1.0 2.624 * [taylor]: Taking taylor expansion of k in k 2.624 * [backup-simplify]: Simplify 0 into 0 2.624 * [backup-simplify]: Simplify 1 into 1 2.624 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.624 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.624 * [taylor]: Taking taylor expansion of 2.0 in k 2.624 * [backup-simplify]: Simplify 2.0 into 2.0 2.624 * [taylor]: Taking taylor expansion of (* n PI) in k 2.624 * [taylor]: Taking taylor expansion of n in k 2.624 * [backup-simplify]: Simplify n into n 2.624 * [taylor]: Taking taylor expansion of PI in k 2.624 * [backup-simplify]: Simplify PI into PI 2.625 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.625 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.625 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.625 * [backup-simplify]: Simplify (- 0) into 0 2.625 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.625 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.625 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.626 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.626 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 2.626 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.626 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.626 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.626 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.626 * [taylor]: Taking taylor expansion of 0.25 in n 2.626 * [backup-simplify]: Simplify 0.25 into 0.25 2.626 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.626 * [taylor]: Taking taylor expansion of 1.0 in n 2.626 * [backup-simplify]: Simplify 1.0 into 1.0 2.626 * [taylor]: Taking taylor expansion of k in n 2.626 * [backup-simplify]: Simplify k into k 2.626 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.626 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.626 * [taylor]: Taking taylor expansion of 2.0 in n 2.626 * [backup-simplify]: Simplify 2.0 into 2.0 2.626 * [taylor]: Taking taylor expansion of (* n PI) in n 2.626 * [taylor]: Taking taylor expansion of n in n 2.626 * [backup-simplify]: Simplify 0 into 0 2.626 * [backup-simplify]: Simplify 1 into 1 2.626 * [taylor]: Taking taylor expansion of PI in n 2.626 * [backup-simplify]: Simplify PI into PI 2.626 * [backup-simplify]: Simplify (* 0 PI) into 0 2.626 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.627 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.628 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.629 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.629 * [backup-simplify]: Simplify (- k) into (- k) 2.629 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.629 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.630 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.630 * [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)))) 2.631 * [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))))) 2.631 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 2.631 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.631 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.631 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.631 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.631 * [taylor]: Taking taylor expansion of 0.25 in n 2.631 * [backup-simplify]: Simplify 0.25 into 0.25 2.631 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.631 * [taylor]: Taking taylor expansion of 1.0 in n 2.631 * [backup-simplify]: Simplify 1.0 into 1.0 2.631 * [taylor]: Taking taylor expansion of k in n 2.631 * [backup-simplify]: Simplify k into k 2.631 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.631 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.631 * [taylor]: Taking taylor expansion of 2.0 in n 2.631 * [backup-simplify]: Simplify 2.0 into 2.0 2.631 * [taylor]: Taking taylor expansion of (* n PI) in n 2.631 * [taylor]: Taking taylor expansion of n in n 2.631 * [backup-simplify]: Simplify 0 into 0 2.631 * [backup-simplify]: Simplify 1 into 1 2.631 * [taylor]: Taking taylor expansion of PI in n 2.631 * [backup-simplify]: Simplify PI into PI 2.632 * [backup-simplify]: Simplify (* 0 PI) into 0 2.632 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.633 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.634 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.634 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.634 * [backup-simplify]: Simplify (- k) into (- k) 2.634 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.634 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.636 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.636 * [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)))) 2.637 * [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))))) 2.638 * [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) 2.638 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2) in k 2.638 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.638 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.638 * [taylor]: Taking taylor expansion of 0.25 in k 2.638 * [backup-simplify]: Simplify 0.25 into 0.25 2.638 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.639 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.639 * [taylor]: Taking taylor expansion of 1.0 in k 2.639 * [backup-simplify]: Simplify 1.0 into 1.0 2.639 * [taylor]: Taking taylor expansion of k in k 2.639 * [backup-simplify]: Simplify 0 into 0 2.639 * [backup-simplify]: Simplify 1 into 1 2.639 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.639 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.639 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.639 * [taylor]: Taking taylor expansion of 2.0 in k 2.639 * [backup-simplify]: Simplify 2.0 into 2.0 2.639 * [taylor]: Taking taylor expansion of PI in k 2.639 * [backup-simplify]: Simplify PI into PI 2.639 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.640 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.640 * [taylor]: Taking taylor expansion of (log n) in k 2.640 * [taylor]: Taking taylor expansion of n in k 2.640 * [backup-simplify]: Simplify n into n 2.640 * [backup-simplify]: Simplify (log n) into (log n) 2.640 * [backup-simplify]: Simplify (- 0) into 0 2.640 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.641 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.641 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.642 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.643 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.644 * [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) 2.645 * [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) 2.645 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.646 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.647 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.647 * [backup-simplify]: Simplify (- 0) into 0 2.647 * [backup-simplify]: Simplify (+ 0 0) into 0 2.648 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.648 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.649 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.650 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.652 * [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 2.652 * [taylor]: Taking taylor expansion of 0 in k 2.652 * [backup-simplify]: Simplify 0 into 0 2.652 * [backup-simplify]: Simplify 0 into 0 2.652 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.653 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.654 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.654 * [backup-simplify]: Simplify (+ 0 0) into 0 2.654 * [backup-simplify]: Simplify (- 1) into -1 2.654 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.655 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.657 * [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)))) 2.658 * [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)))))) 2.669 * [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))))) 2.672 * [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))))) 2.672 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.673 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.675 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.675 * [backup-simplify]: Simplify (- 0) into 0 2.675 * [backup-simplify]: Simplify (+ 0 0) into 0 2.676 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.677 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.677 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.679 * [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 2.680 * [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 2.680 * [taylor]: Taking taylor expansion of 0 in k 2.680 * [backup-simplify]: Simplify 0 into 0 2.680 * [backup-simplify]: Simplify 0 into 0 2.680 * [backup-simplify]: Simplify 0 into 0 2.681 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.683 * [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 2.684 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.684 * [backup-simplify]: Simplify (+ 0 0) into 0 2.684 * [backup-simplify]: Simplify (- 0) into 0 2.684 * [backup-simplify]: Simplify (+ 0 0) into 0 2.686 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.687 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.689 * [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))))) 2.700 * [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))))) 2.705 * [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))))) 2.712 * [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)))))) 2.713 * [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) 2.713 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in (n k) around 0 2.713 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in k 2.713 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.713 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.713 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.714 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.714 * [taylor]: Taking taylor expansion of 0.25 in k 2.714 * [backup-simplify]: Simplify 0.25 into 0.25 2.714 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.714 * [taylor]: Taking taylor expansion of 1.0 in k 2.714 * [backup-simplify]: Simplify 1.0 into 1.0 2.714 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.714 * [taylor]: Taking taylor expansion of k in k 2.714 * [backup-simplify]: Simplify 0 into 0 2.714 * [backup-simplify]: Simplify 1 into 1 2.714 * [backup-simplify]: Simplify (/ 1 1) into 1 2.714 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.714 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.714 * [taylor]: Taking taylor expansion of 2.0 in k 2.714 * [backup-simplify]: Simplify 2.0 into 2.0 2.714 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.714 * [taylor]: Taking taylor expansion of PI in k 2.714 * [backup-simplify]: Simplify PI into PI 2.714 * [taylor]: Taking taylor expansion of n in k 2.714 * [backup-simplify]: Simplify n into n 2.714 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.714 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.714 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.714 * [backup-simplify]: Simplify (- 1) into -1 2.715 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.715 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.715 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.715 * [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))))) 2.715 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 2.715 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.715 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.715 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.715 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.715 * [taylor]: Taking taylor expansion of 0.25 in n 2.715 * [backup-simplify]: Simplify 0.25 into 0.25 2.715 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.715 * [taylor]: Taking taylor expansion of 1.0 in n 2.715 * [backup-simplify]: Simplify 1.0 into 1.0 2.715 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.715 * [taylor]: Taking taylor expansion of k in n 2.715 * [backup-simplify]: Simplify k into k 2.715 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.715 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.715 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.715 * [taylor]: Taking taylor expansion of 2.0 in n 2.715 * [backup-simplify]: Simplify 2.0 into 2.0 2.715 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.715 * [taylor]: Taking taylor expansion of PI in n 2.716 * [backup-simplify]: Simplify PI into PI 2.716 * [taylor]: Taking taylor expansion of n in n 2.716 * [backup-simplify]: Simplify 0 into 0 2.716 * [backup-simplify]: Simplify 1 into 1 2.716 * [backup-simplify]: Simplify (/ PI 1) into PI 2.716 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.717 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.717 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.717 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.717 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.718 * [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))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.719 * [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))))) 2.719 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 2.719 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.719 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.719 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.719 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.719 * [taylor]: Taking taylor expansion of 0.25 in n 2.719 * [backup-simplify]: Simplify 0.25 into 0.25 2.719 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.719 * [taylor]: Taking taylor expansion of 1.0 in n 2.719 * [backup-simplify]: Simplify 1.0 into 1.0 2.719 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.719 * [taylor]: Taking taylor expansion of k in n 2.719 * [backup-simplify]: Simplify k into k 2.719 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.719 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.719 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.719 * [taylor]: Taking taylor expansion of 2.0 in n 2.719 * [backup-simplify]: Simplify 2.0 into 2.0 2.720 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.720 * [taylor]: Taking taylor expansion of PI in n 2.720 * [backup-simplify]: Simplify PI into PI 2.720 * [taylor]: Taking taylor expansion of n in n 2.720 * [backup-simplify]: Simplify 0 into 0 2.720 * [backup-simplify]: Simplify 1 into 1 2.720 * [backup-simplify]: Simplify (/ PI 1) into PI 2.720 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.721 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.721 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.721 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.721 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.722 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.722 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.723 * [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))))) 2.725 * [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) 2.725 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) in k 2.725 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.725 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.725 * [taylor]: Taking taylor expansion of 0.25 in k 2.725 * [backup-simplify]: Simplify 0.25 into 0.25 2.725 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.725 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.725 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.725 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.725 * [taylor]: Taking taylor expansion of 2.0 in k 2.725 * [backup-simplify]: Simplify 2.0 into 2.0 2.725 * [taylor]: Taking taylor expansion of PI in k 2.725 * [backup-simplify]: Simplify PI into PI 2.725 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.726 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.726 * [taylor]: Taking taylor expansion of (log n) in k 2.726 * [taylor]: Taking taylor expansion of n in k 2.726 * [backup-simplify]: Simplify n into n 2.726 * [backup-simplify]: Simplify (log n) into (log n) 2.726 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.726 * [taylor]: Taking taylor expansion of 1.0 in k 2.726 * [backup-simplify]: Simplify 1.0 into 1.0 2.726 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.726 * [taylor]: Taking taylor expansion of k in k 2.726 * [backup-simplify]: Simplify 0 into 0 2.726 * [backup-simplify]: Simplify 1 into 1 2.726 * [backup-simplify]: Simplify (/ 1 1) into 1 2.726 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.727 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.727 * [backup-simplify]: Simplify (- 1) into -1 2.727 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.728 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.729 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.729 * [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))))) 2.731 * [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) 2.731 * [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) 2.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.732 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.733 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.733 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.734 * [backup-simplify]: Simplify (- 0) into 0 2.734 * [backup-simplify]: Simplify (+ 0 0) into 0 2.734 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.735 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.736 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.737 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.738 * [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 2.739 * [taylor]: Taking taylor expansion of 0 in k 2.739 * [backup-simplify]: Simplify 0 into 0 2.739 * [backup-simplify]: Simplify 0 into 0 2.740 * [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 2.740 * [backup-simplify]: Simplify 0 into 0 2.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.741 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.743 * [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 2.743 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.743 * [backup-simplify]: Simplify (- 0) into 0 2.743 * [backup-simplify]: Simplify (+ 0 0) into 0 2.744 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.745 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.746 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.747 * [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 2.749 * [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 2.749 * [taylor]: Taking taylor expansion of 0 in k 2.749 * [backup-simplify]: Simplify 0 into 0 2.749 * [backup-simplify]: Simplify 0 into 0 2.749 * [backup-simplify]: Simplify 0 into 0 2.750 * [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 2.750 * [backup-simplify]: Simplify 0 into 0 2.751 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.752 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.754 * [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 2.755 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.755 * [backup-simplify]: Simplify (- 0) into 0 2.755 * [backup-simplify]: Simplify (+ 0 0) into 0 2.762 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.763 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.764 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.765 * [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 2.767 * [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 2.767 * [taylor]: Taking taylor expansion of 0 in k 2.767 * [backup-simplify]: Simplify 0 into 0 2.767 * [backup-simplify]: Simplify 0 into 0 2.768 * [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) 2.769 * [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) 2.769 * [approximate]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in (n k) around 0 2.769 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in k 2.769 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.769 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.769 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.769 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.769 * [taylor]: Taking taylor expansion of 0.25 in k 2.769 * [backup-simplify]: Simplify 0.25 into 0.25 2.769 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.769 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.769 * [taylor]: Taking taylor expansion of k in k 2.769 * [backup-simplify]: Simplify 0 into 0 2.769 * [backup-simplify]: Simplify 1 into 1 2.770 * [backup-simplify]: Simplify (/ 1 1) into 1 2.770 * [taylor]: Taking taylor expansion of 1.0 in k 2.770 * [backup-simplify]: Simplify 1.0 into 1.0 2.770 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.770 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.770 * [taylor]: Taking taylor expansion of -2.0 in k 2.770 * [backup-simplify]: Simplify -2.0 into -2.0 2.770 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.770 * [taylor]: Taking taylor expansion of PI in k 2.770 * [backup-simplify]: Simplify PI into PI 2.770 * [taylor]: Taking taylor expansion of n in k 2.770 * [backup-simplify]: Simplify n into n 2.770 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.770 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.770 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.770 * [backup-simplify]: Simplify (+ 1 0) into 1 2.770 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.771 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.771 * [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)))))) 2.771 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 2.771 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.771 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.771 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.771 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.771 * [taylor]: Taking taylor expansion of 0.25 in n 2.771 * [backup-simplify]: Simplify 0.25 into 0.25 2.771 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.771 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.771 * [taylor]: Taking taylor expansion of k in n 2.771 * [backup-simplify]: Simplify k into k 2.771 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.771 * [taylor]: Taking taylor expansion of 1.0 in n 2.771 * [backup-simplify]: Simplify 1.0 into 1.0 2.771 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.771 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.771 * [taylor]: Taking taylor expansion of -2.0 in n 2.771 * [backup-simplify]: Simplify -2.0 into -2.0 2.771 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.771 * [taylor]: Taking taylor expansion of PI in n 2.771 * [backup-simplify]: Simplify PI into PI 2.771 * [taylor]: Taking taylor expansion of n in n 2.771 * [backup-simplify]: Simplify 0 into 0 2.771 * [backup-simplify]: Simplify 1 into 1 2.771 * [backup-simplify]: Simplify (/ PI 1) into PI 2.772 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.772 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.772 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.772 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 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)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.775 * [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))))) 2.775 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 2.775 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.775 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.775 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.775 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.775 * [taylor]: Taking taylor expansion of 0.25 in n 2.775 * [backup-simplify]: Simplify 0.25 into 0.25 2.775 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.775 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.775 * [taylor]: Taking taylor expansion of k in n 2.775 * [backup-simplify]: Simplify k into k 2.775 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.775 * [taylor]: Taking taylor expansion of 1.0 in n 2.775 * [backup-simplify]: Simplify 1.0 into 1.0 2.775 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.775 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.775 * [taylor]: Taking taylor expansion of -2.0 in n 2.775 * [backup-simplify]: Simplify -2.0 into -2.0 2.775 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.775 * [taylor]: Taking taylor expansion of PI in n 2.775 * [backup-simplify]: Simplify PI into PI 2.775 * [taylor]: Taking taylor expansion of n in n 2.775 * [backup-simplify]: Simplify 0 into 0 2.775 * [backup-simplify]: Simplify 1 into 1 2.775 * [backup-simplify]: Simplify (/ PI 1) into PI 2.776 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.776 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.776 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.776 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.777 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.778 * [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)))) 2.779 * [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))))) 2.780 * [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) 2.780 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) in k 2.780 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.780 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.780 * [taylor]: Taking taylor expansion of 0.25 in k 2.780 * [backup-simplify]: Simplify 0.25 into 0.25 2.780 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.780 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.780 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.780 * [taylor]: Taking taylor expansion of k in k 2.780 * [backup-simplify]: Simplify 0 into 0 2.780 * [backup-simplify]: Simplify 1 into 1 2.781 * [backup-simplify]: Simplify (/ 1 1) into 1 2.781 * [taylor]: Taking taylor expansion of 1.0 in k 2.781 * [backup-simplify]: Simplify 1.0 into 1.0 2.781 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.781 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.781 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.781 * [taylor]: Taking taylor expansion of -2.0 in k 2.781 * [backup-simplify]: Simplify -2.0 into -2.0 2.781 * [taylor]: Taking taylor expansion of PI in k 2.781 * [backup-simplify]: Simplify PI into PI 2.781 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.782 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.782 * [taylor]: Taking taylor expansion of (log n) in k 2.782 * [taylor]: Taking taylor expansion of n in k 2.782 * [backup-simplify]: Simplify n into n 2.782 * [backup-simplify]: Simplify (log n) into (log n) 2.782 * [backup-simplify]: Simplify (+ 1 0) into 1 2.782 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.783 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.783 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.784 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.785 * [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))))) 2.786 * [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) 2.787 * [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) 2.788 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.788 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.789 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.789 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.789 * [backup-simplify]: Simplify (+ 0 0) into 0 2.790 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.791 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.791 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.792 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.794 * [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 2.794 * [taylor]: Taking taylor expansion of 0 in k 2.794 * [backup-simplify]: Simplify 0 into 0 2.794 * [backup-simplify]: Simplify 0 into 0 2.795 * [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 2.795 * [backup-simplify]: Simplify 0 into 0 2.796 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.797 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.798 * [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 2.798 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.799 * [backup-simplify]: Simplify (+ 0 0) into 0 2.799 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.800 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.801 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.802 * [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 2.804 * [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 2.804 * [taylor]: Taking taylor expansion of 0 in k 2.804 * [backup-simplify]: Simplify 0 into 0 2.804 * [backup-simplify]: Simplify 0 into 0 2.804 * [backup-simplify]: Simplify 0 into 0 2.806 * [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 2.806 * [backup-simplify]: Simplify 0 into 0 2.806 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.807 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.810 * [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 2.810 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.810 * [backup-simplify]: Simplify (+ 0 0) into 0 2.811 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.812 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.813 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.814 * [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 2.816 * [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 2.816 * [taylor]: Taking taylor expansion of 0 in k 2.816 * [backup-simplify]: Simplify 0 into 0 2.816 * [backup-simplify]: Simplify 0 into 0 2.817 * [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) 2.817 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1) 2.818 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.818 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.818 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.818 * [taylor]: Taking taylor expansion of 2.0 in n 2.818 * [backup-simplify]: Simplify 2.0 into 2.0 2.818 * [taylor]: Taking taylor expansion of (* n PI) in n 2.818 * [taylor]: Taking taylor expansion of n in n 2.818 * [backup-simplify]: Simplify 0 into 0 2.818 * [backup-simplify]: Simplify 1 into 1 2.818 * [taylor]: Taking taylor expansion of PI in n 2.818 * [backup-simplify]: Simplify PI into PI 2.818 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.818 * [taylor]: Taking taylor expansion of 2.0 in n 2.818 * [backup-simplify]: Simplify 2.0 into 2.0 2.818 * [taylor]: Taking taylor expansion of (* n PI) in n 2.818 * [taylor]: Taking taylor expansion of n in n 2.818 * [backup-simplify]: Simplify 0 into 0 2.818 * [backup-simplify]: Simplify 1 into 1 2.818 * [taylor]: Taking taylor expansion of PI in n 2.818 * [backup-simplify]: Simplify PI into PI 2.818 * [backup-simplify]: Simplify (* 0 PI) into 0 2.818 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.818 * [backup-simplify]: Simplify 0 into 0 2.819 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.820 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.820 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.821 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.822 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.822 * [backup-simplify]: Simplify 0 into 0 2.822 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.823 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.823 * [backup-simplify]: Simplify 0 into 0 2.824 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.824 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.824 * [backup-simplify]: Simplify 0 into 0 2.825 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.826 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.826 * [backup-simplify]: Simplify 0 into 0 2.827 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.827 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.828 * [backup-simplify]: Simplify 0 into 0 2.828 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.829 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.829 * [backup-simplify]: Simplify 0 into 0 2.830 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.830 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.830 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.830 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.830 * [taylor]: Taking taylor expansion of 2.0 in n 2.830 * [backup-simplify]: Simplify 2.0 into 2.0 2.830 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.830 * [taylor]: Taking taylor expansion of PI in n 2.830 * [backup-simplify]: Simplify PI into PI 2.830 * [taylor]: Taking taylor expansion of n in n 2.830 * [backup-simplify]: Simplify 0 into 0 2.830 * [backup-simplify]: Simplify 1 into 1 2.831 * [backup-simplify]: Simplify (/ PI 1) into PI 2.831 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.831 * [taylor]: Taking taylor expansion of 2.0 in n 2.831 * [backup-simplify]: Simplify 2.0 into 2.0 2.831 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.831 * [taylor]: Taking taylor expansion of PI in n 2.831 * [backup-simplify]: Simplify PI into PI 2.831 * [taylor]: Taking taylor expansion of n in n 2.831 * [backup-simplify]: Simplify 0 into 0 2.831 * [backup-simplify]: Simplify 1 into 1 2.831 * [backup-simplify]: Simplify (/ PI 1) into PI 2.831 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.832 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.832 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.833 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.833 * [backup-simplify]: Simplify 0 into 0 2.833 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.834 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.834 * [backup-simplify]: Simplify 0 into 0 2.834 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.835 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.835 * [backup-simplify]: Simplify 0 into 0 2.836 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.836 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.836 * [backup-simplify]: Simplify 0 into 0 2.837 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.838 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.838 * [backup-simplify]: Simplify 0 into 0 2.838 * [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 2.839 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.839 * [backup-simplify]: Simplify 0 into 0 2.840 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.840 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.840 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.840 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.840 * [taylor]: Taking taylor expansion of -2.0 in n 2.840 * [backup-simplify]: Simplify -2.0 into -2.0 2.840 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.840 * [taylor]: Taking taylor expansion of PI in n 2.840 * [backup-simplify]: Simplify PI into PI 2.840 * [taylor]: Taking taylor expansion of n in n 2.840 * [backup-simplify]: Simplify 0 into 0 2.840 * [backup-simplify]: Simplify 1 into 1 2.840 * [backup-simplify]: Simplify (/ PI 1) into PI 2.840 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.841 * [taylor]: Taking taylor expansion of -2.0 in n 2.841 * [backup-simplify]: Simplify -2.0 into -2.0 2.841 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.841 * [taylor]: Taking taylor expansion of PI in n 2.841 * [backup-simplify]: Simplify PI into PI 2.841 * [taylor]: Taking taylor expansion of n in n 2.841 * [backup-simplify]: Simplify 0 into 0 2.841 * [backup-simplify]: Simplify 1 into 1 2.841 * [backup-simplify]: Simplify (/ PI 1) into PI 2.841 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.842 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.842 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.842 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.842 * [backup-simplify]: Simplify 0 into 0 2.843 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.844 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.844 * [backup-simplify]: Simplify 0 into 0 2.844 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.845 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.845 * [backup-simplify]: Simplify 0 into 0 2.845 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.846 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.846 * [backup-simplify]: Simplify 0 into 0 2.847 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.848 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.848 * [backup-simplify]: Simplify 0 into 0 2.848 * [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 2.849 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.849 * [backup-simplify]: Simplify 0 into 0 2.849 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.849 * * * [progress]: simplifying candidates 2.860 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ 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(* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* 2 (/ (/ (- h2 h1) h0) 2)) (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* h0 h4) (/ (/ (- h2 h1) h0) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))))) (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)))) (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) 1) (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (pow h3 (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ h2 h0) 2))) (* (pow (* (* h0 h4) h3) (/ (/ h2 h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (expm1 (* (* h0 h4) h3)) (log1p (* (* h0 h4) h3)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (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)) 2.872 * * [simplify]: iteration 0 : 899 enodes (cost 2444 ) 2.887 * * [simplify]: iteration 1 : 3720 enodes (cost 2245 ) 2.946 * * [simplify]: iteration 2 : 5002 enodes (cost 2200 ) 2.956 * * * [progress]: adding candidates to table 3.681 * * [progress]: iteration 4 / 4 3.681 * * * [progress]: picking best candidate 3.697 * * * * [pick]: Picked # 3.697 * * * [progress]: localizing error 3.715 * * * [progress]: generating rewritten candidates 3.716 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2) 3.726 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2) 3.733 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 3.763 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 3.777 * * * [progress]: generating series expansions 3.777 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2) 3.778 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) 3.778 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in (k) around 0 3.778 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 3.778 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 3.778 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 3.778 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.778 * [taylor]: Taking taylor expansion of 0.5 in k 3.778 * [backup-simplify]: Simplify 0.5 into 0.5 3.778 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.778 * [taylor]: Taking taylor expansion of 1.0 in k 3.779 * [backup-simplify]: Simplify 1.0 into 1.0 3.779 * [taylor]: Taking taylor expansion of k in k 3.779 * [backup-simplify]: Simplify 0 into 0 3.779 * [backup-simplify]: Simplify 1 into 1 3.779 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.779 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.779 * [taylor]: Taking taylor expansion of 2.0 in k 3.779 * [backup-simplify]: Simplify 2.0 into 2.0 3.779 * [taylor]: Taking taylor expansion of PI in k 3.779 * [backup-simplify]: Simplify PI into PI 3.779 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.780 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.780 * [backup-simplify]: Simplify (- 0) into 0 3.780 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.780 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.782 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 3.783 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 3.783 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 3.783 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 3.783 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 3.783 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.783 * [taylor]: Taking taylor expansion of 0.5 in k 3.783 * [backup-simplify]: Simplify 0.5 into 0.5 3.783 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.783 * [taylor]: Taking taylor expansion of 1.0 in k 3.783 * [backup-simplify]: Simplify 1.0 into 1.0 3.783 * [taylor]: Taking taylor expansion of k in k 3.783 * [backup-simplify]: Simplify 0 into 0 3.783 * [backup-simplify]: Simplify 1 into 1 3.783 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.783 * [taylor]: Taking taylor expansion of (* 2.0 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 PI in k 3.783 * [backup-simplify]: Simplify PI into PI 3.784 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.784 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.784 * [backup-simplify]: Simplify (- 0) into 0 3.785 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.785 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.786 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 3.787 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 3.788 * [backup-simplify]: Simplify (pow (* 2.0 PI) 0.5) into (pow (* 2.0 PI) 0.5) 3.789 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.790 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.790 * [backup-simplify]: Simplify (- 1) into -1 3.790 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.791 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 3.793 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 PI)))) into (- (* 0.5 (log (* 2.0 PI)))) 3.800 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1)))) into (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) 3.804 * [backup-simplify]: Simplify (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) into (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) 3.805 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.807 * [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 3.807 * [backup-simplify]: Simplify (- 0) into 0 3.807 * [backup-simplify]: Simplify (+ 0 0) into 0 3.808 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 3.809 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 PI))))) into 0 3.817 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) 3.821 * [backup-simplify]: Simplify (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) into (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) 3.831 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) (pow k 2)) (+ (* (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) k) (pow (* 2.0 PI) 0.5))) into (- (+ (* 0.125 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) (pow (* 2.0 PI) 0.5)) (* 0.5 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) 3.831 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) 3.831 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in (k) around 0 3.831 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.831 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 3.831 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 3.831 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.831 * [taylor]: Taking taylor expansion of 0.5 in k 3.832 * [backup-simplify]: Simplify 0.5 into 0.5 3.832 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.832 * [taylor]: Taking taylor expansion of 1.0 in k 3.832 * [backup-simplify]: Simplify 1.0 into 1.0 3.832 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.832 * [taylor]: Taking taylor expansion of k in k 3.832 * [backup-simplify]: Simplify 0 into 0 3.832 * [backup-simplify]: Simplify 1 into 1 3.832 * [backup-simplify]: Simplify (/ 1 1) into 1 3.832 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.832 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.832 * [taylor]: Taking taylor expansion of 2.0 in k 3.832 * [backup-simplify]: Simplify 2.0 into 2.0 3.832 * [taylor]: Taking taylor expansion of PI in k 3.832 * [backup-simplify]: Simplify PI into PI 3.832 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.833 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.833 * [backup-simplify]: Simplify (- 1) into -1 3.833 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.834 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.835 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 3.835 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))) 3.835 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.835 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 3.835 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 3.835 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.835 * [taylor]: Taking taylor expansion of 0.5 in k 3.835 * [backup-simplify]: Simplify 0.5 into 0.5 3.835 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.835 * [taylor]: Taking taylor expansion of 1.0 in k 3.835 * [backup-simplify]: Simplify 1.0 into 1.0 3.835 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.835 * [taylor]: Taking taylor expansion of k in k 3.835 * [backup-simplify]: Simplify 0 into 0 3.835 * [backup-simplify]: Simplify 1 into 1 3.836 * [backup-simplify]: Simplify (/ 1 1) into 1 3.836 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.836 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.836 * [taylor]: Taking taylor expansion of 2.0 in k 3.836 * [backup-simplify]: Simplify 2.0 into 2.0 3.836 * [taylor]: Taking taylor expansion of PI in k 3.836 * [backup-simplify]: Simplify PI into PI 3.836 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.837 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.837 * [backup-simplify]: Simplify (- 1) into -1 3.837 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.837 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.838 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 3.839 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))) 3.840 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))) 3.840 * [backup-simplify]: Simplify 0 into 0 3.840 * [backup-simplify]: Simplify 0 into 0 3.840 * [backup-simplify]: Simplify 0 into 0 3.840 * [backup-simplify]: Simplify 0 into 0 3.840 * [backup-simplify]: Simplify 0 into 0 3.840 * [backup-simplify]: Simplify 0 into 0 3.841 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) 3.841 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) 3.841 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in (k) around 0 3.841 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.841 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 3.841 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 3.841 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.841 * [taylor]: Taking taylor expansion of 0.5 in k 3.841 * [backup-simplify]: Simplify 0.5 into 0.5 3.841 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.841 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.841 * [taylor]: Taking taylor expansion of k in k 3.841 * [backup-simplify]: Simplify 0 into 0 3.841 * [backup-simplify]: Simplify 1 into 1 3.842 * [backup-simplify]: Simplify (/ 1 1) into 1 3.842 * [taylor]: Taking taylor expansion of 1.0 in k 3.842 * [backup-simplify]: Simplify 1.0 into 1.0 3.842 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.842 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.842 * [taylor]: Taking taylor expansion of 2.0 in k 3.842 * [backup-simplify]: Simplify 2.0 into 2.0 3.842 * [taylor]: Taking taylor expansion of PI in k 3.842 * [backup-simplify]: Simplify PI into PI 3.842 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.843 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.843 * [backup-simplify]: Simplify (+ 1 0) into 1 3.843 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.844 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 3.845 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 3.845 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.845 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 3.845 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 3.845 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.845 * [taylor]: Taking taylor expansion of 0.5 in k 3.845 * [backup-simplify]: Simplify 0.5 into 0.5 3.845 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.845 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.845 * [taylor]: Taking taylor expansion of k in k 3.845 * [backup-simplify]: Simplify 0 into 0 3.845 * [backup-simplify]: Simplify 1 into 1 3.845 * [backup-simplify]: Simplify (/ 1 1) into 1 3.845 * [taylor]: Taking taylor expansion of 1.0 in k 3.845 * [backup-simplify]: Simplify 1.0 into 1.0 3.845 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.845 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.845 * [taylor]: Taking taylor expansion of 2.0 in k 3.845 * [backup-simplify]: Simplify 2.0 into 2.0 3.845 * [taylor]: Taking taylor expansion of PI in k 3.845 * [backup-simplify]: Simplify PI into PI 3.846 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.846 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.847 * [backup-simplify]: Simplify (+ 1 0) into 1 3.847 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.848 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 3.849 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 3.849 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 3.849 * [backup-simplify]: Simplify 0 into 0 3.849 * [backup-simplify]: Simplify 0 into 0 3.849 * [backup-simplify]: Simplify 0 into 0 3.849 * [backup-simplify]: Simplify 0 into 0 3.850 * [backup-simplify]: Simplify 0 into 0 3.850 * [backup-simplify]: Simplify 0 into 0 3.850 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) 3.850 * * * * [progress]: [ 2 / 4 ] generating series at (2 2) 3.850 * [backup-simplify]: Simplify (pow n (/ (- 1.0 k) 2.0)) into (pow n (* 0.5 (- 1.0 k))) 3.850 * [approximate]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in (n k) around 0 3.850 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in k 3.850 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in k 3.851 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in k 3.851 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.851 * [taylor]: Taking taylor expansion of 0.5 in k 3.851 * [backup-simplify]: Simplify 0.5 into 0.5 3.851 * [taylor]: Taking taylor expansion of (- 1.0 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 k in k 3.851 * [backup-simplify]: Simplify 0 into 0 3.851 * [backup-simplify]: Simplify 1 into 1 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 * [backup-simplify]: Simplify (- 0) into 0 3.851 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.852 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.852 * [backup-simplify]: Simplify (* 0.5 (log n)) into (* 0.5 (log n)) 3.852 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 3.852 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 3.852 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 3.852 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 3.852 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.852 * [taylor]: Taking taylor expansion of 0.5 in n 3.852 * [backup-simplify]: Simplify 0.5 into 0.5 3.852 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.852 * [taylor]: Taking taylor expansion of 1.0 in n 3.852 * [backup-simplify]: Simplify 1.0 into 1.0 3.852 * [taylor]: Taking taylor expansion of k in n 3.852 * [backup-simplify]: Simplify k into k 3.852 * [taylor]: Taking taylor expansion of (log n) in n 3.852 * [taylor]: Taking taylor expansion of n in n 3.852 * [backup-simplify]: Simplify 0 into 0 3.852 * [backup-simplify]: Simplify 1 into 1 3.852 * [backup-simplify]: Simplify (log 1) into 0 3.852 * [backup-simplify]: Simplify (- k) into (- k) 3.852 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.852 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.853 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.853 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 3.853 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 3.853 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 3.853 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 3.853 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 3.853 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.853 * [taylor]: Taking taylor expansion of 0.5 in n 3.853 * [backup-simplify]: Simplify 0.5 into 0.5 3.853 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.853 * [taylor]: Taking taylor expansion of 1.0 in n 3.853 * [backup-simplify]: Simplify 1.0 into 1.0 3.853 * [taylor]: Taking taylor expansion of k in n 3.853 * [backup-simplify]: Simplify k into k 3.853 * [taylor]: Taking taylor expansion of (log n) in n 3.853 * [taylor]: Taking taylor expansion of n in n 3.853 * [backup-simplify]: Simplify 0 into 0 3.853 * [backup-simplify]: Simplify 1 into 1 3.853 * [backup-simplify]: Simplify (log 1) into 0 3.853 * [backup-simplify]: Simplify (- k) into (- k) 3.853 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.853 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.854 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.854 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 3.854 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 3.854 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (log n)))) in k 3.854 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (log n))) in k 3.854 * [taylor]: Taking taylor expansion of 0.5 in k 3.854 * [backup-simplify]: Simplify 0.5 into 0.5 3.854 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (log n)) in k 3.854 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.854 * [taylor]: Taking taylor expansion of 1.0 in k 3.854 * [backup-simplify]: Simplify 1.0 into 1.0 3.854 * [taylor]: Taking taylor expansion of k in k 3.854 * [backup-simplify]: Simplify 0 into 0 3.854 * [backup-simplify]: Simplify 1 into 1 3.854 * [taylor]: Taking taylor expansion of (log n) in k 3.854 * [taylor]: Taking taylor expansion of n in k 3.854 * [backup-simplify]: Simplify n into n 3.854 * [backup-simplify]: Simplify (log n) into (log n) 3.854 * [backup-simplify]: Simplify (- 0) into 0 3.855 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.855 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.855 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (log n))) into (* 0.5 (log n)) 3.855 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 3.855 * [backup-simplify]: Simplify (pow n 0.5) into (pow n 0.5) 3.856 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.856 * [backup-simplify]: Simplify (- 0) into 0 3.856 * [backup-simplify]: Simplify (+ 0 0) into 0 3.863 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.864 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.864 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (log n))) into 0 3.864 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.865 * [taylor]: Taking taylor expansion of 0 in k 3.865 * [backup-simplify]: Simplify 0 into 0 3.865 * [backup-simplify]: Simplify 0 into 0 3.865 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.865 * [backup-simplify]: Simplify (- 1) into -1 3.866 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.866 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (log n))) into (- (log n)) 3.866 * [backup-simplify]: Simplify (+ (* 0.5 (- (log n))) (* 0 (* 1.0 (log n)))) into (- (* 0.5 (log n))) 3.866 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 1) 1)))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 3.867 * [backup-simplify]: Simplify (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 3.868 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 3.868 * [backup-simplify]: Simplify (- 0) into 0 3.868 * [backup-simplify]: Simplify (+ 0 0) into 0 3.869 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.869 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.869 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 3.870 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.870 * [taylor]: Taking taylor expansion of 0 in k 3.870 * [backup-simplify]: Simplify 0 into 0 3.870 * [backup-simplify]: Simplify 0 into 0 3.870 * [backup-simplify]: Simplify 0 into 0 3.871 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.872 * [backup-simplify]: Simplify (- 0) into 0 3.872 * [backup-simplify]: Simplify (+ 0 0) into 0 3.872 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (log n)))) into 0 3.873 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (log n))) (* 0 (* 1.0 (log n))))) into 0 3.873 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 3.873 * [backup-simplify]: Simplify (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 3.874 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) (* k 1)) (pow n 0.5))) into (- (+ (* 0.125 (* (* (pow k 2) (pow (log n) 2)) (pow (pow n 1.0) 0.5))) (pow n 0.5)) (* 0.5 (* (* k (log n)) (pow (pow n 1.0) 0.5)))) 3.874 * [backup-simplify]: Simplify (pow (/ 1 n) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) 3.874 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.874 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.874 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in k 3.874 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in k 3.874 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.874 * [taylor]: Taking taylor expansion of 0.5 in k 3.874 * [backup-simplify]: Simplify 0.5 into 0.5 3.874 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.874 * [taylor]: Taking taylor expansion of 1.0 in k 3.875 * [backup-simplify]: Simplify 1.0 into 1.0 3.875 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.875 * [taylor]: Taking taylor expansion of k in k 3.875 * [backup-simplify]: Simplify 0 into 0 3.875 * [backup-simplify]: Simplify 1 into 1 3.875 * [backup-simplify]: Simplify (/ 1 1) into 1 3.875 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 3.875 * [taylor]: Taking taylor expansion of (/ 1 n) in k 3.875 * [taylor]: Taking taylor expansion of n in k 3.875 * [backup-simplify]: Simplify n into n 3.875 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 3.875 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 3.875 * [backup-simplify]: Simplify (- 1) into -1 3.875 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.876 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.876 * [backup-simplify]: Simplify (* -0.5 (log (/ 1 n))) into (* -0.5 (log (/ 1 n))) 3.876 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) into (exp (* 0.5 (* (log (/ 1 n)) (- 1.0 (/ 1 k))))) 3.876 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.876 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 3.876 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 3.876 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.876 * [taylor]: Taking taylor expansion of 0.5 in n 3.876 * [backup-simplify]: Simplify 0.5 into 0.5 3.876 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.876 * [taylor]: Taking taylor expansion of 1.0 in n 3.876 * [backup-simplify]: Simplify 1.0 into 1.0 3.876 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.876 * [taylor]: Taking taylor expansion of k in n 3.876 * [backup-simplify]: Simplify k into k 3.876 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.876 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 3.876 * [taylor]: Taking taylor expansion of (/ 1 n) in n 3.876 * [taylor]: Taking taylor expansion of n in n 3.876 * [backup-simplify]: Simplify 0 into 0 3.876 * [backup-simplify]: Simplify 1 into 1 3.876 * [backup-simplify]: Simplify (/ 1 1) into 1 3.877 * [backup-simplify]: Simplify (log 1) into 0 3.877 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.877 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.877 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.877 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.877 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (log n) (- 1.0 (/ 1 k)))) 3.877 * [backup-simplify]: Simplify (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) 3.877 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.877 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 3.877 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 3.877 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.877 * [taylor]: Taking taylor expansion of 0.5 in n 3.877 * [backup-simplify]: Simplify 0.5 into 0.5 3.877 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.878 * [taylor]: Taking taylor expansion of 1.0 in n 3.878 * [backup-simplify]: Simplify 1.0 into 1.0 3.878 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.878 * [taylor]: Taking taylor expansion of k in n 3.878 * [backup-simplify]: Simplify k into k 3.878 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.878 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 3.878 * [taylor]: Taking taylor expansion of (/ 1 n) in n 3.878 * [taylor]: Taking taylor expansion of n in n 3.878 * [backup-simplify]: Simplify 0 into 0 3.878 * [backup-simplify]: Simplify 1 into 1 3.878 * [backup-simplify]: Simplify (/ 1 1) into 1 3.878 * [backup-simplify]: Simplify (log 1) into 0 3.878 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.878 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.878 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.879 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.879 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (log n) (- 1.0 (/ 1 k)))) 3.879 * [backup-simplify]: Simplify (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) 3.879 * [taylor]: Taking taylor expansion of (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) in k 3.879 * [taylor]: Taking taylor expansion of (* -0.5 (* (log n) (- 1.0 (/ 1 k)))) in k 3.879 * [taylor]: Taking taylor expansion of -0.5 in k 3.879 * [backup-simplify]: Simplify -0.5 into -0.5 3.879 * [taylor]: Taking taylor expansion of (* (log n) (- 1.0 (/ 1 k))) in k 3.879 * [taylor]: Taking taylor expansion of (log n) in k 3.879 * [taylor]: Taking taylor expansion of n in k 3.879 * [backup-simplify]: Simplify n into n 3.879 * [backup-simplify]: Simplify (log n) into (log n) 3.879 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.879 * [taylor]: Taking taylor expansion of 1.0 in k 3.879 * [backup-simplify]: Simplify 1.0 into 1.0 3.879 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.879 * [taylor]: Taking taylor expansion of k in k 3.879 * [backup-simplify]: Simplify 0 into 0 3.879 * [backup-simplify]: Simplify 1 into 1 3.879 * [backup-simplify]: Simplify (/ 1 1) into 1 3.880 * [backup-simplify]: Simplify (- 1) into -1 3.880 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.880 * [backup-simplify]: Simplify (* (log n) -1) into (* -1 (log n)) 3.880 * [backup-simplify]: Simplify (* -0.5 (* -1 (log n))) into (* 0.5 (log n)) 3.880 * [backup-simplify]: Simplify (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) 3.880 * [backup-simplify]: Simplify (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) 3.881 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.881 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.881 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.882 * [backup-simplify]: Simplify (- 0) into 0 3.882 * [backup-simplify]: Simplify (+ 0 0) into 0 3.882 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.882 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.883 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 3.883 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.883 * [taylor]: Taking taylor expansion of 0 in k 3.883 * [backup-simplify]: Simplify 0 into 0 3.883 * [backup-simplify]: Simplify 0 into 0 3.883 * [backup-simplify]: Simplify 0 into 0 3.884 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.885 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 3.885 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.885 * [backup-simplify]: Simplify (- 0) into 0 3.886 * [backup-simplify]: Simplify (+ 0 0) into 0 3.886 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 3.886 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.887 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 3.887 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.888 * [taylor]: Taking taylor expansion of 0 in k 3.888 * [backup-simplify]: Simplify 0 into 0 3.888 * [backup-simplify]: Simplify 0 into 0 3.888 * [backup-simplify]: Simplify 0 into 0 3.888 * [backup-simplify]: Simplify 0 into 0 3.888 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.891 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 3.891 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.891 * [backup-simplify]: Simplify (- 0) into 0 3.891 * [backup-simplify]: Simplify (+ 0 0) into 0 3.892 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 3.892 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.893 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 3.894 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.894 * [taylor]: Taking taylor expansion of 0 in k 3.894 * [backup-simplify]: Simplify 0 into 0 3.894 * [backup-simplify]: Simplify 0 into 0 3.894 * [backup-simplify]: Simplify (exp (* -0.5 (* (log (/ 1 n)) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* -0.5 (* (- 1.0 k) (log (/ 1 n))))) 3.894 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) 3.894 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.894 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.894 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in k 3.894 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in k 3.894 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.894 * [taylor]: Taking taylor expansion of 0.5 in k 3.894 * [backup-simplify]: Simplify 0.5 into 0.5 3.894 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.894 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.894 * [taylor]: Taking taylor expansion of k in k 3.894 * [backup-simplify]: Simplify 0 into 0 3.894 * [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 (/ -1 n)) in k 3.895 * [taylor]: Taking taylor expansion of (/ -1 n) in k 3.895 * [taylor]: Taking taylor expansion of -1 in k 3.895 * [backup-simplify]: Simplify -1 into -1 3.895 * [taylor]: Taking taylor expansion of n in k 3.895 * [backup-simplify]: Simplify n into n 3.895 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 3.895 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 3.895 * [backup-simplify]: Simplify (+ 1 0) into 1 3.895 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.895 * [backup-simplify]: Simplify (* 0.5 (log (/ -1 n))) into (* 0.5 (log (/ -1 n))) 3.896 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (/ -1 n))))) 3.896 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.896 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 3.896 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 3.896 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.896 * [taylor]: Taking taylor expansion of 0.5 in n 3.896 * [backup-simplify]: Simplify 0.5 into 0.5 3.896 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.896 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.896 * [taylor]: Taking taylor expansion of k in n 3.896 * [backup-simplify]: Simplify k into k 3.896 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.896 * [taylor]: Taking taylor expansion of 1.0 in n 3.896 * [backup-simplify]: Simplify 1.0 into 1.0 3.896 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 3.896 * [taylor]: Taking taylor expansion of (/ -1 n) in n 3.896 * [taylor]: Taking taylor expansion of -1 in n 3.896 * [backup-simplify]: Simplify -1 into -1 3.896 * [taylor]: Taking taylor expansion of n in n 3.896 * [backup-simplify]: Simplify 0 into 0 3.896 * [backup-simplify]: Simplify 1 into 1 3.896 * [backup-simplify]: Simplify (/ -1 1) into -1 3.896 * [backup-simplify]: Simplify (log -1) into (log -1) 3.896 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.897 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.897 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 3.897 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 3.898 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 3.898 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.898 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 3.898 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 3.898 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.898 * [taylor]: Taking taylor expansion of 0.5 in n 3.898 * [backup-simplify]: Simplify 0.5 into 0.5 3.898 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.898 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.898 * [taylor]: Taking taylor expansion of k in n 3.898 * [backup-simplify]: Simplify k into k 3.898 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.898 * [taylor]: Taking taylor expansion of 1.0 in n 3.898 * [backup-simplify]: Simplify 1.0 into 1.0 3.898 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 3.898 * [taylor]: Taking taylor expansion of (/ -1 n) in n 3.898 * [taylor]: Taking taylor expansion of -1 in n 3.898 * [backup-simplify]: Simplify -1 into -1 3.898 * [taylor]: Taking taylor expansion of n in n 3.898 * [backup-simplify]: Simplify 0 into 0 3.898 * [backup-simplify]: Simplify 1 into 1 3.898 * [backup-simplify]: Simplify (/ -1 1) into -1 3.899 * [backup-simplify]: Simplify (log -1) into (log -1) 3.899 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.899 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.899 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 3.900 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 3.900 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 3.900 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) in k 3.900 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) in k 3.900 * [taylor]: Taking taylor expansion of 0.5 in k 3.900 * [backup-simplify]: Simplify 0.5 into 0.5 3.900 * [taylor]: Taking taylor expansion of (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)) in k 3.900 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 3.900 * [taylor]: Taking taylor expansion of (log -1) in k 3.900 * [taylor]: Taking taylor expansion of -1 in k 3.900 * [backup-simplify]: Simplify -1 into -1 3.900 * [backup-simplify]: Simplify (log -1) into (log -1) 3.901 * [taylor]: Taking taylor expansion of (log n) in k 3.901 * [taylor]: Taking taylor expansion of n in k 3.901 * [backup-simplify]: Simplify n into n 3.901 * [backup-simplify]: Simplify (log n) into (log n) 3.901 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.901 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.901 * [taylor]: Taking taylor expansion of k in k 3.901 * [backup-simplify]: Simplify 0 into 0 3.901 * [backup-simplify]: Simplify 1 into 1 3.901 * [backup-simplify]: Simplify (/ 1 1) into 1 3.901 * [taylor]: Taking taylor expansion of 1.0 in k 3.901 * [backup-simplify]: Simplify 1.0 into 1.0 3.901 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.901 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 3.902 * [backup-simplify]: Simplify (+ 1 0) into 1 3.902 * [backup-simplify]: Simplify (* (- (log -1) (log n)) 1) into (- (log -1) (log n)) 3.902 * [backup-simplify]: Simplify (* 0.5 (- (log -1) (log n))) into (* 0.5 (- (log -1) (log n))) 3.903 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 3.903 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 3.904 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.904 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 3.904 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.905 * [backup-simplify]: Simplify (+ 0 0) into 0 3.905 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.905 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 3.906 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log -1) (log n)))) into 0 3.907 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.907 * [taylor]: Taking taylor expansion of 0 in k 3.907 * [backup-simplify]: Simplify 0 into 0 3.907 * [backup-simplify]: Simplify 0 into 0 3.907 * [backup-simplify]: Simplify 0 into 0 3.907 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.909 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 3.909 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.909 * [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 -1)) into (- (log -1) (log n)) 3.910 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 3.912 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (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 3.912 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.915 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 1)))) 6) into 0 3.915 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.915 * [backup-simplify]: Simplify (+ 0 0) into 0 3.916 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 3.916 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 3.917 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 3.918 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.918 * [taylor]: Taking taylor expansion of 0 in k 3.918 * [backup-simplify]: Simplify 0 into 0 3.918 * [backup-simplify]: Simplify 0 into 0 3.919 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log -1) (log (/ -1 n)))))) 3.919 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 3.919 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 PI) (* 0.5 (- 1.0 k))))) 3.919 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 PI) (* 0.5 (- 1.0 k))))) in (k) around 0 3.919 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 PI) (* 0.5 (- 1.0 k))))) in k 3.919 * [taylor]: Taking taylor expansion of 1.0 in k 3.920 * [backup-simplify]: Simplify 1.0 into 1.0 3.920 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 PI) (* 0.5 (- 1.0 k)))) in k 3.920 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.920 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.920 * [taylor]: Taking taylor expansion of k in k 3.920 * [backup-simplify]: Simplify 0 into 0 3.920 * [backup-simplify]: Simplify 1 into 1 3.920 * [backup-simplify]: Simplify (/ 1 1) into 1 3.920 * [backup-simplify]: Simplify (sqrt 0) into 0 3.921 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.921 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 3.921 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 3.921 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 3.921 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.921 * [taylor]: Taking taylor expansion of 0.5 in k 3.921 * [backup-simplify]: Simplify 0.5 into 0.5 3.921 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.921 * [taylor]: Taking taylor expansion of 1.0 in k 3.921 * [backup-simplify]: Simplify 1.0 into 1.0 3.921 * [taylor]: Taking taylor expansion of k in k 3.921 * [backup-simplify]: Simplify 0 into 0 3.921 * [backup-simplify]: Simplify 1 into 1 3.921 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.921 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.921 * [taylor]: Taking taylor expansion of 2.0 in k 3.921 * [backup-simplify]: Simplify 2.0 into 2.0 3.921 * [taylor]: Taking taylor expansion of PI in k 3.921 * [backup-simplify]: Simplify PI into PI 3.922 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.922 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.922 * [backup-simplify]: Simplify (- 0) into 0 3.923 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.923 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.924 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 3.925 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 3.925 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 PI) (* 0.5 (- 1.0 k))))) in k 3.925 * [taylor]: Taking taylor expansion of 1.0 in k 3.925 * [backup-simplify]: Simplify 1.0 into 1.0 3.925 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 PI) (* 0.5 (- 1.0 k)))) in k 3.925 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.925 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.925 * [taylor]: Taking taylor expansion of k in k 3.925 * [backup-simplify]: Simplify 0 into 0 3.925 * [backup-simplify]: Simplify 1 into 1 3.926 * [backup-simplify]: Simplify (/ 1 1) into 1 3.926 * [backup-simplify]: Simplify (sqrt 0) into 0 3.927 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.927 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 3.927 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 3.927 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 3.927 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.927 * [taylor]: Taking taylor expansion of 0.5 in k 3.927 * [backup-simplify]: Simplify 0.5 into 0.5 3.927 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.927 * [taylor]: Taking taylor expansion of 1.0 in k 3.927 * [backup-simplify]: Simplify 1.0 into 1.0 3.927 * [taylor]: Taking taylor expansion of k in k 3.927 * [backup-simplify]: Simplify 0 into 0 3.927 * [backup-simplify]: Simplify 1 into 1 3.927 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.927 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.927 * [taylor]: Taking taylor expansion of 2.0 in k 3.927 * [backup-simplify]: Simplify 2.0 into 2.0 3.927 * [taylor]: Taking taylor expansion of PI in k 3.927 * [backup-simplify]: Simplify PI into PI 3.927 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.928 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.928 * [backup-simplify]: Simplify (- 0) into 0 3.928 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.929 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.930 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 3.931 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 3.931 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 PI) 0.5)) into 0 3.932 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.932 * [backup-simplify]: Simplify 0 into 0 3.932 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.933 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.933 * [backup-simplify]: Simplify (- 1) into -1 3.934 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.934 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 3.937 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 PI)))) into (- (* 0.5 (log (* 2.0 PI)))) 3.943 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1)))) into (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) 3.947 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)))) (* +nan.0 (pow (* 2.0 PI) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) 3.952 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) 3.962 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) 3.963 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.965 * [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 3.965 * [backup-simplify]: Simplify (- 0) into 0 3.965 * [backup-simplify]: Simplify (+ 0 0) into 0 3.966 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 3.966 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 PI))))) into 0 3.975 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) 3.975 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.977 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.988 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)))) (* +nan.0 (pow (* 2.0 PI) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))) 4.003 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))) 4.012 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))) 4.013 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.016 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 4.016 * [backup-simplify]: Simplify (- 0) into 0 4.016 * [backup-simplify]: Simplify (+ 0 0) into 0 4.017 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 4.018 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 PI)))))) into 0 4.028 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 PI)) 3) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) 4.028 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.031 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.058 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 PI)) 3) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)))) (* +nan.0 (pow (* 2.0 PI) 0.5))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))))) 4.085 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))))))) (+ (* 0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)))))))) 4.104 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))))))) 4.142 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))) k) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))) into (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (+ (* +nan.0 (* k (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))))))))))) 4.143 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* 2.0 PI) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))))) 4.143 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))))) in (k) around 0 4.143 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.143 * [taylor]: Taking taylor expansion of 1.0 in k 4.143 * [backup-simplify]: Simplify 1.0 into 1.0 4.143 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.143 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.143 * [taylor]: Taking taylor expansion of k in k 4.143 * [backup-simplify]: Simplify 0 into 0 4.143 * [backup-simplify]: Simplify 1 into 1 4.143 * [backup-simplify]: Simplify (sqrt 0) into 0 4.144 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.144 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.144 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 4.144 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 4.144 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.144 * [taylor]: Taking taylor expansion of 0.5 in k 4.144 * [backup-simplify]: Simplify 0.5 into 0.5 4.144 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.144 * [taylor]: Taking taylor expansion of 1.0 in k 4.144 * [backup-simplify]: Simplify 1.0 into 1.0 4.144 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.144 * [taylor]: Taking taylor expansion of k in k 4.144 * [backup-simplify]: Simplify 0 into 0 4.144 * [backup-simplify]: Simplify 1 into 1 4.145 * [backup-simplify]: Simplify (/ 1 1) into 1 4.145 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.145 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.145 * [taylor]: Taking taylor expansion of 2.0 in k 4.145 * [backup-simplify]: Simplify 2.0 into 2.0 4.145 * [taylor]: Taking taylor expansion of PI in k 4.145 * [backup-simplify]: Simplify PI into PI 4.145 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.146 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.146 * [backup-simplify]: Simplify (- 1) into -1 4.146 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.146 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.147 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 4.148 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))) 4.148 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.148 * [taylor]: Taking taylor expansion of 1.0 in k 4.148 * [backup-simplify]: Simplify 1.0 into 1.0 4.148 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.148 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.148 * [taylor]: Taking taylor expansion of k in k 4.148 * [backup-simplify]: Simplify 0 into 0 4.148 * [backup-simplify]: Simplify 1 into 1 4.148 * [backup-simplify]: Simplify (sqrt 0) into 0 4.149 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.149 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.149 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 4.149 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 4.149 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.149 * [taylor]: Taking taylor expansion of 0.5 in k 4.149 * [backup-simplify]: Simplify 0.5 into 0.5 4.149 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.149 * [taylor]: Taking taylor expansion of 1.0 in k 4.149 * [backup-simplify]: Simplify 1.0 into 1.0 4.149 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.149 * [taylor]: Taking taylor expansion of k in k 4.149 * [backup-simplify]: Simplify 0 into 0 4.149 * [backup-simplify]: Simplify 1 into 1 4.150 * [backup-simplify]: Simplify (/ 1 1) into 1 4.150 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.150 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.150 * [taylor]: Taking taylor expansion of 2.0 in k 4.150 * [backup-simplify]: Simplify 2.0 into 2.0 4.150 * [taylor]: Taking taylor expansion of PI in k 4.150 * [backup-simplify]: Simplify PI into PI 4.150 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.151 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.151 * [backup-simplify]: Simplify (- 1) into -1 4.151 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.151 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.152 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 4.153 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))) 4.154 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k)))))) into 0 4.154 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.154 * [backup-simplify]: Simplify 0 into 0 4.155 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) 4.156 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) 4.157 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) 4.159 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.160 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) 4.161 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) 4.162 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) 4.164 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.165 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) 4.168 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) 4.168 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))))) 4.171 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 (/ 1 k)))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) (pow k 3)))))))) 4.171 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* 2.0 PI) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 4.171 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k) around 0 4.171 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.172 * [taylor]: Taking taylor expansion of 1.0 in k 4.172 * [backup-simplify]: Simplify 1.0 into 1.0 4.172 * [taylor]: Taking taylor expansion of (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.172 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.172 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 4.172 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 4.172 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.172 * [taylor]: Taking taylor expansion of 0.5 in k 4.172 * [backup-simplify]: Simplify 0.5 into 0.5 4.172 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.172 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.172 * [taylor]: Taking taylor expansion of k in k 4.172 * [backup-simplify]: Simplify 0 into 0 4.172 * [backup-simplify]: Simplify 1 into 1 4.172 * [backup-simplify]: Simplify (/ 1 1) into 1 4.172 * [taylor]: Taking taylor expansion of 1.0 in k 4.172 * [backup-simplify]: Simplify 1.0 into 1.0 4.172 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.172 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.172 * [taylor]: Taking taylor expansion of 2.0 in k 4.172 * [backup-simplify]: Simplify 2.0 into 2.0 4.172 * [taylor]: Taking taylor expansion of PI in k 4.172 * [backup-simplify]: Simplify PI into PI 4.172 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.173 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.173 * [backup-simplify]: Simplify (+ 1 0) into 1 4.174 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.175 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 4.175 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 4.175 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.175 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.175 * [taylor]: Taking taylor expansion of -1 in k 4.175 * [backup-simplify]: Simplify -1 into -1 4.175 * [taylor]: Taking taylor expansion of k in k 4.175 * [backup-simplify]: Simplify 0 into 0 4.175 * [backup-simplify]: Simplify 1 into 1 4.176 * [backup-simplify]: Simplify (/ -1 1) into -1 4.176 * [backup-simplify]: Simplify (sqrt 0) into 0 4.177 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.177 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 4.177 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.177 * [taylor]: Taking taylor expansion of 1.0 in k 4.177 * [backup-simplify]: Simplify 1.0 into 1.0 4.177 * [taylor]: Taking taylor expansion of (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.177 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.177 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 4.178 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 4.178 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.178 * [taylor]: Taking taylor expansion of 0.5 in k 4.178 * [backup-simplify]: Simplify 0.5 into 0.5 4.178 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.178 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.178 * [taylor]: Taking taylor expansion of k in k 4.178 * [backup-simplify]: Simplify 0 into 0 4.178 * [backup-simplify]: Simplify 1 into 1 4.178 * [backup-simplify]: Simplify (/ 1 1) into 1 4.178 * [taylor]: Taking taylor expansion of 1.0 in k 4.178 * [backup-simplify]: Simplify 1.0 into 1.0 4.178 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.178 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.178 * [taylor]: Taking taylor expansion of 2.0 in k 4.178 * [backup-simplify]: Simplify 2.0 into 2.0 4.178 * [taylor]: Taking taylor expansion of PI in k 4.178 * [backup-simplify]: Simplify PI into PI 4.178 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.179 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.179 * [backup-simplify]: Simplify (+ 1 0) into 1 4.179 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.180 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 4.181 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 4.181 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.181 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.181 * [taylor]: Taking taylor expansion of -1 in k 4.181 * [backup-simplify]: Simplify -1 into -1 4.181 * [taylor]: Taking taylor expansion of k in k 4.181 * [backup-simplify]: Simplify 0 into 0 4.181 * [backup-simplify]: Simplify 1 into 1 4.181 * [backup-simplify]: Simplify (/ -1 1) into -1 4.182 * [backup-simplify]: Simplify (sqrt 0) into 0 4.182 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.183 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 4.184 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 4.185 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 4.185 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.187 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.188 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 4.189 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 4.190 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 4.191 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.193 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.195 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 4.198 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 4.199 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 4.202 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (/ 1 (- k))) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) k)) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))))))))) 4.202 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 4.202 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.202 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.202 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.202 * [taylor]: Taking taylor expansion of 1.0 in k 4.202 * [backup-simplify]: Simplify 1.0 into 1.0 4.202 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.202 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.202 * [taylor]: Taking taylor expansion of k in k 4.202 * [backup-simplify]: Simplify 0 into 0 4.202 * [backup-simplify]: Simplify 1 into 1 4.202 * [backup-simplify]: Simplify (/ 1 1) into 1 4.202 * [backup-simplify]: Simplify (sqrt 0) into 0 4.203 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.203 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.203 * [taylor]: Taking taylor expansion of 1.0 in k 4.203 * [backup-simplify]: Simplify 1.0 into 1.0 4.203 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.203 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.203 * [taylor]: Taking taylor expansion of k in k 4.203 * [backup-simplify]: Simplify 0 into 0 4.203 * [backup-simplify]: Simplify 1 into 1 4.204 * [backup-simplify]: Simplify (/ 1 1) into 1 4.204 * [backup-simplify]: Simplify (sqrt 0) into 0 4.205 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.205 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.205 * [backup-simplify]: Simplify 0 into 0 4.206 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.206 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.206 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.208 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.209 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.209 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.210 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.212 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.213 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.213 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.214 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.214 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.214 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.214 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.214 * [taylor]: Taking taylor expansion of 1.0 in k 4.214 * [backup-simplify]: Simplify 1.0 into 1.0 4.214 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.214 * [taylor]: Taking taylor expansion of k in k 4.214 * [backup-simplify]: Simplify 0 into 0 4.214 * [backup-simplify]: Simplify 1 into 1 4.215 * [backup-simplify]: Simplify (sqrt 0) into 0 4.215 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.215 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.215 * [taylor]: Taking taylor expansion of 1.0 in k 4.215 * [backup-simplify]: Simplify 1.0 into 1.0 4.215 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.215 * [taylor]: Taking taylor expansion of k in k 4.215 * [backup-simplify]: Simplify 0 into 0 4.215 * [backup-simplify]: Simplify 1 into 1 4.216 * [backup-simplify]: Simplify (sqrt 0) into 0 4.223 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.224 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.224 * [backup-simplify]: Simplify 0 into 0 4.225 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.225 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.227 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.228 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.228 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.230 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.231 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.231 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.232 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 4.232 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.232 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.232 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -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 4.233 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.233 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.233 * [taylor]: Taking taylor expansion of -1 in k 4.233 * [backup-simplify]: Simplify -1 into -1 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 * [backup-simplify]: Simplify (sqrt 0) into 0 4.234 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.234 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.234 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.234 * [taylor]: Taking taylor expansion of 1.0 in k 4.234 * [backup-simplify]: Simplify 1.0 into 1.0 4.234 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.234 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.234 * [taylor]: Taking taylor expansion of -1 in k 4.234 * [backup-simplify]: Simplify -1 into -1 4.234 * [taylor]: Taking taylor expansion of k in k 4.234 * [backup-simplify]: Simplify 0 into 0 4.234 * [backup-simplify]: Simplify 1 into 1 4.235 * [backup-simplify]: Simplify (/ -1 1) into -1 4.235 * [backup-simplify]: Simplify (sqrt 0) into 0 4.235 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.236 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.236 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.236 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.238 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.239 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.239 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.242 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.244 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.245 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.245 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 4.245 * * * [progress]: simplifying candidates 4.248 * [simplify]: Simplifying: (expm1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (+ (log 2.0) (log PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ 1.0 2.0)) (pow (* 2.0 PI) (/ k 2.0)) (pow (* 2.0 PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (pow (* 2.0 PI) (/ 1 1)) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (pow (* 2.0 PI) (/ 1 1)) (pow (* 2.0 PI) 1) (pow (* 2.0 PI) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow n (/ (- 1.0 k) 2.0))) (log1p (pow n (/ (- 1.0 k) 2.0))) (* (log n) (/ (- 1.0 k) 2.0)) (* (log n) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)) (pow n (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow n (sqrt (/ (- 1.0 k) 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow n (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow n (/ (sqrt (- 1.0 k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n 1) (pow n (- 1.0 k)) (pow (* (cbrt n) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow 1 (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow n (/ (- 1.0 k) 2.0))) (exp (pow n (/ (- 1.0 k) 2.0))) (* (cbrt (pow n (/ (- 1.0 k) 2.0))) (cbrt (pow n (/ (- 1.0 k) 2.0)))) (cbrt (pow n (/ (- 1.0 k) 2.0))) (* (* (pow n (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log 2.0) (log PI)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log 2.0) (log PI)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* 2.0 PI) (/ 1.0 2.0))) (* (sqrt k) (pow (* 2.0 PI) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) 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(- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) (pow k 3)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) k)) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 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))))) 4.249 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* h0 h3) (/ (- h2 h1) h0))) (log1p (pow (* h0 h3) (/ (- h2 h1) h0))) (* (+ (log h0) (log h3)) (/ (- h2 h1) h0)) (* (log (* h0 h3)) (/ (- h2 h1) h0)) (* (log (* h0 h3)) (/ (- h2 h1) h0)) (* 1 (/ (- h2 h1) h0)) (* 1 (/ (- h2 h1) h0)) (pow (* h0 h3) (/ h2 h0)) (pow (* h0 h3) (/ h1 h0)) (pow (* h0 h3) (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0)))) 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(- h2 h1) h0))) (* (/ 1 (sqrt h1)) (pow (* h0 h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* h0 h3) (/ h2 h0))) (* h2 (pow (* h0 h3) (/ (- h2 h1) h0))) (expm1 (/ h2 (sqrt h1))) (log1p (/ h2 (sqrt h1))) (- (log h2) (log (sqrt h1))) (log (/ h2 (sqrt h1))) (exp (/ h2 (sqrt h1))) (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (cbrt (/ h2 (sqrt h1))) (cbrt (/ h2 (sqrt h1)))) (cbrt (/ h2 (sqrt h1))) (* (* (/ h2 (sqrt h1)) (/ h2 (sqrt h1))) (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (sqrt (/ h2 (sqrt h1))) (- h2) (- (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (cbrt h2) (cbrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (cbrt h2) (sqrt (cbrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) (sqrt 1)) (/ (cbrt h2) (sqrt h1)) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) 1) (/ (cbrt h2) (sqrt h1)) (/ (sqrt h2) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (sqrt h2) (cbrt (sqrt h1))) (/ (sqrt h2) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (sqrt h2) (sqrt (cbrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt 1)) (/ (sqrt h2) (sqrt h1)) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) 1) (/ (sqrt h2) (sqrt h1)) (/ 1 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (cbrt (sqrt h1))) (/ 1 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (cbrt h1))) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 (sqrt 1)) (/ h2 (sqrt h1)) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 1) (/ h2 (sqrt h1)) (/ 1 (sqrt h1)) (/ (sqrt h1) h2) (/ h2 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (sqrt h1))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h1))) (/ h2 1) (/ (sqrt h1) (cbrt h2)) (/ (sqrt h1) (sqrt h2)) (/ (sqrt h1) h2) (- (+ (* h6 (* (* (pow h1 2) (pow (log (* h0 h3)) 2)) (pow (* (pow h0 h2) (pow h3 h2)) h5))) (pow (* h0 h3) h5)) (* h5 (* (* h1 (log (* h0 h3))) (pow (* (pow h0 h2) (pow h3 h2)) h5)))) (exp (* h5 (* (- h2 h1) (log (* h0 h3))))) (exp (* h5 (* (- h2 h1) (log (* h0 h3))))) (- (+ (* h6 (* (* (pow h1 2) (pow (log h4) 2)) (pow (pow h4 h2) h5))) (pow h4 h5)) (* h5 (* (* h1 (log h4)) (pow (pow h4 h2) h5)))) (exp (* h7 (* (- h2 h1) (log (/ 1 h4))))) (exp (* h5 (* (- h2 h1) (- (log -1) (log (/ -1 h4)))))) (- (+ (* h8 (* (pow h1 2) (pow (* (pow h0 h2) (pow h3 h2)) h5))) (- (+ (* h8 (* (* (pow h1 2) (log (* h0 h3))) (pow (* (pow h3 h2) (pow h0 h2)) h5))) (- (+ (* h8 (* h1 (pow (* (pow h3 h2) (pow h0 h2)) h5))) (- (+ (* h8 (* (* h1 (log (* h0 h3))) (pow (* (pow h3 h2) (pow h0 h2)) h5))) (- (+ (* h8 (* (* (pow h1 2) (pow (log (* h0 h3)) 2)) (pow (* (pow h3 h2) (pow h0 h2)) h5))) (- (* h8 (pow (* (pow h3 h2) (pow h0 h2)) h5))))))))))))) (- (+ (* h8 (/ (exp (* h5 (* (- h2 h1) (log (* h0 h3))))) (pow h1 2))) (- (+ (* h8 (/ (exp (* h5 (* (- h2 h1) (log (* h0 h3))))) h1)) (- (* h8 (/ (exp (* h5 (* (- h2 h1) (log (* h0 h3))))) (pow h1 3)))))))) (- (+ (* h8 (/ (exp (* h5 (* (- h2 h1) (log (* h0 h3))))) (pow h1 2))) (- (+ (* h8 (/ (exp (* h5 (* (- h2 h1) (log (* h0 h3))))) h1)) (- (* h8 (exp (* h5 (* (- h2 h1) (log (* h0 h3))))))))))) (- (+ (* h8 h1) (- (+ (* h8 (pow h1 2)) (- h8))))) (- (+ (* h8 (/ 1 (pow h1 2))) (- (+ (* h8 (/ 1 h1)) (- (* h8 (/ 1 (pow h1 3)))))))) (- (+ (* h8 (/ 1 (pow h1 2))) (- (+ (* h8 (/ 1 h1)) (- h8))))) 4.257 * * [simplify]: iteration 0 : 844 enodes (cost 1367 ) 4.270 * * [simplify]: iteration 1 : 3255 enodes (cost 1284 ) 4.317 * * [simplify]: iteration 2 : 5001 enodes (cost 1267 ) 4.323 * * * [progress]: adding candidates to table 4.819 * [progress]: [Phase 3 of 3] Extracting. 4.819 * * [regime]: Finding splitpoints for: (# # # # # # #) 4.822 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 4.822 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 4.855 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 4.884 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 4.917 * * * [regime]: Found split indices: #