11.426 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.083 * * * [progress]: [2/2] Setting up program. 0.086 * [progress]: [Phase 2 of 3] Improving. 0.086 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.086 * [simplify]: Sending expressions to egg_math: (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) 0.088 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.089 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.091 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.094 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.099 * * [simplify]: iteration 4 : 1034 enodes (cost 8 ) 0.122 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.122 * * [progress]: iteration 1 / 4 0.123 * * * [progress]: picking best candidate 0.125 * * * * [pick]: Picked # 0.125 * * * [progress]: localizing error 0.138 * * * [progress]: generating rewritten candidates 0.138 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.163 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.180 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.185 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.230 * * * [progress]: generating series expansions 0.231 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.231 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 0.231 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.231 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.231 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.231 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.232 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.232 * [taylor]: Taking taylor expansion of 0.5 in k 0.232 * [backup-simplify]: Simplify 0.5 into 0.5 0.232 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.232 * [taylor]: Taking taylor expansion of 1.0 in k 0.232 * [backup-simplify]: Simplify 1.0 into 1.0 0.232 * [taylor]: Taking taylor expansion of k in k 0.232 * [backup-simplify]: Simplify 0 into 0 0.232 * [backup-simplify]: Simplify 1 into 1 0.232 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.232 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.232 * [taylor]: Taking taylor expansion of 2.0 in k 0.232 * [backup-simplify]: Simplify 2.0 into 2.0 0.232 * [taylor]: Taking taylor expansion of (* n PI) in k 0.232 * [taylor]: Taking taylor expansion of n in k 0.232 * [backup-simplify]: Simplify n into n 0.232 * [taylor]: Taking taylor expansion of PI in k 0.232 * [backup-simplify]: Simplify PI into PI 0.232 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.232 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.232 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.232 * [backup-simplify]: Simplify (- 0) into 0 0.233 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.233 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.233 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.233 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.233 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.233 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.233 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.233 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.233 * [taylor]: Taking taylor expansion of 0.5 in n 0.233 * [backup-simplify]: Simplify 0.5 into 0.5 0.233 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.233 * [taylor]: Taking taylor expansion of 1.0 in n 0.233 * [backup-simplify]: Simplify 1.0 into 1.0 0.233 * [taylor]: Taking taylor expansion of k in n 0.233 * [backup-simplify]: Simplify k into k 0.233 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.233 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.233 * [taylor]: Taking taylor expansion of 2.0 in n 0.233 * [backup-simplify]: Simplify 2.0 into 2.0 0.233 * [taylor]: Taking taylor expansion of (* n PI) in n 0.233 * [taylor]: Taking taylor expansion of n in n 0.233 * [backup-simplify]: Simplify 0 into 0 0.233 * [backup-simplify]: Simplify 1 into 1 0.233 * [taylor]: Taking taylor expansion of PI in n 0.233 * [backup-simplify]: Simplify PI into PI 0.234 * [backup-simplify]: Simplify (* 0 PI) into 0 0.234 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.235 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.236 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.237 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.237 * [backup-simplify]: Simplify (- k) into (- k) 0.237 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.237 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.237 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.238 * [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)))) 0.239 * [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))))) 0.239 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.239 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.239 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.239 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.239 * [taylor]: Taking taylor expansion of 0.5 in n 0.239 * [backup-simplify]: Simplify 0.5 into 0.5 0.239 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.239 * [taylor]: Taking taylor expansion of 1.0 in n 0.239 * [backup-simplify]: Simplify 1.0 into 1.0 0.239 * [taylor]: Taking taylor expansion of k in n 0.239 * [backup-simplify]: Simplify k into k 0.239 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.239 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.239 * [taylor]: Taking taylor expansion of 2.0 in n 0.239 * [backup-simplify]: Simplify 2.0 into 2.0 0.239 * [taylor]: Taking taylor expansion of (* n PI) in n 0.239 * [taylor]: Taking taylor expansion of n in n 0.239 * [backup-simplify]: Simplify 0 into 0 0.239 * [backup-simplify]: Simplify 1 into 1 0.239 * [taylor]: Taking taylor expansion of PI in n 0.239 * [backup-simplify]: Simplify PI into PI 0.240 * [backup-simplify]: Simplify (* 0 PI) into 0 0.240 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.241 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.242 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.242 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.242 * [backup-simplify]: Simplify (- k) into (- k) 0.243 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.243 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.243 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.244 * [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)))) 0.245 * [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))))) 0.245 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.245 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.245 * [taylor]: Taking taylor expansion of 0.5 in k 0.245 * [backup-simplify]: Simplify 0.5 into 0.5 0.245 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.245 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.245 * [taylor]: Taking taylor expansion of 1.0 in k 0.245 * [backup-simplify]: Simplify 1.0 into 1.0 0.245 * [taylor]: Taking taylor expansion of k in k 0.245 * [backup-simplify]: Simplify 0 into 0 0.245 * [backup-simplify]: Simplify 1 into 1 0.245 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.245 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.245 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.245 * [taylor]: Taking taylor expansion of 2.0 in k 0.245 * [backup-simplify]: Simplify 2.0 into 2.0 0.245 * [taylor]: Taking taylor expansion of PI in k 0.245 * [backup-simplify]: Simplify PI into PI 0.245 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.246 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.246 * [taylor]: Taking taylor expansion of (log n) in k 0.246 * [taylor]: Taking taylor expansion of n in k 0.246 * [backup-simplify]: Simplify n into n 0.246 * [backup-simplify]: Simplify (log n) into (log n) 0.246 * [backup-simplify]: Simplify (- 0) into 0 0.247 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.247 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.248 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.249 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.249 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.250 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.251 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.251 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.252 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.252 * [backup-simplify]: Simplify (- 0) into 0 0.253 * [backup-simplify]: Simplify (+ 0 0) into 0 0.253 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 0.254 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.255 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.256 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.256 * [taylor]: Taking taylor expansion of 0 in k 0.256 * [backup-simplify]: Simplify 0 into 0 0.256 * [backup-simplify]: Simplify 0 into 0 0.256 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.257 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.258 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.258 * [backup-simplify]: Simplify (+ 0 0) into 0 0.258 * [backup-simplify]: Simplify (- 1) into -1 0.258 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.259 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.261 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 0.262 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0.264 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0.265 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.266 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.267 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.268 * [backup-simplify]: Simplify (- 0) into 0 0.268 * [backup-simplify]: Simplify (+ 0 0) into 0 0.268 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 0.269 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.270 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.271 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.271 * [taylor]: Taking taylor expansion of 0 in k 0.271 * [backup-simplify]: Simplify 0 into 0 0.271 * [backup-simplify]: Simplify 0 into 0 0.272 * [backup-simplify]: Simplify 0 into 0 0.272 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.274 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.275 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 0.275 * [backup-simplify]: Simplify (+ 0 0) into 0 0.275 * [backup-simplify]: Simplify (- 0) into 0 0.276 * [backup-simplify]: Simplify (+ 0 0) into 0 0.277 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.278 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 0.280 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0.284 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0.294 * [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)))))) 0.295 * [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)))) 0.295 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.295 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.295 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.295 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.295 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.295 * [taylor]: Taking taylor expansion of 0.5 in k 0.295 * [backup-simplify]: Simplify 0.5 into 0.5 0.295 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.295 * [taylor]: Taking taylor expansion of 1.0 in k 0.295 * [backup-simplify]: Simplify 1.0 into 1.0 0.295 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.295 * [taylor]: Taking taylor expansion of k in k 0.295 * [backup-simplify]: Simplify 0 into 0 0.295 * [backup-simplify]: Simplify 1 into 1 0.295 * [backup-simplify]: Simplify (/ 1 1) into 1 0.295 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.295 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.295 * [taylor]: Taking taylor expansion of 2.0 in k 0.295 * [backup-simplify]: Simplify 2.0 into 2.0 0.295 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.295 * [taylor]: Taking taylor expansion of PI in k 0.295 * [backup-simplify]: Simplify PI into PI 0.295 * [taylor]: Taking taylor expansion of n in k 0.295 * [backup-simplify]: Simplify n into n 0.295 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.295 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.295 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.296 * [backup-simplify]: Simplify (- 1) into -1 0.296 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.296 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.296 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.296 * [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))))) 0.296 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.296 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.296 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.297 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.297 * [taylor]: Taking taylor expansion of 0.5 in n 0.297 * [backup-simplify]: Simplify 0.5 into 0.5 0.297 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.297 * [taylor]: Taking taylor expansion of 1.0 in n 0.297 * [backup-simplify]: Simplify 1.0 into 1.0 0.297 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.297 * [taylor]: Taking taylor expansion of k in n 0.297 * [backup-simplify]: Simplify k into k 0.297 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.297 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.297 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.297 * [taylor]: Taking taylor expansion of 2.0 in n 0.297 * [backup-simplify]: Simplify 2.0 into 2.0 0.297 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.297 * [taylor]: Taking taylor expansion of PI in n 0.297 * [backup-simplify]: Simplify PI into PI 0.297 * [taylor]: Taking taylor expansion of n in n 0.297 * [backup-simplify]: Simplify 0 into 0 0.297 * [backup-simplify]: Simplify 1 into 1 0.297 * [backup-simplify]: Simplify (/ PI 1) into PI 0.298 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.298 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.298 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.298 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.298 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.299 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.300 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.301 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.301 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.301 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.301 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.301 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.301 * [taylor]: Taking taylor expansion of 0.5 in n 0.301 * [backup-simplify]: Simplify 0.5 into 0.5 0.301 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.301 * [taylor]: Taking taylor expansion of 1.0 in n 0.301 * [backup-simplify]: Simplify 1.0 into 1.0 0.301 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.301 * [taylor]: Taking taylor expansion of k in n 0.301 * [backup-simplify]: Simplify k into k 0.301 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.301 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.301 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.301 * [taylor]: Taking taylor expansion of 2.0 in n 0.301 * [backup-simplify]: Simplify 2.0 into 2.0 0.301 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.301 * [taylor]: Taking taylor expansion of PI in n 0.301 * [backup-simplify]: Simplify PI into PI 0.301 * [taylor]: Taking taylor expansion of n in n 0.301 * [backup-simplify]: Simplify 0 into 0 0.301 * [backup-simplify]: Simplify 1 into 1 0.301 * [backup-simplify]: Simplify (/ PI 1) into PI 0.302 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.302 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.302 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.302 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.303 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.303 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.304 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.305 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.305 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.305 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.305 * [taylor]: Taking taylor expansion of 0.5 in k 0.305 * [backup-simplify]: Simplify 0.5 into 0.5 0.305 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.305 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.305 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.305 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.305 * [taylor]: Taking taylor expansion of 2.0 in k 0.305 * [backup-simplify]: Simplify 2.0 into 2.0 0.305 * [taylor]: Taking taylor expansion of PI in k 0.305 * [backup-simplify]: Simplify PI into PI 0.305 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.306 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.306 * [taylor]: Taking taylor expansion of (log n) in k 0.306 * [taylor]: Taking taylor expansion of n in k 0.306 * [backup-simplify]: Simplify n into n 0.306 * [backup-simplify]: Simplify (log n) into (log n) 0.306 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.306 * [taylor]: Taking taylor expansion of 1.0 in k 0.306 * [backup-simplify]: Simplify 1.0 into 1.0 0.306 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.306 * [taylor]: Taking taylor expansion of k in k 0.306 * [backup-simplify]: Simplify 0 into 0 0.306 * [backup-simplify]: Simplify 1 into 1 0.306 * [backup-simplify]: Simplify (/ 1 1) into 1 0.306 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.307 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.307 * [backup-simplify]: Simplify (- 1) into -1 0.308 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.308 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.309 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 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))))) 0.310 * [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 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.312 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.312 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.313 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.313 * [backup-simplify]: Simplify (- 0) into 0 0.313 * [backup-simplify]: Simplify (+ 0 0) into 0 0.313 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.314 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.315 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.316 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.316 * [taylor]: Taking taylor expansion of 0 in k 0.316 * [backup-simplify]: Simplify 0 into 0 0.316 * [backup-simplify]: Simplify 0 into 0 0.316 * [backup-simplify]: Simplify 0 into 0 0.317 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.317 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.319 * [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 0.319 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.319 * [backup-simplify]: Simplify (- 0) into 0 0.320 * [backup-simplify]: Simplify (+ 0 0) into 0 0.320 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 0.321 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.322 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 0.323 * [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 0.323 * [taylor]: Taking taylor expansion of 0 in k 0.323 * [backup-simplify]: Simplify 0 into 0 0.323 * [backup-simplify]: Simplify 0 into 0 0.323 * [backup-simplify]: Simplify 0 into 0 0.323 * [backup-simplify]: Simplify 0 into 0 0.324 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.325 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.327 * [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 0.328 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.328 * [backup-simplify]: Simplify (- 0) into 0 0.328 * [backup-simplify]: Simplify (+ 0 0) into 0 0.329 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 0.330 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.331 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 0.332 * [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 0.332 * [taylor]: Taking taylor expansion of 0 in k 0.332 * [backup-simplify]: Simplify 0 into 0 0.332 * [backup-simplify]: Simplify 0 into 0 0.333 * [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)))) 0.334 * [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))) 0.334 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.334 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.334 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.334 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.334 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.334 * [taylor]: Taking taylor expansion of 0.5 in k 0.334 * [backup-simplify]: Simplify 0.5 into 0.5 0.334 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.334 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.334 * [taylor]: Taking taylor expansion of k in k 0.334 * [backup-simplify]: Simplify 0 into 0 0.334 * [backup-simplify]: Simplify 1 into 1 0.334 * [backup-simplify]: Simplify (/ 1 1) into 1 0.334 * [taylor]: Taking taylor expansion of 1.0 in k 0.334 * [backup-simplify]: Simplify 1.0 into 1.0 0.334 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.334 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.334 * [taylor]: Taking taylor expansion of -2.0 in k 0.334 * [backup-simplify]: Simplify -2.0 into -2.0 0.334 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.334 * [taylor]: Taking taylor expansion of PI in k 0.334 * [backup-simplify]: Simplify PI into PI 0.334 * [taylor]: Taking taylor expansion of n in k 0.335 * [backup-simplify]: Simplify n into n 0.335 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.335 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.335 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.335 * [backup-simplify]: Simplify (+ 1 0) into 1 0.335 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.335 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.335 * [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)))))) 0.335 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.335 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.335 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.335 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.335 * [taylor]: Taking taylor expansion of 0.5 in n 0.336 * [backup-simplify]: Simplify 0.5 into 0.5 0.336 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.336 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.336 * [taylor]: Taking taylor expansion of k in n 0.336 * [backup-simplify]: Simplify k into k 0.336 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.336 * [taylor]: Taking taylor expansion of 1.0 in n 0.336 * [backup-simplify]: Simplify 1.0 into 1.0 0.336 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.336 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.336 * [taylor]: Taking taylor expansion of -2.0 in n 0.336 * [backup-simplify]: Simplify -2.0 into -2.0 0.336 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.336 * [taylor]: Taking taylor expansion of PI in n 0.336 * [backup-simplify]: Simplify PI into PI 0.336 * [taylor]: Taking taylor expansion of n in n 0.336 * [backup-simplify]: Simplify 0 into 0 0.336 * [backup-simplify]: Simplify 1 into 1 0.336 * [backup-simplify]: Simplify (/ PI 1) into PI 0.336 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.337 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.337 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.337 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.338 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.339 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.339 * [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))))) 0.339 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.339 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.339 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.339 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.339 * [taylor]: Taking taylor expansion of 0.5 in n 0.339 * [backup-simplify]: Simplify 0.5 into 0.5 0.340 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.340 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.340 * [taylor]: Taking taylor expansion of k in n 0.340 * [backup-simplify]: Simplify k into k 0.340 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.340 * [taylor]: Taking taylor expansion of 1.0 in n 0.340 * [backup-simplify]: Simplify 1.0 into 1.0 0.340 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.340 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.340 * [taylor]: Taking taylor expansion of -2.0 in n 0.340 * [backup-simplify]: Simplify -2.0 into -2.0 0.340 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.340 * [taylor]: Taking taylor expansion of PI in n 0.340 * [backup-simplify]: Simplify PI into PI 0.340 * [taylor]: Taking taylor expansion of n in n 0.340 * [backup-simplify]: Simplify 0 into 0 0.340 * [backup-simplify]: Simplify 1 into 1 0.340 * [backup-simplify]: Simplify (/ PI 1) into PI 0.340 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.341 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.341 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.341 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.342 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.343 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.343 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.343 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.344 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.344 * [taylor]: Taking taylor expansion of 0.5 in k 0.344 * [backup-simplify]: Simplify 0.5 into 0.5 0.344 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.344 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.344 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.344 * [taylor]: Taking taylor expansion of k in k 0.344 * [backup-simplify]: Simplify 0 into 0 0.344 * [backup-simplify]: Simplify 1 into 1 0.344 * [backup-simplify]: Simplify (/ 1 1) into 1 0.344 * [taylor]: Taking taylor expansion of 1.0 in k 0.344 * [backup-simplify]: Simplify 1.0 into 1.0 0.344 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.344 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.344 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.344 * [taylor]: Taking taylor expansion of -2.0 in k 0.344 * [backup-simplify]: Simplify -2.0 into -2.0 0.344 * [taylor]: Taking taylor expansion of PI in k 0.344 * [backup-simplify]: Simplify PI into PI 0.344 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.345 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.345 * [taylor]: Taking taylor expansion of (log n) in k 0.345 * [taylor]: Taking taylor expansion of n in k 0.345 * [backup-simplify]: Simplify n into n 0.345 * [backup-simplify]: Simplify (log n) into (log n) 0.345 * [backup-simplify]: Simplify (+ 1 0) into 1 0.345 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.346 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 0.347 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 0.347 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 0.348 * [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 * [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 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.350 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.351 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.351 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.351 * [backup-simplify]: Simplify (+ 0 0) into 0 0.351 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 0.352 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.353 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.354 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.354 * [taylor]: Taking taylor expansion of 0 in k 0.354 * [backup-simplify]: Simplify 0 into 0 0.354 * [backup-simplify]: Simplify 0 into 0 0.354 * [backup-simplify]: Simplify 0 into 0 0.355 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.355 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.357 * [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 0.357 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.357 * [backup-simplify]: Simplify (+ 0 0) into 0 0.358 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 0.358 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.359 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 0.361 * [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 0.361 * [taylor]: Taking taylor expansion of 0 in k 0.361 * [backup-simplify]: Simplify 0 into 0 0.361 * [backup-simplify]: Simplify 0 into 0 0.361 * [backup-simplify]: Simplify 0 into 0 0.361 * [backup-simplify]: Simplify 0 into 0 0.361 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.362 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.365 * [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 0.365 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.365 * [backup-simplify]: Simplify (+ 0 0) into 0 0.366 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.367 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.368 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 0.370 * [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 0.370 * [taylor]: Taking taylor expansion of 0 in k 0.370 * [backup-simplify]: Simplify 0 into 0 0.370 * [backup-simplify]: Simplify 0 into 0 0.370 * [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)))))) 0.370 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.371 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.371 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.371 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.371 * [taylor]: Taking taylor expansion of 2.0 in n 0.371 * [backup-simplify]: Simplify 2.0 into 2.0 0.371 * [taylor]: Taking taylor expansion of (* n PI) in n 0.371 * [taylor]: Taking taylor expansion of n in n 0.371 * [backup-simplify]: Simplify 0 into 0 0.371 * [backup-simplify]: Simplify 1 into 1 0.371 * [taylor]: Taking taylor expansion of PI in n 0.371 * [backup-simplify]: Simplify PI into PI 0.371 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.371 * [taylor]: Taking taylor expansion of 2.0 in n 0.371 * [backup-simplify]: Simplify 2.0 into 2.0 0.371 * [taylor]: Taking taylor expansion of (* n PI) in n 0.371 * [taylor]: Taking taylor expansion of n in n 0.371 * [backup-simplify]: Simplify 0 into 0 0.371 * [backup-simplify]: Simplify 1 into 1 0.371 * [taylor]: Taking taylor expansion of PI in n 0.371 * [backup-simplify]: Simplify PI into PI 0.371 * [backup-simplify]: Simplify (* 0 PI) into 0 0.372 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.372 * [backup-simplify]: Simplify 0 into 0 0.373 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.373 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.374 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.374 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.375 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.375 * [backup-simplify]: Simplify 0 into 0 0.376 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.376 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.376 * [backup-simplify]: Simplify 0 into 0 0.377 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.378 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.378 * [backup-simplify]: Simplify 0 into 0 0.379 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.379 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 0.379 * [backup-simplify]: Simplify 0 into 0 0.384 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 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 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.385 * [backup-simplify]: Simplify 0 into 0 0.386 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.387 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.387 * [backup-simplify]: Simplify 0 into 0 0.387 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.388 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 0.388 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.388 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.388 * [taylor]: Taking taylor expansion of 2.0 in n 0.388 * [backup-simplify]: Simplify 2.0 into 2.0 0.388 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.388 * [taylor]: Taking taylor expansion of PI in n 0.388 * [backup-simplify]: Simplify PI into PI 0.388 * [taylor]: Taking taylor expansion of n in n 0.388 * [backup-simplify]: Simplify 0 into 0 0.388 * [backup-simplify]: Simplify 1 into 1 0.388 * [backup-simplify]: Simplify (/ PI 1) into PI 0.388 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.388 * [taylor]: Taking taylor expansion of 2.0 in n 0.388 * [backup-simplify]: Simplify 2.0 into 2.0 0.388 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.388 * [taylor]: Taking taylor expansion of PI in n 0.388 * [backup-simplify]: Simplify PI into PI 0.388 * [taylor]: Taking taylor expansion of n in n 0.388 * [backup-simplify]: Simplify 0 into 0 0.388 * [backup-simplify]: Simplify 1 into 1 0.389 * [backup-simplify]: Simplify (/ PI 1) into PI 0.389 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.389 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.390 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.390 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.390 * [backup-simplify]: Simplify 0 into 0 0.391 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.392 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.392 * [backup-simplify]: Simplify 0 into 0 0.392 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.393 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.393 * [backup-simplify]: Simplify 0 into 0 0.394 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.394 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.394 * [backup-simplify]: Simplify 0 into 0 0.395 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.396 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.396 * [backup-simplify]: Simplify 0 into 0 0.396 * [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 0.397 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.397 * [backup-simplify]: Simplify 0 into 0 0.397 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.398 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.398 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.398 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.398 * [taylor]: Taking taylor expansion of -2.0 in n 0.398 * [backup-simplify]: Simplify -2.0 into -2.0 0.398 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.398 * [taylor]: Taking taylor expansion of PI in n 0.398 * [backup-simplify]: Simplify PI into PI 0.398 * [taylor]: Taking taylor expansion of n in n 0.398 * [backup-simplify]: Simplify 0 into 0 0.398 * [backup-simplify]: Simplify 1 into 1 0.398 * [backup-simplify]: Simplify (/ PI 1) into PI 0.398 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.398 * [taylor]: Taking taylor expansion of -2.0 in n 0.398 * [backup-simplify]: Simplify -2.0 into -2.0 0.398 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.398 * [taylor]: Taking taylor expansion of PI in n 0.398 * [backup-simplify]: Simplify PI into PI 0.398 * [taylor]: Taking taylor expansion of n in n 0.398 * [backup-simplify]: Simplify 0 into 0 0.398 * [backup-simplify]: Simplify 1 into 1 0.399 * [backup-simplify]: Simplify (/ PI 1) into PI 0.399 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.399 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.400 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.400 * [backup-simplify]: Simplify (+ (* -2.0 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)))) into 0 0.401 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.401 * [backup-simplify]: Simplify 0 into 0 0.402 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.403 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.403 * [backup-simplify]: Simplify 0 into 0 0.403 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.404 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.404 * [backup-simplify]: Simplify 0 into 0 0.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.405 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 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)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.407 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.407 * [backup-simplify]: Simplify 0 into 0 0.407 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.407 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.407 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.407 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.407 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.407 * [taylor]: Taking taylor expansion of 1.0 in k 0.407 * [backup-simplify]: Simplify 1.0 into 1.0 0.407 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.407 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.407 * [taylor]: Taking taylor expansion of k in k 0.407 * [backup-simplify]: Simplify 0 into 0 0.407 * [backup-simplify]: Simplify 1 into 1 0.408 * [backup-simplify]: Simplify (/ 1 1) into 1 0.408 * [backup-simplify]: Simplify (sqrt 0) into 0 0.409 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.409 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.409 * [taylor]: Taking taylor expansion of 1.0 in k 0.409 * [backup-simplify]: Simplify 1.0 into 1.0 0.409 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.409 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.409 * [taylor]: Taking taylor expansion of k in k 0.409 * [backup-simplify]: Simplify 0 into 0 0.409 * [backup-simplify]: Simplify 1 into 1 0.409 * [backup-simplify]: Simplify (/ 1 1) into 1 0.409 * [backup-simplify]: Simplify (sqrt 0) into 0 0.410 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.410 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.410 * [backup-simplify]: Simplify 0 into 0 0.411 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.411 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.412 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.414 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.415 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.415 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.415 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.417 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.419 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.419 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.420 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 0.420 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 0.420 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.420 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.420 * [taylor]: Taking taylor expansion of 1.0 in k 0.420 * [backup-simplify]: Simplify 1.0 into 1.0 0.420 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.420 * [taylor]: Taking taylor expansion of k in k 0.420 * [backup-simplify]: Simplify 0 into 0 0.420 * [backup-simplify]: Simplify 1 into 1 0.420 * [backup-simplify]: Simplify (sqrt 0) into 0 0.421 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.421 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.421 * [taylor]: Taking taylor expansion of 1.0 in k 0.421 * [backup-simplify]: Simplify 1.0 into 1.0 0.421 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.421 * [taylor]: Taking taylor expansion of k in k 0.421 * [backup-simplify]: Simplify 0 into 0 0.421 * [backup-simplify]: Simplify 1 into 1 0.421 * [backup-simplify]: Simplify (sqrt 0) into 0 0.422 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.422 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.422 * [backup-simplify]: Simplify 0 into 0 0.423 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.423 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.425 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.426 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.426 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.428 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.430 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.430 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.431 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 0.431 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.431 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.431 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.431 * [taylor]: Taking taylor expansion of 1.0 in k 0.431 * [backup-simplify]: Simplify 1.0 into 1.0 0.431 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.431 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.431 * [taylor]: Taking taylor expansion of -1 in k 0.431 * [backup-simplify]: Simplify -1 into -1 0.431 * [taylor]: Taking taylor expansion of k in k 0.431 * [backup-simplify]: Simplify 0 into 0 0.431 * [backup-simplify]: Simplify 1 into 1 0.431 * [backup-simplify]: Simplify (/ -1 1) into -1 0.432 * [backup-simplify]: Simplify (sqrt 0) into 0 0.432 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.433 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.433 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.433 * [taylor]: Taking taylor expansion of 1.0 in k 0.433 * [backup-simplify]: Simplify 1.0 into 1.0 0.433 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.433 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.433 * [taylor]: Taking taylor expansion of -1 in k 0.433 * [backup-simplify]: Simplify -1 into -1 0.433 * [taylor]: Taking taylor expansion of k in k 0.433 * [backup-simplify]: Simplify 0 into 0 0.433 * [backup-simplify]: Simplify 1 into 1 0.433 * [backup-simplify]: Simplify (/ -1 1) into -1 0.433 * [backup-simplify]: Simplify (sqrt 0) into 0 0.434 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.434 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.434 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.436 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.438 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 0.438 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.439 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.441 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.443 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 0.444 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.445 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 0.445 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.445 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 0.445 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 0.445 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.445 * [taylor]: Taking taylor expansion of 1.0 in n 0.445 * [backup-simplify]: Simplify 1.0 into 1.0 0.445 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.445 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.445 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.445 * [taylor]: Taking taylor expansion of k in n 0.445 * [backup-simplify]: Simplify k into k 0.445 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.445 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 0.445 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.445 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 0.445 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.445 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.446 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.446 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.446 * [taylor]: Taking taylor expansion of 0.5 in n 0.446 * [backup-simplify]: Simplify 0.5 into 0.5 0.446 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.446 * [taylor]: Taking taylor expansion of 1.0 in n 0.446 * [backup-simplify]: Simplify 1.0 into 1.0 0.446 * [taylor]: Taking taylor expansion of k in n 0.446 * [backup-simplify]: Simplify k into k 0.446 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.446 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.446 * [taylor]: Taking taylor expansion of 2.0 in n 0.446 * [backup-simplify]: Simplify 2.0 into 2.0 0.446 * [taylor]: Taking taylor expansion of (* n PI) in n 0.446 * [taylor]: Taking taylor expansion of n in n 0.446 * [backup-simplify]: Simplify 0 into 0 0.446 * [backup-simplify]: Simplify 1 into 1 0.446 * [taylor]: Taking taylor expansion of PI in n 0.446 * [backup-simplify]: Simplify PI into PI 0.446 * [backup-simplify]: Simplify (* 0 PI) into 0 0.446 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.447 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.448 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.449 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.449 * [backup-simplify]: Simplify (- k) into (- k) 0.449 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.449 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.450 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.450 * [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)))) 0.451 * [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))))) 0.451 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.451 * [taylor]: Taking taylor expansion of 1.0 in k 0.451 * [backup-simplify]: Simplify 1.0 into 1.0 0.451 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.451 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.451 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.451 * [taylor]: Taking taylor expansion of k in k 0.451 * [backup-simplify]: Simplify 0 into 0 0.451 * [backup-simplify]: Simplify 1 into 1 0.451 * [backup-simplify]: Simplify (/ 1 1) into 1 0.452 * [backup-simplify]: Simplify (sqrt 0) into 0 0.452 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.452 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.453 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.453 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.453 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.453 * [taylor]: Taking taylor expansion of 0.5 in k 0.453 * [backup-simplify]: Simplify 0.5 into 0.5 0.453 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.453 * [taylor]: Taking taylor expansion of 1.0 in k 0.453 * [backup-simplify]: Simplify 1.0 into 1.0 0.453 * [taylor]: Taking taylor expansion of k in k 0.453 * [backup-simplify]: Simplify 0 into 0 0.453 * [backup-simplify]: Simplify 1 into 1 0.453 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.453 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.453 * [taylor]: Taking taylor expansion of 2.0 in k 0.453 * [backup-simplify]: Simplify 2.0 into 2.0 0.453 * [taylor]: Taking taylor expansion of (* n PI) in k 0.453 * [taylor]: Taking taylor expansion of n in k 0.453 * [backup-simplify]: Simplify n into n 0.453 * [taylor]: Taking taylor expansion of PI in k 0.453 * [backup-simplify]: Simplify PI into PI 0.453 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.453 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.453 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.453 * [backup-simplify]: Simplify (- 0) into 0 0.453 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.454 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.454 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.454 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.454 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.454 * [taylor]: Taking taylor expansion of 1.0 in k 0.454 * [backup-simplify]: Simplify 1.0 into 1.0 0.454 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.454 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.454 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.454 * [taylor]: Taking taylor expansion of k in k 0.454 * [backup-simplify]: Simplify 0 into 0 0.454 * [backup-simplify]: Simplify 1 into 1 0.454 * [backup-simplify]: Simplify (/ 1 1) into 1 0.454 * [backup-simplify]: Simplify (sqrt 0) into 0 0.455 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.455 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.455 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.455 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.455 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.455 * [taylor]: Taking taylor expansion of 0.5 in k 0.455 * [backup-simplify]: Simplify 0.5 into 0.5 0.455 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.455 * [taylor]: Taking taylor expansion of 1.0 in k 0.455 * [backup-simplify]: Simplify 1.0 into 1.0 0.455 * [taylor]: Taking taylor expansion of k in k 0.455 * [backup-simplify]: Simplify 0 into 0 0.455 * [backup-simplify]: Simplify 1 into 1 0.455 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.455 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.455 * [taylor]: Taking taylor expansion of 2.0 in k 0.455 * [backup-simplify]: Simplify 2.0 into 2.0 0.455 * [taylor]: Taking taylor expansion of (* n PI) in k 0.455 * [taylor]: Taking taylor expansion of n in k 0.456 * [backup-simplify]: Simplify n into n 0.456 * [taylor]: Taking taylor expansion of PI in k 0.456 * [backup-simplify]: Simplify PI into PI 0.456 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.456 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.456 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.456 * [backup-simplify]: Simplify (- 0) into 0 0.456 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.456 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.456 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.457 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.457 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 0.457 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.457 * [taylor]: Taking taylor expansion of 0 in n 0.457 * [backup-simplify]: Simplify 0 into 0 0.457 * [backup-simplify]: Simplify 0 into 0 0.457 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 0.458 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 0.458 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 0.458 * [backup-simplify]: Simplify (- 1) into -1 0.459 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.460 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 0.460 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 0.460 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (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))) 0.461 * [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))) 0.462 * [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))) 0.462 * [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 0.462 * [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 0.463 * [taylor]: Taking taylor expansion of +nan.0 in n 0.463 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.463 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.463 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.463 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.463 * [taylor]: Taking taylor expansion of 0.5 in n 0.463 * [backup-simplify]: Simplify 0.5 into 0.5 0.463 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.463 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.463 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.463 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.463 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.463 * [taylor]: Taking taylor expansion of 1.0 in n 0.463 * [backup-simplify]: Simplify 1.0 into 1.0 0.463 * [taylor]: Taking taylor expansion of (log PI) in n 0.463 * [taylor]: Taking taylor expansion of PI in n 0.463 * [backup-simplify]: Simplify PI into PI 0.463 * [backup-simplify]: Simplify (log PI) into (log PI) 0.464 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.465 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.465 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.465 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.465 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.465 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.465 * [taylor]: Taking taylor expansion of 1.0 in n 0.465 * [backup-simplify]: Simplify 1.0 into 1.0 0.465 * [taylor]: Taking taylor expansion of (log n) in n 0.465 * [taylor]: Taking taylor expansion of n in n 0.465 * [backup-simplify]: Simplify 0 into 0 0.465 * [backup-simplify]: Simplify 1 into 1 0.465 * [backup-simplify]: Simplify (log 1) into 0 0.465 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.465 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.465 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.465 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.465 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.465 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.465 * [taylor]: Taking taylor expansion of 1.0 in n 0.465 * [backup-simplify]: Simplify 1.0 into 1.0 0.465 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.465 * [taylor]: Taking taylor expansion of 2.0 in n 0.465 * [backup-simplify]: Simplify 2.0 into 2.0 0.466 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.466 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.467 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.467 * [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) 0.468 * [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) 0.469 * [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)) 0.470 * [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))) 0.471 * [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) 0.472 * [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)) 0.472 * [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))) 0.473 * [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))) 0.473 * [backup-simplify]: Simplify 0 into 0 0.474 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 0.474 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 0.481 * [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 0.481 * [backup-simplify]: Simplify (- 0) into 0 0.481 * [backup-simplify]: Simplify (+ 0 0) into 0 0.482 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.483 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 0.483 * [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))) 0.484 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.485 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.487 * [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)))))))) 0.490 * [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)))))))) 0.490 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 0.491 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 0.491 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 0.491 * [taylor]: Taking taylor expansion of +nan.0 in n 0.491 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.491 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.491 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.491 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.491 * [taylor]: Taking taylor expansion of 0.5 in n 0.491 * [backup-simplify]: Simplify 0.5 into 0.5 0.491 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.491 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.491 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.491 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.491 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.491 * [taylor]: Taking taylor expansion of 1.0 in n 0.491 * [backup-simplify]: Simplify 1.0 into 1.0 0.491 * [taylor]: Taking taylor expansion of (log PI) in n 0.491 * [taylor]: Taking taylor expansion of PI in n 0.491 * [backup-simplify]: Simplify PI into PI 0.491 * [backup-simplify]: Simplify (log PI) into (log PI) 0.492 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.493 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.493 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.493 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.493 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.493 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.493 * [taylor]: Taking taylor expansion of 1.0 in n 0.493 * [backup-simplify]: Simplify 1.0 into 1.0 0.493 * [taylor]: Taking taylor expansion of (log n) in n 0.493 * [taylor]: Taking taylor expansion of n in n 0.493 * [backup-simplify]: Simplify 0 into 0 0.493 * [backup-simplify]: Simplify 1 into 1 0.493 * [backup-simplify]: Simplify (log 1) into 0 0.493 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.493 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.493 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.493 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.493 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.494 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.494 * [taylor]: Taking taylor expansion of 1.0 in n 0.494 * [backup-simplify]: Simplify 1.0 into 1.0 0.494 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.494 * [taylor]: Taking taylor expansion of 2.0 in n 0.494 * [backup-simplify]: Simplify 2.0 into 2.0 0.494 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.495 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.496 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.496 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 0.497 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 0.498 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 0.499 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 0.499 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.500 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 0.500 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 0.500 * [taylor]: Taking taylor expansion of +nan.0 in n 0.500 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.500 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 0.500 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.500 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.500 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.500 * [taylor]: Taking taylor expansion of 0.5 in n 0.500 * [backup-simplify]: Simplify 0.5 into 0.5 0.500 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.500 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.500 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.500 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.500 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.500 * [taylor]: Taking taylor expansion of 1.0 in n 0.500 * [backup-simplify]: Simplify 1.0 into 1.0 0.500 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.500 * [taylor]: Taking taylor expansion of 2.0 in n 0.500 * [backup-simplify]: Simplify 2.0 into 2.0 0.500 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.501 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.501 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.502 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.502 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.502 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.502 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.502 * [taylor]: Taking taylor expansion of 1.0 in n 0.502 * [backup-simplify]: Simplify 1.0 into 1.0 0.502 * [taylor]: Taking taylor expansion of (log PI) in n 0.502 * [taylor]: Taking taylor expansion of PI in n 0.502 * [backup-simplify]: Simplify PI into PI 0.502 * [backup-simplify]: Simplify (log PI) into (log PI) 0.502 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.503 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.503 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.503 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.503 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.503 * [taylor]: Taking taylor expansion of 1.0 in n 0.504 * [backup-simplify]: Simplify 1.0 into 1.0 0.504 * [taylor]: Taking taylor expansion of (log n) in n 0.504 * [taylor]: Taking taylor expansion of n in n 0.504 * [backup-simplify]: Simplify 0 into 0 0.504 * [backup-simplify]: Simplify 1 into 1 0.504 * [backup-simplify]: Simplify (log 1) into 0 0.504 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.504 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.504 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.505 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.505 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.506 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.507 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.508 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.508 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.508 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.508 * [taylor]: Taking taylor expansion of 2.0 in n 0.508 * [backup-simplify]: Simplify 2.0 into 2.0 0.508 * [taylor]: Taking taylor expansion of (* n PI) in n 0.508 * [taylor]: Taking taylor expansion of n in n 0.508 * [backup-simplify]: Simplify 0 into 0 0.508 * [backup-simplify]: Simplify 1 into 1 0.508 * [taylor]: Taking taylor expansion of PI in n 0.508 * [backup-simplify]: Simplify PI into PI 0.509 * [backup-simplify]: Simplify (* 0 PI) into 0 0.509 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.510 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.511 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.511 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.512 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 0.513 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.514 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.516 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.517 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))) 0.521 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.524 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.528 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.528 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 0.529 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 0.530 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 0.531 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 0.531 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.531 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.532 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 0.532 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 0.533 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 0.533 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 0.534 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 0.535 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 0.536 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 0.538 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 0.539 * [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 0.540 * [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 0.540 * [backup-simplify]: Simplify (- 0) into 0 0.540 * [backup-simplify]: Simplify 0 into 0 0.540 * [backup-simplify]: Simplify 0 into 0 0.541 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.542 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 0.543 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 0.544 * [backup-simplify]: Simplify (- 0) into 0 0.544 * [backup-simplify]: Simplify (+ 0 0) into 0 0.545 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 0.545 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 0.546 * [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))) 0.547 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.549 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.552 * [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)))))))) 0.558 * [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)))))))) 0.559 * [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 0.559 * [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 0.559 * [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 0.559 * [taylor]: Taking taylor expansion of +nan.0 in n 0.559 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.559 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.559 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.559 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.559 * [taylor]: Taking taylor expansion of 0.5 in n 0.559 * [backup-simplify]: Simplify 0.5 into 0.5 0.559 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.559 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.559 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.559 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.559 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.559 * [taylor]: Taking taylor expansion of 1.0 in n 0.559 * [backup-simplify]: Simplify 1.0 into 1.0 0.559 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.559 * [taylor]: Taking taylor expansion of 2.0 in n 0.559 * [backup-simplify]: Simplify 2.0 into 2.0 0.559 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.560 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.561 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.561 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.561 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.561 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.561 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.561 * [taylor]: Taking taylor expansion of 1.0 in n 0.561 * [backup-simplify]: Simplify 1.0 into 1.0 0.561 * [taylor]: Taking taylor expansion of (log n) in n 0.561 * [taylor]: Taking taylor expansion of n in n 0.561 * [backup-simplify]: Simplify 0 into 0 0.561 * [backup-simplify]: Simplify 1 into 1 0.561 * [backup-simplify]: Simplify (log 1) into 0 0.561 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.561 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.561 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.561 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.561 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.561 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.561 * [taylor]: Taking taylor expansion of 1.0 in n 0.561 * [backup-simplify]: Simplify 1.0 into 1.0 0.562 * [taylor]: Taking taylor expansion of (log PI) in n 0.562 * [taylor]: Taking taylor expansion of PI in n 0.562 * [backup-simplify]: Simplify PI into PI 0.562 * [backup-simplify]: Simplify (log PI) into (log PI) 0.562 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.563 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.564 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.564 * [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) 0.565 * [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)) 0.566 * [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))) 0.567 * [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) 0.567 * [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 0.567 * [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 0.567 * [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 0.567 * [taylor]: Taking taylor expansion of +nan.0 in n 0.567 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.567 * [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 0.567 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.567 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.567 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.567 * [taylor]: Taking taylor expansion of 0.5 in n 0.567 * [backup-simplify]: Simplify 0.5 into 0.5 0.567 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.567 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.567 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.567 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.567 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.567 * [taylor]: Taking taylor expansion of 1.0 in n 0.567 * [backup-simplify]: Simplify 1.0 into 1.0 0.567 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.567 * [taylor]: Taking taylor expansion of 2.0 in n 0.567 * [backup-simplify]: Simplify 2.0 into 2.0 0.568 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.568 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.569 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.569 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.569 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.569 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.569 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.569 * [taylor]: Taking taylor expansion of 1.0 in n 0.569 * [backup-simplify]: Simplify 1.0 into 1.0 0.569 * [taylor]: Taking taylor expansion of (log PI) in n 0.569 * [taylor]: Taking taylor expansion of PI in n 0.569 * [backup-simplify]: Simplify PI into PI 0.570 * [backup-simplify]: Simplify (log PI) into (log PI) 0.570 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.571 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.571 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.571 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.571 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) 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 n) in n 0.571 * [taylor]: Taking taylor expansion of n in n 0.571 * [backup-simplify]: Simplify 0 into 0 0.571 * [backup-simplify]: Simplify 1 into 1 0.571 * [backup-simplify]: Simplify (log 1) into 0 0.572 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.572 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.572 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.572 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.573 * [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) 0.574 * [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)) 0.580 * [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))) 0.581 * [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) 0.581 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.581 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.581 * [taylor]: Taking taylor expansion of 2.0 in n 0.581 * [backup-simplify]: Simplify 2.0 into 2.0 0.581 * [taylor]: Taking taylor expansion of (* n PI) in n 0.581 * [taylor]: Taking taylor expansion of n in n 0.581 * [backup-simplify]: Simplify 0 into 0 0.581 * [backup-simplify]: Simplify 1 into 1 0.581 * [taylor]: Taking taylor expansion of PI in n 0.581 * [backup-simplify]: Simplify PI into PI 0.582 * [backup-simplify]: Simplify (* 0 PI) into 0 0.582 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.583 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.584 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.584 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.584 * [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 0.584 * [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 0.584 * [taylor]: Taking taylor expansion of +nan.0 in n 0.584 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.584 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 0.585 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.585 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.585 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.585 * [taylor]: Taking taylor expansion of 0.5 in n 0.585 * [backup-simplify]: Simplify 0.5 into 0.5 0.585 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.585 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.585 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.585 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.585 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.585 * [taylor]: Taking taylor expansion of 1.0 in n 0.585 * [backup-simplify]: Simplify 1.0 into 1.0 0.585 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.585 * [taylor]: Taking taylor expansion of 2.0 in n 0.585 * [backup-simplify]: Simplify 2.0 into 2.0 0.585 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.586 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.587 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.587 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.587 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.587 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.587 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.587 * [taylor]: Taking taylor expansion of 1.0 in n 0.587 * [backup-simplify]: Simplify 1.0 into 1.0 0.587 * [taylor]: Taking taylor expansion of (log PI) in n 0.587 * [taylor]: Taking taylor expansion of PI in n 0.587 * [backup-simplify]: Simplify PI into PI 0.587 * [backup-simplify]: Simplify (log PI) into (log PI) 0.588 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.589 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.589 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.589 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.589 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.589 * [taylor]: Taking taylor expansion of 1.0 in n 0.589 * [backup-simplify]: Simplify 1.0 into 1.0 0.589 * [taylor]: Taking taylor expansion of (log n) in n 0.589 * [taylor]: Taking taylor expansion of n in n 0.589 * [backup-simplify]: Simplify 0 into 0 0.589 * [backup-simplify]: Simplify 1 into 1 0.589 * [backup-simplify]: Simplify (log 1) into 0 0.589 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.589 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.589 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.590 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.591 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.591 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.592 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.593 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.593 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.593 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.593 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.593 * [taylor]: Taking taylor expansion of 2.0 in n 0.593 * [backup-simplify]: Simplify 2.0 into 2.0 0.593 * [taylor]: Taking taylor expansion of (* n PI) in n 0.593 * [taylor]: Taking taylor expansion of n in n 0.593 * [backup-simplify]: Simplify 0 into 0 0.593 * [backup-simplify]: Simplify 1 into 1 0.593 * [taylor]: Taking taylor expansion of PI in n 0.593 * [backup-simplify]: Simplify PI into PI 0.593 * [backup-simplify]: Simplify (* 0 PI) into 0 0.594 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.595 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.595 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.596 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.597 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.598 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.599 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.600 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.602 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.602 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.603 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.605 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 0.606 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.608 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.610 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.616 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))))))))))) 0.624 * [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)))))))))))) 0.633 * [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)))))))))))))) 0.642 * [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)))))))))))))) 0.651 * [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)))))))))))))) 0.666 * [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)))))))))))))))))))))) 0.666 * [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)))))) 0.666 * [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 0.666 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.666 * [taylor]: Taking taylor expansion of 1.0 in n 0.666 * [backup-simplify]: Simplify 1.0 into 1.0 0.666 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.666 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.666 * [taylor]: Taking taylor expansion of k in n 0.666 * [backup-simplify]: Simplify k into k 0.666 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 0.666 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 0.666 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.667 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.667 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.667 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.667 * [taylor]: Taking taylor expansion of 0.5 in n 0.667 * [backup-simplify]: Simplify 0.5 into 0.5 0.667 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.667 * [taylor]: Taking taylor expansion of 1.0 in n 0.667 * [backup-simplify]: Simplify 1.0 into 1.0 0.667 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.667 * [taylor]: Taking taylor expansion of k in n 0.667 * [backup-simplify]: Simplify k into k 0.667 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.667 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.667 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.671 * [taylor]: Taking taylor expansion of 2.0 in n 0.671 * [backup-simplify]: Simplify 2.0 into 2.0 0.671 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.671 * [taylor]: Taking taylor expansion of PI in n 0.671 * [backup-simplify]: Simplify PI into PI 0.671 * [taylor]: Taking taylor expansion of n in n 0.671 * [backup-simplify]: Simplify 0 into 0 0.671 * [backup-simplify]: Simplify 1 into 1 0.672 * [backup-simplify]: Simplify (/ PI 1) into PI 0.672 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.673 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.673 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.673 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.673 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.674 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.675 * [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)))) 0.675 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.676 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.676 * [taylor]: Taking taylor expansion of 1.0 in k 0.676 * [backup-simplify]: Simplify 1.0 into 1.0 0.676 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.676 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.676 * [taylor]: Taking taylor expansion of k in k 0.676 * [backup-simplify]: Simplify 0 into 0 0.676 * [backup-simplify]: Simplify 1 into 1 0.676 * [backup-simplify]: Simplify (sqrt 0) into 0 0.677 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.677 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.677 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.677 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.677 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.677 * [taylor]: Taking taylor expansion of 0.5 in k 0.677 * [backup-simplify]: Simplify 0.5 into 0.5 0.677 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.677 * [taylor]: Taking taylor expansion of 1.0 in k 0.677 * [backup-simplify]: Simplify 1.0 into 1.0 0.677 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.677 * [taylor]: Taking taylor expansion of k in k 0.677 * [backup-simplify]: Simplify 0 into 0 0.677 * [backup-simplify]: Simplify 1 into 1 0.677 * [backup-simplify]: Simplify (/ 1 1) into 1 0.677 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.677 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.677 * [taylor]: Taking taylor expansion of 2.0 in k 0.677 * [backup-simplify]: Simplify 2.0 into 2.0 0.677 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.677 * [taylor]: Taking taylor expansion of PI in k 0.677 * [backup-simplify]: Simplify PI into PI 0.677 * [taylor]: Taking taylor expansion of n in k 0.677 * [backup-simplify]: Simplify n into n 0.677 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.677 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.678 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.678 * [backup-simplify]: Simplify (- 1) into -1 0.678 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.678 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.678 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.678 * [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))))) 0.679 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.679 * [taylor]: Taking taylor expansion of 1.0 in k 0.679 * [backup-simplify]: Simplify 1.0 into 1.0 0.679 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.679 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.679 * [taylor]: Taking taylor expansion of k in k 0.679 * [backup-simplify]: Simplify 0 into 0 0.679 * [backup-simplify]: Simplify 1 into 1 0.679 * [backup-simplify]: Simplify (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))))) 0.682 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 0.682 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.682 * [taylor]: Taking taylor expansion of 0 in n 0.682 * [backup-simplify]: Simplify 0 into 0 0.682 * [backup-simplify]: Simplify 0 into 0 0.682 * [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))))))) 0.683 * [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))))))) 0.683 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.683 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.683 * [taylor]: Taking taylor expansion of +nan.0 in n 0.683 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.683 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.683 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.683 * [taylor]: Taking taylor expansion of 0.5 in n 0.683 * [backup-simplify]: Simplify 0.5 into 0.5 0.683 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.683 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.683 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.683 * [taylor]: Taking taylor expansion of 2.0 in n 0.683 * [backup-simplify]: Simplify 2.0 into 2.0 0.683 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.683 * [taylor]: Taking taylor expansion of PI in n 0.683 * [backup-simplify]: Simplify PI into PI 0.683 * [taylor]: Taking taylor expansion of n in n 0.683 * [backup-simplify]: Simplify 0 into 0 0.683 * [backup-simplify]: Simplify 1 into 1 0.683 * [backup-simplify]: Simplify (/ PI 1) into PI 0.684 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.684 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.684 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.684 * [taylor]: Taking taylor expansion of 1.0 in n 0.684 * [backup-simplify]: Simplify 1.0 into 1.0 0.684 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.684 * [taylor]: Taking taylor expansion of k in n 0.684 * [backup-simplify]: Simplify k into k 0.684 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.685 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.685 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.685 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.686 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.687 * [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)))) 0.688 * [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))))) 0.688 * [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)))))) 0.689 * [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))))))) 0.690 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.690 * [backup-simplify]: Simplify 0 into 0 0.692 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.692 * [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))))))) 0.693 * [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))))))) 0.693 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.693 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.693 * [taylor]: Taking taylor expansion of +nan.0 in n 0.693 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.693 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.693 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.693 * [taylor]: Taking taylor expansion of 0.5 in n 0.693 * [backup-simplify]: Simplify 0.5 into 0.5 0.693 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.693 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.693 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.693 * [taylor]: Taking taylor expansion of 2.0 in n 0.693 * [backup-simplify]: Simplify 2.0 into 2.0 0.693 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.693 * [taylor]: Taking taylor expansion of PI in n 0.693 * [backup-simplify]: Simplify PI into PI 0.693 * [taylor]: Taking taylor expansion of n in n 0.693 * [backup-simplify]: Simplify 0 into 0 0.693 * [backup-simplify]: Simplify 1 into 1 0.694 * [backup-simplify]: Simplify (/ PI 1) into PI 0.694 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.694 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.695 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.695 * [taylor]: Taking taylor expansion of 1.0 in n 0.695 * [backup-simplify]: Simplify 1.0 into 1.0 0.695 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.695 * [taylor]: Taking taylor expansion of k in n 0.695 * [backup-simplify]: Simplify k into k 0.695 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.695 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.696 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.696 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.696 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.697 * [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)))) 0.698 * [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))))) 0.698 * [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)))))) 0.699 * [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))))))) 0.700 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.701 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.701 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.701 * [backup-simplify]: Simplify (- 0) into 0 0.701 * [backup-simplify]: Simplify (+ 0 0) into 0 0.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.703 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.704 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.705 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 0.707 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.708 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 0.708 * [backup-simplify]: Simplify (- 0) into 0 0.708 * [backup-simplify]: Simplify 0 into 0 0.708 * [backup-simplify]: Simplify 0 into 0 0.710 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.711 * [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))))))) 0.712 * [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))))))) 0.712 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.712 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.712 * [taylor]: Taking taylor expansion of +nan.0 in n 0.712 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.712 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.712 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.712 * [taylor]: Taking taylor expansion of 0.5 in n 0.712 * [backup-simplify]: Simplify 0.5 into 0.5 0.712 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.712 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.712 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.712 * [taylor]: Taking taylor expansion of 2.0 in n 0.712 * [backup-simplify]: Simplify 2.0 into 2.0 0.712 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.712 * [taylor]: Taking taylor expansion of PI in n 0.712 * [backup-simplify]: Simplify PI into PI 0.712 * [taylor]: Taking taylor expansion of n in n 0.712 * [backup-simplify]: Simplify 0 into 0 0.712 * [backup-simplify]: Simplify 1 into 1 0.712 * [backup-simplify]: Simplify (/ PI 1) into PI 0.712 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.713 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.713 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.713 * [taylor]: Taking taylor expansion of 1.0 in n 0.713 * [backup-simplify]: Simplify 1.0 into 1.0 0.713 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.713 * [taylor]: Taking taylor expansion of k in n 0.713 * [backup-simplify]: Simplify k into k 0.713 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.714 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.714 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.714 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.715 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.716 * [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)))) 0.716 * [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))))) 0.717 * [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)))))) 0.718 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.719 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.721 * [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)))))))) 0.722 * [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)))) 0.722 * [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 0.722 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.722 * [taylor]: Taking taylor expansion of 1.0 in n 0.722 * [backup-simplify]: Simplify 1.0 into 1.0 0.722 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.722 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.722 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.722 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.722 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.722 * [taylor]: Taking taylor expansion of 0.5 in n 0.722 * [backup-simplify]: Simplify 0.5 into 0.5 0.722 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.722 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.722 * [taylor]: Taking taylor expansion of k in n 0.722 * [backup-simplify]: Simplify k into k 0.722 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.722 * [taylor]: Taking taylor expansion of 1.0 in n 0.722 * [backup-simplify]: Simplify 1.0 into 1.0 0.722 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.722 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.722 * [taylor]: Taking taylor expansion of -2.0 in n 0.722 * [backup-simplify]: Simplify -2.0 into -2.0 0.722 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.722 * [taylor]: Taking taylor expansion of PI in n 0.722 * [backup-simplify]: Simplify PI into PI 0.722 * [taylor]: Taking taylor expansion of n in n 0.722 * [backup-simplify]: Simplify 0 into 0 0.722 * [backup-simplify]: Simplify 1 into 1 0.723 * [backup-simplify]: Simplify (/ PI 1) into PI 0.723 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.724 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.724 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.724 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.725 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.725 * [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)))) 0.726 * [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))))) 0.726 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.726 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.726 * [taylor]: Taking taylor expansion of -1 in n 0.726 * [backup-simplify]: Simplify -1 into -1 0.726 * [taylor]: Taking taylor expansion of k in n 0.726 * [backup-simplify]: Simplify k into k 0.726 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 0.726 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 0.726 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 0.726 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 0.727 * [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))) 0.727 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.727 * [taylor]: Taking taylor expansion of 1.0 in k 0.727 * [backup-simplify]: Simplify 1.0 into 1.0 0.727 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.727 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.727 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.727 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.727 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.727 * [taylor]: Taking taylor expansion of 0.5 in k 0.727 * [backup-simplify]: Simplify 0.5 into 0.5 0.727 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.727 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.727 * [taylor]: Taking taylor expansion of k in k 0.727 * [backup-simplify]: Simplify 0 into 0 0.727 * [backup-simplify]: Simplify 1 into 1 0.728 * [backup-simplify]: Simplify (/ 1 1) into 1 0.728 * [taylor]: Taking taylor expansion of 1.0 in k 0.728 * [backup-simplify]: Simplify 1.0 into 1.0 0.728 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.728 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.728 * [taylor]: Taking taylor expansion of -2.0 in k 0.728 * [backup-simplify]: Simplify -2.0 into -2.0 0.728 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.728 * [taylor]: Taking taylor expansion of PI in k 0.728 * [backup-simplify]: Simplify PI into PI 0.728 * [taylor]: Taking taylor expansion of n in k 0.728 * [backup-simplify]: Simplify n into n 0.728 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.728 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.728 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.728 * [backup-simplify]: Simplify (+ 1 0) into 1 0.729 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.729 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.729 * [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)))))) 0.729 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.729 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.729 * [taylor]: Taking taylor expansion of -1 in k 0.729 * [backup-simplify]: Simplify -1 into -1 0.729 * [taylor]: Taking taylor expansion of k in k 0.729 * [backup-simplify]: Simplify 0 into 0 0.729 * [backup-simplify]: Simplify 1 into 1 0.729 * [backup-simplify]: Simplify (/ -1 1) into -1 0.729 * [backup-simplify]: Simplify (sqrt 0) into 0 0.730 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.730 * [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))))))) 0.730 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 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 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.730 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.730 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.730 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.730 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.730 * [taylor]: Taking taylor expansion of 0.5 in k 0.730 * [backup-simplify]: Simplify 0.5 into 0.5 0.731 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.731 * [taylor]: Taking taylor expansion of (/ 1 k) in k 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 * [taylor]: Taking taylor expansion of 1.0 in k 0.731 * [backup-simplify]: Simplify 1.0 into 1.0 0.731 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.731 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.731 * [taylor]: Taking taylor expansion of -2.0 in k 0.731 * [backup-simplify]: Simplify -2.0 into -2.0 0.731 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.731 * [taylor]: Taking taylor expansion of PI in k 0.731 * [backup-simplify]: Simplify PI into PI 0.731 * [taylor]: Taking taylor expansion of n in k 0.731 * [backup-simplify]: Simplify n into n 0.731 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.731 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.731 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.731 * [backup-simplify]: Simplify (+ 1 0) into 1 0.732 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.732 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.732 * [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)))))) 0.732 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.732 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.732 * [taylor]: Taking taylor expansion of -1 in k 0.732 * [backup-simplify]: Simplify -1 into -1 0.732 * [taylor]: Taking taylor expansion of k in k 0.732 * [backup-simplify]: Simplify 0 into 0 0.732 * [backup-simplify]: Simplify 1 into 1 0.732 * [backup-simplify]: Simplify (/ -1 1) into -1 0.732 * [backup-simplify]: Simplify (sqrt 0) into 0 0.733 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.733 * [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))))))) 0.734 * [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))))))) 0.734 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.734 * [taylor]: Taking taylor expansion of +nan.0 in n 0.734 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.734 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.734 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.734 * [taylor]: Taking taylor expansion of 0.5 in n 0.734 * [backup-simplify]: Simplify 0.5 into 0.5 0.734 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.734 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.734 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.734 * [taylor]: Taking taylor expansion of k in n 0.734 * [backup-simplify]: Simplify k into k 0.734 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.734 * [taylor]: Taking taylor expansion of 1.0 in n 0.734 * [backup-simplify]: Simplify 1.0 into 1.0 0.734 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.734 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.734 * [taylor]: Taking taylor expansion of -2.0 in n 0.734 * [backup-simplify]: Simplify -2.0 into -2.0 0.734 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.734 * [taylor]: Taking taylor expansion of PI in n 0.734 * [backup-simplify]: Simplify PI into PI 0.734 * [taylor]: Taking taylor expansion of n in n 0.734 * [backup-simplify]: Simplify 0 into 0 0.734 * [backup-simplify]: Simplify 1 into 1 0.734 * [backup-simplify]: Simplify (/ PI 1) into PI 0.735 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.735 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.735 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.736 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.737 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.737 * [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)))) 0.738 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.739 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.740 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.742 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.743 * [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)))))))) 0.743 * [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)))))))) 0.743 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.743 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.743 * [taylor]: Taking taylor expansion of +nan.0 in n 0.743 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.743 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.743 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.743 * [taylor]: Taking taylor expansion of 0.5 in n 0.743 * [backup-simplify]: Simplify 0.5 into 0.5 0.743 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.743 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.743 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.743 * [taylor]: Taking taylor expansion of k in n 0.743 * [backup-simplify]: Simplify k into k 0.743 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.743 * [taylor]: Taking taylor expansion of 1.0 in n 0.743 * [backup-simplify]: Simplify 1.0 into 1.0 0.743 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.743 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.743 * [taylor]: Taking taylor expansion of -2.0 in n 0.743 * [backup-simplify]: Simplify -2.0 into -2.0 0.743 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.743 * [taylor]: Taking taylor expansion of PI in n 0.743 * [backup-simplify]: Simplify PI into PI 0.743 * [taylor]: Taking taylor expansion of n in n 0.743 * [backup-simplify]: Simplify 0 into 0 0.743 * [backup-simplify]: Simplify 1 into 1 0.744 * [backup-simplify]: Simplify (/ PI 1) into PI 0.744 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.745 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.745 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.745 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.746 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.747 * [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)))) 0.748 * [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))))) 0.748 * [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)))))) 0.749 * [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))))))) 0.750 * [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))))))) 0.750 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.751 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.752 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.752 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.752 * [backup-simplify]: Simplify (+ 0 0) into 0 0.753 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.754 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.755 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 0.756 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.757 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 0.757 * [backup-simplify]: Simplify 0 into 0 0.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.759 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.760 * [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)))))))) 0.761 * [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)))))))) 0.761 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.761 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.761 * [taylor]: Taking taylor expansion of +nan.0 in n 0.761 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.761 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.761 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.761 * [taylor]: Taking taylor expansion of 0.5 in n 0.761 * [backup-simplify]: Simplify 0.5 into 0.5 0.761 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.761 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.761 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.761 * [taylor]: Taking taylor expansion of k in n 0.761 * [backup-simplify]: Simplify k into k 0.761 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.761 * [taylor]: Taking taylor expansion of 1.0 in n 0.761 * [backup-simplify]: Simplify 1.0 into 1.0 0.761 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.761 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.761 * [taylor]: Taking taylor expansion of -2.0 in n 0.761 * [backup-simplify]: Simplify -2.0 into -2.0 0.761 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.761 * [taylor]: Taking taylor expansion of PI in n 0.761 * [backup-simplify]: Simplify PI into PI 0.761 * [taylor]: Taking taylor expansion of n in n 0.761 * [backup-simplify]: Simplify 0 into 0 0.761 * [backup-simplify]: Simplify 1 into 1 0.762 * [backup-simplify]: Simplify (/ PI 1) into PI 0.762 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.762 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.763 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.763 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.764 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.765 * [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)))) 0.766 * [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))))) 0.773 * [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)))))) 0.774 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 0.775 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 0.778 * [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 0.780 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 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(- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) 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(log (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (+ (log (/ h2 (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (log (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (exp (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 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)))))))))))) 0.790 * * [simplify]: iteration 0 : 950 enodes (cost 1461 ) 0.806 * * [simplify]: iteration 1 : 3924 enodes (cost 1358 ) 0.868 * * [simplify]: iteration 2 : 5002 enodes (cost 1344 ) 0.875 * * * [progress]: adding candidates to table 1.279 * * [progress]: iteration 2 / 4 1.279 * * * [progress]: picking best candidate 1.300 * * * * [pick]: Picked # 1.300 * * * [progress]: localizing error 1.316 * * * [progress]: generating rewritten candidates 1.316 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 1.345 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 1.369 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1) 1.386 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1) 1.416 * * * [progress]: generating series expansions 1.416 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 1.417 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 1.417 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 1.417 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 1.417 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.417 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.417 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 1.417 * [taylor]: Taking taylor expansion of 0.25 in k 1.417 * [backup-simplify]: Simplify 0.25 into 0.25 1.417 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.417 * [taylor]: Taking taylor expansion of 1.0 in k 1.417 * [backup-simplify]: Simplify 1.0 into 1.0 1.417 * [taylor]: Taking taylor expansion of k in k 1.417 * [backup-simplify]: Simplify 0 into 0 1.417 * [backup-simplify]: Simplify 1 into 1 1.417 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.417 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.417 * [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) 1.418 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.418 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.418 * [backup-simplify]: Simplify (- 0) into 0 1.418 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.419 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 1.419 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 1.419 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 1.419 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.419 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.419 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.419 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.419 * [taylor]: Taking taylor expansion of 0.25 in n 1.419 * [backup-simplify]: Simplify 0.25 into 0.25 1.419 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.419 * [taylor]: Taking taylor expansion of 1.0 in n 1.419 * [backup-simplify]: Simplify 1.0 into 1.0 1.419 * [taylor]: Taking taylor expansion of k in n 1.419 * [backup-simplify]: Simplify k into k 1.419 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.419 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.419 * [taylor]: Taking taylor expansion of 2.0 in n 1.419 * [backup-simplify]: Simplify 2.0 into 2.0 1.419 * [taylor]: Taking taylor expansion of (* n PI) in n 1.419 * [taylor]: Taking taylor expansion of n in n 1.419 * [backup-simplify]: Simplify 0 into 0 1.419 * [backup-simplify]: Simplify 1 into 1 1.419 * [taylor]: Taking taylor expansion of PI in n 1.419 * [backup-simplify]: Simplify PI into PI 1.419 * [backup-simplify]: Simplify (* 0 PI) into 0 1.420 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.421 * [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 (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.423 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.424 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.424 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.424 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.424 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.425 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.425 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.425 * [taylor]: Taking taylor expansion of 0.25 in n 1.425 * [backup-simplify]: Simplify 0.25 into 0.25 1.425 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.425 * [taylor]: Taking taylor expansion of 1.0 in n 1.425 * [backup-simplify]: Simplify 1.0 into 1.0 1.425 * [taylor]: Taking taylor expansion of k in n 1.425 * [backup-simplify]: Simplify k into k 1.425 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.425 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.425 * [taylor]: Taking taylor expansion of 2.0 in n 1.425 * [backup-simplify]: Simplify 2.0 into 2.0 1.425 * [taylor]: Taking taylor expansion of (* n PI) in n 1.425 * [taylor]: Taking taylor expansion of n in n 1.425 * [backup-simplify]: Simplify 0 into 0 1.425 * [backup-simplify]: Simplify 1 into 1 1.425 * [taylor]: Taking taylor expansion of PI in n 1.425 * [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) 1.428 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.428 * [backup-simplify]: Simplify (- k) into (- k) 1.428 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.428 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.429 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.429 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.430 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.430 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.430 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.430 * [taylor]: Taking taylor expansion of 0.25 in k 1.430 * [backup-simplify]: Simplify 0.25 into 0.25 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 1.431 * [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) 1.432 * [backup-simplify]: Simplify (- 0) into 0 1.432 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.433 * [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))) 1.434 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 1.435 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.435 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.436 * [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 1.437 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.438 * [backup-simplify]: Simplify (- 0) into 0 1.438 * [backup-simplify]: Simplify (+ 0 0) into 0 1.438 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 1.439 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.440 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.441 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.441 * [taylor]: Taking taylor expansion of 0 in k 1.441 * [backup-simplify]: Simplify 0 into 0 1.441 * [backup-simplify]: Simplify 0 into 0 1.441 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.442 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.443 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.443 * [backup-simplify]: Simplify (+ 0 0) into 0 1.443 * [backup-simplify]: Simplify (- 1) into -1 1.443 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.444 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.446 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1.448 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.449 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.450 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.451 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.453 * [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 1.453 * [backup-simplify]: Simplify (- 0) into 0 1.453 * [backup-simplify]: Simplify (+ 0 0) into 0 1.454 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.455 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.456 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.457 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.457 * [taylor]: Taking taylor expansion of 0 in k 1.457 * [backup-simplify]: Simplify 0 into 0 1.457 * [backup-simplify]: Simplify 0 into 0 1.457 * [backup-simplify]: Simplify 0 into 0 1.458 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.459 * [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 1.460 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.461 * [backup-simplify]: Simplify (+ 0 0) into 0 1.461 * [backup-simplify]: Simplify (- 0) into 0 1.461 * [backup-simplify]: Simplify (+ 0 0) into 0 1.462 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.464 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.466 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.470 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.483 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 1.484 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 1.484 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 1.484 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 1.484 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.484 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.484 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 1.484 * [taylor]: Taking taylor expansion of 0.25 in k 1.484 * [backup-simplify]: Simplify 0.25 into 0.25 1.484 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.484 * [taylor]: Taking taylor expansion of 1.0 in k 1.484 * [backup-simplify]: Simplify 1.0 into 1.0 1.484 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.484 * [taylor]: Taking taylor expansion of k in k 1.484 * [backup-simplify]: Simplify 0 into 0 1.484 * [backup-simplify]: Simplify 1 into 1 1.485 * [backup-simplify]: Simplify (/ 1 1) into 1 1.485 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.485 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.485 * [taylor]: Taking taylor expansion of 2.0 in k 1.485 * [backup-simplify]: Simplify 2.0 into 2.0 1.485 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.485 * [taylor]: Taking taylor expansion of PI in k 1.485 * [backup-simplify]: Simplify PI into PI 1.485 * [taylor]: Taking taylor expansion of n in k 1.485 * [backup-simplify]: Simplify n into n 1.485 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.485 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.485 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.485 * [backup-simplify]: Simplify (- 1) into -1 1.485 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.486 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 1.486 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 1.486 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.486 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.486 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.486 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.486 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.486 * [taylor]: Taking taylor expansion of 0.25 in n 1.486 * [backup-simplify]: Simplify 0.25 into 0.25 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) 1.487 * [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 (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 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 (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.490 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.490 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.490 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.490 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.490 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.490 * [taylor]: Taking taylor expansion of 0.25 in n 1.490 * [backup-simplify]: Simplify 0.25 into 0.25 1.490 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.490 * [taylor]: Taking taylor expansion of 1.0 in n 1.490 * [backup-simplify]: Simplify 1.0 into 1.0 1.490 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.490 * [taylor]: Taking taylor expansion of k in n 1.490 * [backup-simplify]: Simplify k into k 1.490 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.490 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.490 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.490 * [taylor]: Taking taylor expansion of 2.0 in n 1.490 * [backup-simplify]: Simplify 2.0 into 2.0 1.490 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.490 * [taylor]: Taking taylor expansion of PI in n 1.490 * [backup-simplify]: Simplify PI into PI 1.490 * [taylor]: Taking taylor expansion of n in n 1.490 * [backup-simplify]: Simplify 0 into 0 1.490 * [backup-simplify]: Simplify 1 into 1 1.491 * [backup-simplify]: Simplify (/ PI 1) into PI 1.491 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.492 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.492 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.492 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.492 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.493 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.493 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.494 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.494 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.494 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.494 * [taylor]: Taking taylor expansion of 0.25 in k 1.494 * [backup-simplify]: Simplify 0.25 into 0.25 1.494 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.494 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.494 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.494 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.494 * [taylor]: Taking taylor expansion of 2.0 in k 1.494 * [backup-simplify]: Simplify 2.0 into 2.0 1.494 * [taylor]: Taking taylor expansion of PI in k 1.494 * [backup-simplify]: Simplify PI into PI 1.495 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.495 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.495 * [taylor]: Taking taylor expansion of (log n) in k 1.495 * [taylor]: Taking taylor expansion of n in k 1.495 * [backup-simplify]: Simplify n into n 1.496 * [backup-simplify]: Simplify (log n) into (log n) 1.496 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.496 * [taylor]: Taking taylor expansion of 1.0 in k 1.496 * [backup-simplify]: Simplify 1.0 into 1.0 1.496 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.496 * [taylor]: Taking taylor expansion of k in k 1.496 * [backup-simplify]: Simplify 0 into 0 1.496 * [backup-simplify]: Simplify 1 into 1 1.496 * [backup-simplify]: Simplify (/ 1 1) into 1 1.496 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.497 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.497 * [backup-simplify]: Simplify (- 1) into -1 1.497 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.498 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.498 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 1.499 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.500 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.500 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.501 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.502 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.502 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.502 * [backup-simplify]: Simplify (- 0) into 0 1.503 * [backup-simplify]: Simplify (+ 0 0) into 0 1.503 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.504 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.504 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.506 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.506 * [taylor]: Taking taylor expansion of 0 in k 1.506 * [backup-simplify]: Simplify 0 into 0 1.506 * [backup-simplify]: Simplify 0 into 0 1.506 * [backup-simplify]: Simplify 0 into 0 1.506 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.507 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.508 * [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 1.509 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.509 * [backup-simplify]: Simplify (- 0) into 0 1.509 * [backup-simplify]: Simplify (+ 0 0) into 0 1.510 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.510 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.511 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.513 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.513 * [taylor]: Taking taylor expansion of 0 in k 1.513 * [backup-simplify]: Simplify 0 into 0 1.513 * [backup-simplify]: Simplify 0 into 0 1.513 * [backup-simplify]: Simplify 0 into 0 1.513 * [backup-simplify]: Simplify 0 into 0 1.513 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.514 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.517 * [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 1.517 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.517 * [backup-simplify]: Simplify (- 0) into 0 1.517 * [backup-simplify]: Simplify (+ 0 0) into 0 1.518 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.519 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.520 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.522 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.522 * [taylor]: Taking taylor expansion of 0 in k 1.522 * [backup-simplify]: Simplify 0 into 0 1.522 * [backup-simplify]: Simplify 0 into 0 1.523 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 1.523 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 1.523 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 1.523 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 1.523 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.523 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.523 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 1.523 * [taylor]: Taking taylor expansion of 0.25 in k 1.523 * [backup-simplify]: Simplify 0.25 into 0.25 1.523 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.523 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.523 * [taylor]: Taking taylor expansion of k in k 1.523 * [backup-simplify]: Simplify 0 into 0 1.523 * [backup-simplify]: Simplify 1 into 1 1.524 * [backup-simplify]: Simplify (/ 1 1) into 1 1.524 * [taylor]: Taking taylor expansion of 1.0 in k 1.524 * [backup-simplify]: Simplify 1.0 into 1.0 1.524 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.524 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.524 * [taylor]: Taking taylor expansion of -2.0 in k 1.524 * [backup-simplify]: Simplify -2.0 into -2.0 1.524 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.524 * [taylor]: Taking taylor expansion of PI in k 1.524 * [backup-simplify]: Simplify PI into PI 1.524 * [taylor]: Taking taylor expansion of n in k 1.524 * [backup-simplify]: Simplify n into n 1.524 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.524 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.524 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.524 * [backup-simplify]: Simplify (+ 1 0) into 1 1.524 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 1.524 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 1.525 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.525 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.525 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.525 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.525 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.525 * [taylor]: Taking taylor expansion of 0.25 in n 1.525 * [backup-simplify]: Simplify 0.25 into 0.25 1.525 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.525 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.525 * [taylor]: Taking taylor expansion of k in n 1.525 * [backup-simplify]: Simplify k into k 1.525 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.525 * [taylor]: Taking taylor expansion of 1.0 in n 1.525 * [backup-simplify]: Simplify 1.0 into 1.0 1.525 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.525 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.525 * [taylor]: Taking taylor expansion of -2.0 in n 1.525 * [backup-simplify]: Simplify -2.0 into -2.0 1.525 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.525 * [taylor]: Taking taylor expansion of PI in n 1.525 * [backup-simplify]: Simplify PI into PI 1.525 * [taylor]: Taking taylor expansion of n in n 1.525 * [backup-simplify]: Simplify 0 into 0 1.525 * [backup-simplify]: Simplify 1 into 1 1.525 * [backup-simplify]: Simplify (/ PI 1) into PI 1.526 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.526 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.526 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.526 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.527 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.528 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.529 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.529 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.529 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.529 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.529 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.529 * [taylor]: Taking taylor expansion of 0.25 in n 1.529 * [backup-simplify]: Simplify 0.25 into 0.25 1.529 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.529 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.529 * [taylor]: Taking taylor expansion of k in n 1.529 * [backup-simplify]: Simplify k into k 1.529 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.529 * [taylor]: Taking taylor expansion of 1.0 in n 1.529 * [backup-simplify]: Simplify 1.0 into 1.0 1.529 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.529 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.529 * [taylor]: Taking taylor expansion of -2.0 in n 1.529 * [backup-simplify]: Simplify -2.0 into -2.0 1.529 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.529 * [taylor]: Taking taylor expansion of PI in n 1.529 * [backup-simplify]: Simplify PI into PI 1.529 * [taylor]: Taking taylor expansion of n in n 1.529 * [backup-simplify]: Simplify 0 into 0 1.529 * [backup-simplify]: Simplify 1 into 1 1.529 * [backup-simplify]: Simplify (/ PI 1) into PI 1.530 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.530 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.530 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.530 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.531 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.532 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.533 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.533 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.533 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.533 * [taylor]: Taking taylor expansion of 0.25 in k 1.533 * [backup-simplify]: Simplify 0.25 into 0.25 1.533 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.533 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.533 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.533 * [taylor]: Taking taylor expansion of k in k 1.533 * [backup-simplify]: Simplify 0 into 0 1.533 * [backup-simplify]: Simplify 1 into 1 1.533 * [backup-simplify]: Simplify (/ 1 1) into 1 1.533 * [taylor]: Taking taylor expansion of 1.0 in k 1.533 * [backup-simplify]: Simplify 1.0 into 1.0 1.533 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.533 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.533 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.533 * [taylor]: Taking taylor expansion of -2.0 in k 1.533 * [backup-simplify]: Simplify -2.0 into -2.0 1.533 * [taylor]: Taking taylor expansion of PI in k 1.533 * [backup-simplify]: Simplify PI into PI 1.533 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.534 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.534 * [taylor]: Taking taylor expansion of (log n) in k 1.534 * [taylor]: Taking taylor expansion of n in k 1.534 * [backup-simplify]: Simplify n into n 1.534 * [backup-simplify]: Simplify (log n) into (log n) 1.534 * [backup-simplify]: Simplify (+ 1 0) into 1 1.535 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.535 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.536 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.536 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 1.537 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.538 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.539 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.540 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.540 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.540 * [backup-simplify]: Simplify (+ 0 0) into 0 1.541 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.542 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.542 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.543 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.543 * [taylor]: Taking taylor expansion of 0 in k 1.544 * [backup-simplify]: Simplify 0 into 0 1.544 * [backup-simplify]: Simplify 0 into 0 1.544 * [backup-simplify]: Simplify 0 into 0 1.544 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.545 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.546 * [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 1.547 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.547 * [backup-simplify]: Simplify (+ 0 0) into 0 1.547 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.549 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.550 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.550 * [taylor]: Taking taylor expansion of 0 in k 1.550 * [backup-simplify]: Simplify 0 into 0 1.550 * [backup-simplify]: Simplify 0 into 0 1.551 * [backup-simplify]: Simplify 0 into 0 1.551 * [backup-simplify]: Simplify 0 into 0 1.551 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.552 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.555 * [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 1.555 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.555 * [backup-simplify]: Simplify (+ 0 0) into 0 1.556 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.557 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.558 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.559 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.560 * [taylor]: Taking taylor expansion of 0 in k 1.560 * [backup-simplify]: Simplify 0 into 0 1.560 * [backup-simplify]: Simplify 0 into 0 1.560 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 1.560 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 1.561 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 1.561 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 1.561 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 1.561 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.561 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.561 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 1.561 * [taylor]: Taking taylor expansion of 0.25 in k 1.561 * [backup-simplify]: Simplify 0.25 into 0.25 1.561 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.561 * [taylor]: Taking taylor expansion of 1.0 in k 1.561 * [backup-simplify]: Simplify 1.0 into 1.0 1.561 * [taylor]: Taking taylor expansion of k in k 1.561 * [backup-simplify]: Simplify 0 into 0 1.561 * [backup-simplify]: Simplify 1 into 1 1.561 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.561 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.561 * [taylor]: Taking taylor expansion of 2.0 in k 1.561 * [backup-simplify]: Simplify 2.0 into 2.0 1.561 * [taylor]: Taking taylor expansion of (* n PI) in k 1.561 * [taylor]: Taking taylor expansion of n in k 1.561 * [backup-simplify]: Simplify n into n 1.561 * [taylor]: Taking taylor expansion of PI in k 1.561 * [backup-simplify]: Simplify PI into PI 1.561 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.561 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.561 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.562 * [backup-simplify]: Simplify (- 0) into 0 1.562 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.562 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 1.562 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 1.562 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 1.562 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.562 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.562 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.562 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.562 * [taylor]: Taking taylor expansion of 0.25 in n 1.562 * [backup-simplify]: Simplify 0.25 into 0.25 1.562 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.562 * [taylor]: Taking taylor expansion of 1.0 in n 1.562 * [backup-simplify]: Simplify 1.0 into 1.0 1.562 * [taylor]: Taking taylor expansion of k in n 1.562 * [backup-simplify]: Simplify k into k 1.563 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.563 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.563 * [taylor]: Taking taylor expansion of 2.0 in n 1.563 * [backup-simplify]: Simplify 2.0 into 2.0 1.563 * [taylor]: Taking taylor expansion of (* n PI) in n 1.563 * [taylor]: Taking taylor expansion of n in n 1.563 * [backup-simplify]: Simplify 0 into 0 1.563 * [backup-simplify]: Simplify 1 into 1 1.563 * [taylor]: Taking taylor expansion of PI in n 1.563 * [backup-simplify]: Simplify PI into PI 1.563 * [backup-simplify]: Simplify (* 0 PI) into 0 1.563 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.564 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.565 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.566 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.566 * [backup-simplify]: Simplify (- k) into (- k) 1.566 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.566 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.567 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.567 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.568 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.568 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.568 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.568 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.568 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.568 * [taylor]: Taking taylor expansion of 0.25 in n 1.568 * [backup-simplify]: Simplify 0.25 into 0.25 1.568 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.568 * [taylor]: Taking taylor expansion of 1.0 in n 1.568 * [backup-simplify]: Simplify 1.0 into 1.0 1.568 * [taylor]: Taking taylor expansion of k in n 1.568 * [backup-simplify]: Simplify k into k 1.568 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.568 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.568 * [taylor]: Taking taylor expansion of 2.0 in n 1.568 * [backup-simplify]: Simplify 2.0 into 2.0 1.568 * [taylor]: Taking taylor expansion of (* n PI) in n 1.568 * [taylor]: Taking taylor expansion of n in n 1.568 * [backup-simplify]: Simplify 0 into 0 1.568 * [backup-simplify]: Simplify 1 into 1 1.568 * [taylor]: Taking taylor expansion of PI in n 1.568 * [backup-simplify]: Simplify PI into PI 1.569 * [backup-simplify]: Simplify (* 0 PI) into 0 1.569 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.576 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.577 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.578 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.578 * [backup-simplify]: Simplify (- k) into (- k) 1.578 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.578 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.579 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.579 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.580 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.580 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.580 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.580 * [taylor]: Taking taylor expansion of 0.25 in k 1.580 * [backup-simplify]: Simplify 0.25 into 0.25 1.580 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.580 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.580 * [taylor]: Taking taylor expansion of 1.0 in k 1.580 * [backup-simplify]: Simplify 1.0 into 1.0 1.580 * [taylor]: Taking taylor expansion of k in k 1.580 * [backup-simplify]: Simplify 0 into 0 1.580 * [backup-simplify]: Simplify 1 into 1 1.580 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.580 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.580 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.580 * [taylor]: Taking taylor expansion of 2.0 in k 1.580 * [backup-simplify]: Simplify 2.0 into 2.0 1.580 * [taylor]: Taking taylor expansion of PI in k 1.580 * [backup-simplify]: Simplify PI into PI 1.581 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.581 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.581 * [taylor]: Taking taylor expansion of (log n) in k 1.581 * [taylor]: Taking taylor expansion of n in k 1.581 * [backup-simplify]: Simplify n into n 1.581 * [backup-simplify]: Simplify (log n) into (log n) 1.582 * [backup-simplify]: Simplify (- 0) into 0 1.582 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.583 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.583 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.584 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 1.585 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.585 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.586 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.586 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.587 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.588 * [backup-simplify]: Simplify (- 0) into 0 1.588 * [backup-simplify]: Simplify (+ 0 0) into 0 1.588 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 1.589 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.590 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.591 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.591 * [taylor]: Taking taylor expansion of 0 in k 1.591 * [backup-simplify]: Simplify 0 into 0 1.591 * [backup-simplify]: Simplify 0 into 0 1.591 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.592 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.593 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.593 * [backup-simplify]: Simplify (+ 0 0) into 0 1.593 * [backup-simplify]: Simplify (- 1) into -1 1.593 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.594 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.596 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1.597 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.599 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.600 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.600 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.602 * [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 1.602 * [backup-simplify]: Simplify (- 0) into 0 1.603 * [backup-simplify]: Simplify (+ 0 0) into 0 1.603 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.604 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.605 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.607 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.607 * [taylor]: Taking taylor expansion of 0 in k 1.607 * [backup-simplify]: Simplify 0 into 0 1.607 * [backup-simplify]: Simplify 0 into 0 1.607 * [backup-simplify]: Simplify 0 into 0 1.607 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.609 * [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 1.610 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.610 * [backup-simplify]: Simplify (+ 0 0) into 0 1.611 * [backup-simplify]: Simplify (- 0) into 0 1.611 * [backup-simplify]: Simplify (+ 0 0) into 0 1.612 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.613 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.616 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.619 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.625 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 1.625 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 1.625 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 1.625 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 1.625 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.625 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.625 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 1.625 * [taylor]: Taking taylor expansion of 0.25 in k 1.625 * [backup-simplify]: Simplify 0.25 into 0.25 1.625 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.625 * [taylor]: Taking taylor expansion of 1.0 in k 1.625 * [backup-simplify]: Simplify 1.0 into 1.0 1.625 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.625 * [taylor]: Taking taylor expansion of k in k 1.625 * [backup-simplify]: Simplify 0 into 0 1.625 * [backup-simplify]: Simplify 1 into 1 1.626 * [backup-simplify]: Simplify (/ 1 1) into 1 1.626 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.626 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.626 * [taylor]: Taking taylor expansion of 2.0 in k 1.626 * [backup-simplify]: Simplify 2.0 into 2.0 1.626 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.626 * [taylor]: Taking taylor expansion of PI in k 1.626 * [backup-simplify]: Simplify PI into PI 1.626 * [taylor]: Taking taylor expansion of n in k 1.626 * [backup-simplify]: Simplify n into n 1.626 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.626 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.626 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.626 * [backup-simplify]: Simplify (- 1) into -1 1.626 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.627 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 1.627 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 1.627 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.627 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.627 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.627 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.627 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.627 * [taylor]: Taking taylor expansion of 0.25 in n 1.627 * [backup-simplify]: Simplify 0.25 into 0.25 1.627 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.627 * [taylor]: Taking taylor expansion of 1.0 in n 1.627 * [backup-simplify]: Simplify 1.0 into 1.0 1.627 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.627 * [taylor]: Taking taylor expansion of k in n 1.627 * [backup-simplify]: Simplify k into k 1.627 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.627 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.627 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.627 * [taylor]: Taking taylor expansion of 2.0 in n 1.627 * [backup-simplify]: Simplify 2.0 into 2.0 1.627 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.627 * [taylor]: Taking taylor expansion of PI in n 1.627 * [backup-simplify]: Simplify PI into PI 1.627 * [taylor]: Taking taylor expansion of n in n 1.627 * [backup-simplify]: Simplify 0 into 0 1.627 * [backup-simplify]: Simplify 1 into 1 1.628 * [backup-simplify]: Simplify (/ PI 1) into PI 1.628 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.628 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.629 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.629 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.629 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.630 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.630 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.631 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.631 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.631 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.631 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.631 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.631 * [taylor]: Taking taylor expansion of 0.25 in n 1.631 * [backup-simplify]: Simplify 0.25 into 0.25 1.631 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.631 * [taylor]: Taking taylor expansion of 1.0 in n 1.631 * [backup-simplify]: Simplify 1.0 into 1.0 1.631 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.631 * [taylor]: Taking taylor expansion of k in n 1.631 * [backup-simplify]: Simplify k into k 1.631 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.631 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.631 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.631 * [taylor]: Taking taylor expansion of 2.0 in n 1.631 * [backup-simplify]: Simplify 2.0 into 2.0 1.631 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.631 * [taylor]: Taking taylor expansion of PI in n 1.631 * [backup-simplify]: Simplify PI into PI 1.631 * [taylor]: Taking taylor expansion of n in n 1.631 * [backup-simplify]: Simplify 0 into 0 1.631 * [backup-simplify]: Simplify 1 into 1 1.632 * [backup-simplify]: Simplify (/ PI 1) into PI 1.632 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.633 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.633 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.633 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.633 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.634 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.634 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.635 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.635 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.635 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.635 * [taylor]: Taking taylor expansion of 0.25 in k 1.635 * [backup-simplify]: Simplify 0.25 into 0.25 1.635 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.635 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.635 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.635 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.635 * [taylor]: Taking taylor expansion of 2.0 in k 1.635 * [backup-simplify]: Simplify 2.0 into 2.0 1.635 * [taylor]: Taking taylor expansion of PI in k 1.635 * [backup-simplify]: Simplify PI into PI 1.636 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.636 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.636 * [taylor]: Taking taylor expansion of (log n) in k 1.636 * [taylor]: Taking taylor expansion of n in k 1.636 * [backup-simplify]: Simplify n into n 1.636 * [backup-simplify]: Simplify (log n) into (log n) 1.636 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.636 * [taylor]: Taking taylor expansion of 1.0 in k 1.636 * [backup-simplify]: Simplify 1.0 into 1.0 1.636 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.636 * [taylor]: Taking taylor expansion of k in k 1.636 * [backup-simplify]: Simplify 0 into 0 1.636 * [backup-simplify]: Simplify 1 into 1 1.637 * [backup-simplify]: Simplify (/ 1 1) into 1 1.637 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.637 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.638 * [backup-simplify]: Simplify (- 1) into -1 1.638 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.638 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.639 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 1.640 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.641 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.641 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.642 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.642 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.643 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.643 * [backup-simplify]: Simplify (- 0) into 0 1.643 * [backup-simplify]: Simplify (+ 0 0) into 0 1.643 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.644 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.645 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.646 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.646 * [taylor]: Taking taylor expansion of 0 in k 1.646 * [backup-simplify]: Simplify 0 into 0 1.646 * [backup-simplify]: Simplify 0 into 0 1.646 * [backup-simplify]: Simplify 0 into 0 1.647 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.647 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.649 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.649 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.649 * [backup-simplify]: Simplify (- 0) into 0 1.650 * [backup-simplify]: Simplify (+ 0 0) into 0 1.650 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.651 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.652 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.654 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.654 * [taylor]: Taking taylor expansion of 0 in k 1.654 * [backup-simplify]: Simplify 0 into 0 1.654 * [backup-simplify]: Simplify 0 into 0 1.654 * [backup-simplify]: Simplify 0 into 0 1.654 * [backup-simplify]: Simplify 0 into 0 1.654 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.655 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.658 * [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 1.658 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.658 * [backup-simplify]: Simplify (- 0) into 0 1.659 * [backup-simplify]: Simplify (+ 0 0) into 0 1.659 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.661 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.663 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.663 * [taylor]: Taking taylor expansion of 0 in k 1.663 * [backup-simplify]: Simplify 0 into 0 1.663 * [backup-simplify]: Simplify 0 into 0 1.664 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 1.665 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 1.665 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 1.665 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 1.665 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.665 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.665 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 1.665 * [taylor]: Taking taylor expansion of 0.25 in k 1.665 * [backup-simplify]: Simplify 0.25 into 0.25 1.665 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.665 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.665 * [taylor]: Taking taylor expansion of k in k 1.665 * [backup-simplify]: Simplify 0 into 0 1.665 * [backup-simplify]: Simplify 1 into 1 1.665 * [backup-simplify]: Simplify (/ 1 1) into 1 1.665 * [taylor]: Taking taylor expansion of 1.0 in k 1.665 * [backup-simplify]: Simplify 1.0 into 1.0 1.665 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.665 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.665 * [taylor]: Taking taylor expansion of -2.0 in k 1.665 * [backup-simplify]: Simplify -2.0 into -2.0 1.665 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.665 * [taylor]: Taking taylor expansion of PI in k 1.665 * [backup-simplify]: Simplify PI into PI 1.665 * [taylor]: Taking taylor expansion of n in k 1.665 * [backup-simplify]: Simplify n into n 1.665 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.665 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.665 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.666 * [backup-simplify]: Simplify (+ 1 0) into 1 1.672 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 1.672 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 1.672 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.672 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.672 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.672 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.672 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.672 * [taylor]: Taking taylor expansion of 0.25 in n 1.672 * [backup-simplify]: Simplify 0.25 into 0.25 1.672 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.672 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.672 * [taylor]: Taking taylor expansion of k in n 1.672 * [backup-simplify]: Simplify k into k 1.672 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.672 * [taylor]: Taking taylor expansion of 1.0 in n 1.672 * [backup-simplify]: Simplify 1.0 into 1.0 1.672 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.672 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.672 * [taylor]: Taking taylor expansion of -2.0 in n 1.672 * [backup-simplify]: Simplify -2.0 into -2.0 1.672 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.672 * [taylor]: Taking taylor expansion of PI in n 1.672 * [backup-simplify]: Simplify PI into PI 1.672 * [taylor]: Taking taylor expansion of n in n 1.672 * [backup-simplify]: Simplify 0 into 0 1.672 * [backup-simplify]: Simplify 1 into 1 1.673 * [backup-simplify]: Simplify (/ PI 1) into PI 1.673 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.674 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.674 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.674 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.676 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.676 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.676 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.676 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.676 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.676 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.676 * [taylor]: Taking taylor expansion of 0.25 in n 1.676 * [backup-simplify]: Simplify 0.25 into 0.25 1.676 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.677 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.677 * [taylor]: Taking taylor expansion of k in n 1.677 * [backup-simplify]: Simplify k into k 1.677 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.677 * [taylor]: Taking taylor expansion of 1.0 in n 1.677 * [backup-simplify]: Simplify 1.0 into 1.0 1.677 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.677 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.677 * [taylor]: Taking taylor expansion of -2.0 in n 1.677 * [backup-simplify]: Simplify -2.0 into -2.0 1.677 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.677 * [taylor]: Taking taylor expansion of PI in n 1.677 * [backup-simplify]: Simplify PI into PI 1.677 * [taylor]: Taking taylor expansion of n in n 1.677 * [backup-simplify]: Simplify 0 into 0 1.677 * [backup-simplify]: Simplify 1 into 1 1.677 * [backup-simplify]: Simplify (/ PI 1) into PI 1.677 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.678 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.678 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.678 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.679 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.680 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.680 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.681 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.681 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.681 * [taylor]: Taking taylor expansion of 0.25 in k 1.681 * [backup-simplify]: Simplify 0.25 into 0.25 1.681 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.681 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.681 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.681 * [taylor]: Taking taylor expansion of k in k 1.681 * [backup-simplify]: Simplify 0 into 0 1.681 * [backup-simplify]: Simplify 1 into 1 1.681 * [backup-simplify]: Simplify (/ 1 1) into 1 1.681 * [taylor]: Taking taylor expansion of 1.0 in k 1.681 * [backup-simplify]: Simplify 1.0 into 1.0 1.681 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.681 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.681 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.681 * [taylor]: Taking taylor expansion of -2.0 in k 1.681 * [backup-simplify]: Simplify -2.0 into -2.0 1.681 * [taylor]: Taking taylor expansion of PI in k 1.681 * [backup-simplify]: Simplify PI into PI 1.681 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.682 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.682 * [taylor]: Taking taylor expansion of (log n) in k 1.682 * [taylor]: Taking taylor expansion of n in k 1.682 * [backup-simplify]: Simplify n into n 1.682 * [backup-simplify]: Simplify (log n) into (log n) 1.682 * [backup-simplify]: Simplify (+ 1 0) into 1 1.682 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.683 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.684 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.684 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 1.685 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.686 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.687 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.688 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.688 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.688 * [backup-simplify]: Simplify (+ 0 0) into 0 1.688 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.689 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.690 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.691 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.691 * [taylor]: Taking taylor expansion of 0 in k 1.691 * [backup-simplify]: Simplify 0 into 0 1.691 * [backup-simplify]: Simplify 0 into 0 1.691 * [backup-simplify]: Simplify 0 into 0 1.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.692 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.694 * [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 1.694 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.694 * [backup-simplify]: Simplify (+ 0 0) into 0 1.695 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.696 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.697 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.698 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.698 * [taylor]: Taking taylor expansion of 0 in k 1.698 * [backup-simplify]: Simplify 0 into 0 1.698 * [backup-simplify]: Simplify 0 into 0 1.698 * [backup-simplify]: Simplify 0 into 0 1.698 * [backup-simplify]: Simplify 0 into 0 1.699 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.700 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.702 * [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 1.704 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.704 * [backup-simplify]: Simplify (+ 0 0) into 0 1.705 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.706 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.707 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.708 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.708 * [taylor]: Taking taylor expansion of 0 in k 1.708 * [backup-simplify]: Simplify 0 into 0 1.708 * [backup-simplify]: Simplify 0 into 0 1.709 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 1.709 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1) 1.710 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.710 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.710 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.710 * [taylor]: Taking taylor expansion of 2.0 in n 1.710 * [backup-simplify]: Simplify 2.0 into 2.0 1.710 * [taylor]: Taking taylor expansion of (* n PI) in n 1.710 * [taylor]: Taking taylor expansion of n in n 1.710 * [backup-simplify]: Simplify 0 into 0 1.710 * [backup-simplify]: Simplify 1 into 1 1.710 * [taylor]: Taking taylor expansion of PI in n 1.710 * [backup-simplify]: Simplify PI into PI 1.710 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.710 * [taylor]: Taking taylor expansion of 2.0 in n 1.710 * [backup-simplify]: Simplify 2.0 into 2.0 1.710 * [taylor]: Taking taylor expansion of (* n PI) in n 1.710 * [taylor]: Taking taylor expansion of n in n 1.710 * [backup-simplify]: Simplify 0 into 0 1.710 * [backup-simplify]: Simplify 1 into 1 1.710 * [taylor]: Taking taylor expansion of PI in n 1.710 * [backup-simplify]: Simplify PI into PI 1.710 * [backup-simplify]: Simplify (* 0 PI) into 0 1.711 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.711 * [backup-simplify]: Simplify 0 into 0 1.711 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.712 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.713 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.713 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.714 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.714 * [backup-simplify]: Simplify 0 into 0 1.714 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.715 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.715 * [backup-simplify]: Simplify 0 into 0 1.716 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.717 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.717 * [backup-simplify]: Simplify 0 into 0 1.717 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.718 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.719 * [backup-simplify]: Simplify 0 into 0 1.719 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.720 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.720 * [backup-simplify]: Simplify 0 into 0 1.721 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.722 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.722 * [backup-simplify]: Simplify 0 into 0 1.723 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.723 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.723 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.723 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.723 * [taylor]: Taking taylor expansion of 2.0 in n 1.723 * [backup-simplify]: Simplify 2.0 into 2.0 1.723 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.723 * [taylor]: Taking taylor expansion of PI in n 1.723 * [backup-simplify]: Simplify PI into PI 1.723 * [taylor]: Taking taylor expansion of n in n 1.723 * [backup-simplify]: Simplify 0 into 0 1.723 * [backup-simplify]: Simplify 1 into 1 1.723 * [backup-simplify]: Simplify (/ PI 1) into PI 1.723 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.723 * [taylor]: Taking taylor expansion of 2.0 in n 1.724 * [backup-simplify]: Simplify 2.0 into 2.0 1.724 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.724 * [taylor]: Taking taylor expansion of PI in n 1.724 * [backup-simplify]: Simplify PI into PI 1.724 * [taylor]: Taking taylor expansion of n in n 1.724 * [backup-simplify]: Simplify 0 into 0 1.724 * [backup-simplify]: Simplify 1 into 1 1.724 * [backup-simplify]: Simplify (/ PI 1) into PI 1.724 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.725 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.725 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.725 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.725 * [backup-simplify]: Simplify 0 into 0 1.726 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.727 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.727 * [backup-simplify]: Simplify 0 into 0 1.727 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.728 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.728 * [backup-simplify]: Simplify 0 into 0 1.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.729 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.729 * [backup-simplify]: Simplify 0 into 0 1.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.731 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.731 * [backup-simplify]: Simplify 0 into 0 1.731 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.732 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.732 * [backup-simplify]: Simplify 0 into 0 1.732 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.733 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.733 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.733 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.733 * [taylor]: Taking taylor expansion of -2.0 in n 1.733 * [backup-simplify]: Simplify -2.0 into -2.0 1.733 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.733 * [taylor]: Taking taylor expansion of PI in n 1.733 * [backup-simplify]: Simplify PI into PI 1.733 * [taylor]: Taking taylor expansion of n in n 1.733 * [backup-simplify]: Simplify 0 into 0 1.733 * [backup-simplify]: Simplify 1 into 1 1.733 * [backup-simplify]: Simplify (/ PI 1) into PI 1.733 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.733 * [taylor]: Taking taylor expansion of -2.0 in n 1.733 * [backup-simplify]: Simplify -2.0 into -2.0 1.733 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.733 * [taylor]: Taking taylor expansion of PI in n 1.733 * [backup-simplify]: Simplify PI into PI 1.733 * [taylor]: Taking taylor expansion of n in n 1.733 * [backup-simplify]: Simplify 0 into 0 1.733 * [backup-simplify]: Simplify 1 into 1 1.734 * [backup-simplify]: Simplify (/ PI 1) into PI 1.734 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.734 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.735 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.735 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.735 * [backup-simplify]: Simplify 0 into 0 1.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.736 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.736 * [backup-simplify]: Simplify 0 into 0 1.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.738 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.738 * [backup-simplify]: Simplify 0 into 0 1.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.739 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.739 * [backup-simplify]: Simplify 0 into 0 1.739 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.740 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.740 * [backup-simplify]: Simplify 0 into 0 1.741 * [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 1.742 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.742 * [backup-simplify]: Simplify 0 into 0 1.742 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.742 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1) 1.743 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.743 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.743 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.743 * [taylor]: Taking taylor expansion of 2.0 in n 1.743 * [backup-simplify]: Simplify 2.0 into 2.0 1.743 * [taylor]: Taking taylor expansion of (* n PI) in n 1.743 * [taylor]: Taking taylor expansion of n in n 1.743 * [backup-simplify]: Simplify 0 into 0 1.743 * [backup-simplify]: Simplify 1 into 1 1.743 * [taylor]: Taking taylor expansion of PI in n 1.743 * [backup-simplify]: Simplify PI into PI 1.743 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.743 * [taylor]: Taking taylor expansion of 2.0 in n 1.743 * [backup-simplify]: Simplify 2.0 into 2.0 1.743 * [taylor]: Taking taylor expansion of (* n PI) in n 1.743 * [taylor]: Taking taylor expansion of n in n 1.743 * [backup-simplify]: Simplify 0 into 0 1.743 * [backup-simplify]: Simplify 1 into 1 1.743 * [taylor]: Taking taylor expansion of PI in n 1.743 * [backup-simplify]: Simplify PI into PI 1.743 * [backup-simplify]: Simplify (* 0 PI) into 0 1.743 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.743 * [backup-simplify]: Simplify 0 into 0 1.744 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.745 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.745 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.746 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.747 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.747 * [backup-simplify]: Simplify 0 into 0 1.747 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.748 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.748 * [backup-simplify]: Simplify 0 into 0 1.749 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.749 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.749 * [backup-simplify]: Simplify 0 into 0 1.750 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.751 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.751 * [backup-simplify]: Simplify 0 into 0 1.752 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.753 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.753 * [backup-simplify]: Simplify 0 into 0 1.754 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.755 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.755 * [backup-simplify]: Simplify 0 into 0 1.755 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.755 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.755 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.755 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.755 * [taylor]: Taking taylor expansion of 2.0 in n 1.755 * [backup-simplify]: Simplify 2.0 into 2.0 1.755 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.755 * [taylor]: Taking taylor expansion of PI in n 1.755 * [backup-simplify]: Simplify PI into PI 1.755 * [taylor]: Taking taylor expansion of n in n 1.755 * [backup-simplify]: Simplify 0 into 0 1.755 * [backup-simplify]: Simplify 1 into 1 1.756 * [backup-simplify]: Simplify (/ PI 1) into PI 1.756 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.756 * [taylor]: Taking taylor expansion of 2.0 in n 1.756 * [backup-simplify]: Simplify 2.0 into 2.0 1.756 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.756 * [taylor]: Taking taylor expansion of PI in n 1.756 * [backup-simplify]: Simplify PI into PI 1.756 * [taylor]: Taking taylor expansion of n in n 1.756 * [backup-simplify]: Simplify 0 into 0 1.756 * [backup-simplify]: Simplify 1 into 1 1.756 * [backup-simplify]: Simplify (/ PI 1) into PI 1.757 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.757 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.758 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.758 * [backup-simplify]: Simplify 0 into 0 1.758 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.759 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.759 * [backup-simplify]: Simplify 0 into 0 1.760 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.760 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.760 * [backup-simplify]: Simplify 0 into 0 1.767 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.768 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.768 * [backup-simplify]: Simplify 0 into 0 1.768 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.769 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.769 * [backup-simplify]: Simplify 0 into 0 1.770 * [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 1.771 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.771 * [backup-simplify]: Simplify 0 into 0 1.771 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.772 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.772 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.772 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.772 * [taylor]: Taking taylor expansion of -2.0 in n 1.772 * [backup-simplify]: Simplify -2.0 into -2.0 1.772 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.772 * [taylor]: Taking taylor expansion of PI in n 1.772 * [backup-simplify]: Simplify PI into PI 1.772 * [taylor]: Taking taylor expansion of n in n 1.772 * [backup-simplify]: Simplify 0 into 0 1.772 * [backup-simplify]: Simplify 1 into 1 1.772 * [backup-simplify]: Simplify (/ PI 1) into PI 1.772 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.772 * [taylor]: Taking taylor expansion of -2.0 in n 1.772 * [backup-simplify]: Simplify -2.0 into -2.0 1.772 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.772 * [taylor]: Taking taylor expansion of PI in n 1.772 * [backup-simplify]: Simplify PI into PI 1.772 * [taylor]: Taking taylor expansion of n in n 1.772 * [backup-simplify]: Simplify 0 into 0 1.773 * [backup-simplify]: Simplify 1 into 1 1.773 * [backup-simplify]: Simplify (/ PI 1) into PI 1.773 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.773 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.774 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.774 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.774 * [backup-simplify]: Simplify 0 into 0 1.775 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.776 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.776 * [backup-simplify]: Simplify 0 into 0 1.776 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.777 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.777 * [backup-simplify]: Simplify 0 into 0 1.777 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.778 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.778 * [backup-simplify]: Simplify 0 into 0 1.779 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.780 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.780 * [backup-simplify]: Simplify 0 into 0 1.780 * [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 1.781 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.781 * [backup-simplify]: Simplify 0 into 0 1.781 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.782 * * * [progress]: simplifying candidates 1.785 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (+ (+ (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)) 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(cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 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(/ (/ (- h2 h1) h0) 2)) (pow h3 (/ (/ (- h2 h1) h0) 2)) (log (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (exp (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (/ (- h2 h1) h0) 2)) (* (+ (log (* h0 h4)) (log h3)) (/ (/ (- h2 h1) h0) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (- h2 h1) h0) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 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(* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ 1 (sqrt 2))) (pow (* (* h0 h4) h3) (/ 1 1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (- h2 h1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (- h2 h1) 1)) (pow (* (* h0 h4) h3) 1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* h0 h4) (/ (/ (- h2 h1) h0) 2)) (pow h3 (/ (/ (- h2 h1) h0) 2)) (log (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (exp (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (* (* 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) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) 1.793 * * [simplify]: iteration 0 : 696 enodes (cost 1678 ) 1.805 * * [simplify]: iteration 1 : 2767 enodes (cost 1618 ) 1.846 * * [simplify]: iteration 2 : 5001 enodes (cost 1608 ) 1.854 * * * [progress]: adding candidates to table 2.513 * * [progress]: iteration 3 / 4 2.513 * * * [progress]: picking best candidate 2.536 * * * * [pick]: Picked # 2.536 * * * [progress]: localizing error 2.551 * * * [progress]: generating rewritten candidates 2.551 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.580 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 2.605 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 2.611 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 2.642 * * * [progress]: generating series expansions 2.642 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.643 * [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))) 2.643 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.643 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.643 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.643 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.643 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.643 * [taylor]: Taking taylor expansion of 0.25 in k 2.643 * [backup-simplify]: Simplify 0.25 into 0.25 2.643 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.643 * [taylor]: Taking taylor expansion of 1.0 in k 2.643 * [backup-simplify]: Simplify 1.0 into 1.0 2.643 * [taylor]: Taking taylor expansion of k in k 2.643 * [backup-simplify]: Simplify 0 into 0 2.643 * [backup-simplify]: Simplify 1 into 1 2.643 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.643 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.643 * [taylor]: Taking taylor expansion of 2.0 in k 2.643 * [backup-simplify]: Simplify 2.0 into 2.0 2.643 * [taylor]: Taking taylor expansion of (* n PI) in k 2.643 * [taylor]: Taking taylor expansion of n in k 2.643 * [backup-simplify]: Simplify n into n 2.643 * [taylor]: Taking taylor expansion of PI in k 2.643 * [backup-simplify]: Simplify PI into PI 2.643 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.643 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.643 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.644 * [backup-simplify]: Simplify (- 0) into 0 2.644 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.644 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.644 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.644 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.644 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.644 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.644 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.644 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.644 * [taylor]: Taking taylor expansion of 0.25 in n 2.644 * [backup-simplify]: Simplify 0.25 into 0.25 2.644 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.645 * [taylor]: Taking taylor expansion of 1.0 in n 2.645 * [backup-simplify]: Simplify 1.0 into 1.0 2.645 * [taylor]: Taking taylor expansion of k in n 2.645 * [backup-simplify]: Simplify k into k 2.645 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.645 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.645 * [taylor]: Taking taylor expansion of 2.0 in n 2.645 * [backup-simplify]: Simplify 2.0 into 2.0 2.645 * [taylor]: Taking taylor expansion of (* n PI) in n 2.645 * [taylor]: Taking taylor expansion of n in n 2.645 * [backup-simplify]: Simplify 0 into 0 2.645 * [backup-simplify]: Simplify 1 into 1 2.645 * [taylor]: Taking taylor expansion of PI in n 2.645 * [backup-simplify]: Simplify PI into PI 2.645 * [backup-simplify]: Simplify (* 0 PI) into 0 2.645 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.646 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.647 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.648 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.648 * [backup-simplify]: Simplify (- k) into (- k) 2.648 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.648 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.649 * [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)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.650 * [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))))) 2.650 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.650 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.650 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.650 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.650 * [taylor]: Taking taylor expansion of 0.25 in n 2.650 * [backup-simplify]: Simplify 0.25 into 0.25 2.650 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.650 * [taylor]: Taking taylor expansion of 1.0 in n 2.650 * [backup-simplify]: Simplify 1.0 into 1.0 2.650 * [taylor]: Taking taylor expansion of k in n 2.650 * [backup-simplify]: Simplify k into k 2.650 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.650 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.650 * [taylor]: Taking taylor expansion of 2.0 in n 2.650 * [backup-simplify]: Simplify 2.0 into 2.0 2.650 * [taylor]: Taking taylor expansion of (* n PI) in n 2.650 * [taylor]: Taking taylor expansion of n in n 2.650 * [backup-simplify]: Simplify 0 into 0 2.650 * [backup-simplify]: Simplify 1 into 1 2.650 * [taylor]: Taking taylor expansion of PI in n 2.650 * [backup-simplify]: Simplify PI into PI 2.651 * [backup-simplify]: Simplify (* 0 PI) into 0 2.651 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.652 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.653 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.654 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.654 * [backup-simplify]: Simplify (- k) into (- k) 2.654 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.654 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.655 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.655 * [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)))) 2.656 * [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))))) 2.656 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.656 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.656 * [taylor]: Taking taylor expansion of 0.25 in k 2.656 * [backup-simplify]: Simplify 0.25 into 0.25 2.656 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.656 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.656 * [taylor]: Taking taylor expansion of 1.0 in k 2.656 * [backup-simplify]: Simplify 1.0 into 1.0 2.656 * [taylor]: Taking taylor expansion of k in k 2.656 * [backup-simplify]: Simplify 0 into 0 2.656 * [backup-simplify]: Simplify 1 into 1 2.656 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.656 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.656 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.656 * [taylor]: Taking taylor expansion of 2.0 in k 2.656 * [backup-simplify]: Simplify 2.0 into 2.0 2.656 * [taylor]: Taking taylor expansion of PI in k 2.656 * [backup-simplify]: Simplify PI into PI 2.657 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.657 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.657 * [taylor]: Taking taylor expansion of (log n) in k 2.657 * [taylor]: Taking taylor expansion of n in k 2.657 * [backup-simplify]: Simplify n into n 2.657 * [backup-simplify]: Simplify (log n) into (log n) 2.658 * [backup-simplify]: Simplify (- 0) into 0 2.658 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.659 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.659 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.660 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.661 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.662 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.662 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.663 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.664 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.664 * [backup-simplify]: Simplify (- 0) into 0 2.664 * [backup-simplify]: Simplify (+ 0 0) into 0 2.664 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.665 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.666 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.667 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.667 * [taylor]: Taking taylor expansion of 0 in k 2.667 * [backup-simplify]: Simplify 0 into 0 2.667 * [backup-simplify]: Simplify 0 into 0 2.668 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.669 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.669 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.670 * [backup-simplify]: Simplify (+ 0 0) into 0 2.670 * [backup-simplify]: Simplify (- 1) into -1 2.670 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.671 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.672 * [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)))) 2.674 * [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)))))) 2.676 * [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)))))) 2.677 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.677 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.679 * [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 2.679 * [backup-simplify]: Simplify (- 0) into 0 2.679 * [backup-simplify]: Simplify (+ 0 0) into 0 2.680 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.681 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.682 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.683 * [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 2.683 * [taylor]: Taking taylor expansion of 0 in k 2.683 * [backup-simplify]: Simplify 0 into 0 2.683 * [backup-simplify]: Simplify 0 into 0 2.683 * [backup-simplify]: Simplify 0 into 0 2.684 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.685 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.686 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.687 * [backup-simplify]: Simplify (+ 0 0) into 0 2.687 * [backup-simplify]: Simplify (- 0) into 0 2.687 * [backup-simplify]: Simplify (+ 0 0) into 0 2.688 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.690 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.692 * [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))))) 2.695 * [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))))) 2.701 * [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)))))) 2.701 * [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)))) 2.701 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.701 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.701 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.701 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.701 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.702 * [taylor]: Taking taylor expansion of 0.25 in k 2.702 * [backup-simplify]: Simplify 0.25 into 0.25 2.702 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.702 * [taylor]: Taking taylor expansion of 1.0 in k 2.702 * [backup-simplify]: Simplify 1.0 into 1.0 2.702 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.702 * [taylor]: Taking taylor expansion of k in k 2.702 * [backup-simplify]: Simplify 0 into 0 2.702 * [backup-simplify]: Simplify 1 into 1 2.702 * [backup-simplify]: Simplify (/ 1 1) into 1 2.702 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.702 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.702 * [taylor]: Taking taylor expansion of 2.0 in k 2.702 * [backup-simplify]: Simplify 2.0 into 2.0 2.702 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.702 * [taylor]: Taking taylor expansion of PI in k 2.702 * [backup-simplify]: Simplify PI into PI 2.702 * [taylor]: Taking taylor expansion of n in k 2.702 * [backup-simplify]: Simplify n into n 2.702 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.702 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.702 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.702 * [backup-simplify]: Simplify (- 1) into -1 2.703 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.703 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.703 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.703 * [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))))) 2.703 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.703 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.703 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.703 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.703 * [taylor]: Taking taylor expansion of 0.25 in n 2.703 * [backup-simplify]: Simplify 0.25 into 0.25 2.703 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.703 * [taylor]: Taking taylor expansion of 1.0 in n 2.703 * [backup-simplify]: Simplify 1.0 into 1.0 2.703 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.703 * [taylor]: Taking taylor expansion of k in n 2.703 * [backup-simplify]: Simplify k into k 2.703 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.703 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.703 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.703 * [taylor]: Taking taylor expansion of 2.0 in n 2.703 * [backup-simplify]: Simplify 2.0 into 2.0 2.703 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.703 * [taylor]: Taking taylor expansion of PI in n 2.703 * [backup-simplify]: Simplify PI into PI 2.703 * [taylor]: Taking taylor expansion of n in n 2.703 * [backup-simplify]: Simplify 0 into 0 2.704 * [backup-simplify]: Simplify 1 into 1 2.704 * [backup-simplify]: Simplify (/ PI 1) into PI 2.704 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.705 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.705 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.705 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.705 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.706 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.706 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.707 * [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))))) 2.707 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.707 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.707 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.707 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.707 * [taylor]: Taking taylor expansion of 0.25 in n 2.707 * [backup-simplify]: Simplify 0.25 into 0.25 2.707 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.707 * [taylor]: Taking taylor expansion of 1.0 in n 2.707 * [backup-simplify]: Simplify 1.0 into 1.0 2.707 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.707 * [taylor]: Taking taylor expansion of k in n 2.707 * [backup-simplify]: Simplify k into k 2.707 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.707 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.707 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.707 * [taylor]: Taking taylor expansion of 2.0 in n 2.707 * [backup-simplify]: Simplify 2.0 into 2.0 2.707 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.708 * [taylor]: Taking taylor expansion of PI in n 2.708 * [backup-simplify]: Simplify PI into PI 2.708 * [taylor]: Taking taylor expansion of n in n 2.708 * [backup-simplify]: Simplify 0 into 0 2.708 * [backup-simplify]: Simplify 1 into 1 2.708 * [backup-simplify]: Simplify (/ PI 1) into PI 2.708 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.709 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.709 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.709 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.709 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.710 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.710 * [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)))) 2.711 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.711 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.711 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.712 * [taylor]: Taking taylor expansion of 0.25 in k 2.712 * [backup-simplify]: Simplify 0.25 into 0.25 2.712 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.712 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.712 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.712 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.712 * [taylor]: Taking taylor expansion of 2.0 in k 2.712 * [backup-simplify]: Simplify 2.0 into 2.0 2.712 * [taylor]: Taking taylor expansion of PI in k 2.712 * [backup-simplify]: Simplify PI into PI 2.712 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.713 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.713 * [taylor]: Taking taylor expansion of (log n) in k 2.713 * [taylor]: Taking taylor expansion of n in k 2.713 * [backup-simplify]: Simplify n into n 2.713 * [backup-simplify]: Simplify (log n) into (log n) 2.713 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.713 * [taylor]: Taking taylor expansion of 1.0 in k 2.713 * [backup-simplify]: Simplify 1.0 into 1.0 2.713 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.713 * [taylor]: Taking taylor expansion of k in k 2.713 * [backup-simplify]: Simplify 0 into 0 2.713 * [backup-simplify]: Simplify 1 into 1 2.713 * [backup-simplify]: Simplify (/ 1 1) into 1 2.713 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.714 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.714 * [backup-simplify]: Simplify (- 1) into -1 2.714 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.715 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.715 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.716 * [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))))) 2.717 * [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))))) 2.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.718 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.719 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.719 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.719 * [backup-simplify]: Simplify (- 0) into 0 2.719 * [backup-simplify]: Simplify (+ 0 0) into 0 2.720 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.720 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.721 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.722 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.722 * [taylor]: Taking taylor expansion of 0 in k 2.722 * [backup-simplify]: Simplify 0 into 0 2.722 * [backup-simplify]: Simplify 0 into 0 2.722 * [backup-simplify]: Simplify 0 into 0 2.723 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.724 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.731 * [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 2.731 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.732 * [backup-simplify]: Simplify (- 0) into 0 2.732 * [backup-simplify]: Simplify (+ 0 0) into 0 2.732 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.733 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.734 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.736 * [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 2.736 * [taylor]: Taking taylor expansion of 0 in k 2.736 * [backup-simplify]: Simplify 0 into 0 2.736 * [backup-simplify]: Simplify 0 into 0 2.736 * [backup-simplify]: Simplify 0 into 0 2.736 * [backup-simplify]: Simplify 0 into 0 2.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.737 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.740 * [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 2.740 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.740 * [backup-simplify]: Simplify (- 0) into 0 2.740 * [backup-simplify]: Simplify (+ 0 0) into 0 2.741 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.742 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.743 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.745 * [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 2.745 * [taylor]: Taking taylor expansion of 0 in k 2.745 * [backup-simplify]: Simplify 0 into 0 2.745 * [backup-simplify]: Simplify 0 into 0 2.746 * [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)))) 2.746 * [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))) 2.747 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.747 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.747 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.747 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.747 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.747 * [taylor]: Taking taylor expansion of 0.25 in k 2.747 * [backup-simplify]: Simplify 0.25 into 0.25 2.747 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.747 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.747 * [taylor]: Taking taylor expansion of k in k 2.747 * [backup-simplify]: Simplify 0 into 0 2.747 * [backup-simplify]: Simplify 1 into 1 2.747 * [backup-simplify]: Simplify (/ 1 1) into 1 2.747 * [taylor]: Taking taylor expansion of 1.0 in k 2.747 * [backup-simplify]: Simplify 1.0 into 1.0 2.747 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.747 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.747 * [taylor]: Taking taylor expansion of -2.0 in k 2.747 * [backup-simplify]: Simplify -2.0 into -2.0 2.747 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.747 * [taylor]: Taking taylor expansion of PI in k 2.747 * [backup-simplify]: Simplify PI into PI 2.747 * [taylor]: Taking taylor expansion of n in k 2.747 * [backup-simplify]: Simplify n into n 2.747 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.747 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.747 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.748 * [backup-simplify]: Simplify (+ 1 0) into 1 2.748 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.748 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.748 * [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)))))) 2.748 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.748 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.748 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.748 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.748 * [taylor]: Taking taylor expansion of 0.25 in n 2.748 * [backup-simplify]: Simplify 0.25 into 0.25 2.748 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.748 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.748 * [taylor]: Taking taylor expansion of k in n 2.748 * [backup-simplify]: Simplify k into k 2.748 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.748 * [taylor]: Taking taylor expansion of 1.0 in n 2.748 * [backup-simplify]: Simplify 1.0 into 1.0 2.748 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.748 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.748 * [taylor]: Taking taylor expansion of -2.0 in n 2.748 * [backup-simplify]: Simplify -2.0 into -2.0 2.748 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.748 * [taylor]: Taking taylor expansion of PI in n 2.748 * [backup-simplify]: Simplify PI into PI 2.748 * [taylor]: Taking taylor expansion of n in n 2.748 * [backup-simplify]: Simplify 0 into 0 2.748 * [backup-simplify]: Simplify 1 into 1 2.749 * [backup-simplify]: Simplify (/ PI 1) into PI 2.749 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.750 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.750 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.750 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.751 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.751 * [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)))) 2.752 * [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))))) 2.752 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.752 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.752 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.752 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.752 * [taylor]: Taking taylor expansion of 0.25 in n 2.752 * [backup-simplify]: Simplify 0.25 into 0.25 2.752 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.752 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.752 * [taylor]: Taking taylor expansion of k in n 2.752 * [backup-simplify]: Simplify k into k 2.752 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.752 * [taylor]: Taking taylor expansion of 1.0 in n 2.752 * [backup-simplify]: Simplify 1.0 into 1.0 2.752 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.752 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.752 * [taylor]: Taking taylor expansion of -2.0 in n 2.752 * [backup-simplify]: Simplify -2.0 into -2.0 2.752 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.752 * [taylor]: Taking taylor expansion of PI in n 2.752 * [backup-simplify]: Simplify PI into PI 2.752 * [taylor]: Taking taylor expansion of n in n 2.752 * [backup-simplify]: Simplify 0 into 0 2.752 * [backup-simplify]: Simplify 1 into 1 2.753 * [backup-simplify]: Simplify (/ PI 1) into PI 2.753 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.754 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.754 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.754 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.755 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.755 * [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)))) 2.756 * [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))))) 2.756 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.756 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.756 * [taylor]: Taking taylor expansion of 0.25 in k 2.756 * [backup-simplify]: Simplify 0.25 into 0.25 2.756 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.756 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.756 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.756 * [taylor]: Taking taylor expansion of k in k 2.756 * [backup-simplify]: Simplify 0 into 0 2.756 * [backup-simplify]: Simplify 1 into 1 2.756 * [backup-simplify]: Simplify (/ 1 1) into 1 2.756 * [taylor]: Taking taylor expansion of 1.0 in k 2.756 * [backup-simplify]: Simplify 1.0 into 1.0 2.757 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.757 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.757 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.757 * [taylor]: Taking taylor expansion of -2.0 in k 2.757 * [backup-simplify]: Simplify -2.0 into -2.0 2.757 * [taylor]: Taking taylor expansion of PI in k 2.757 * [backup-simplify]: Simplify PI into PI 2.757 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.757 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.758 * [taylor]: Taking taylor expansion of (log n) in k 2.758 * [taylor]: Taking taylor expansion of n in k 2.758 * [backup-simplify]: Simplify n into n 2.758 * [backup-simplify]: Simplify (log n) into (log n) 2.758 * [backup-simplify]: Simplify (+ 1 0) into 1 2.758 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.759 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.759 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.760 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.760 * [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))))) 2.761 * [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))))) 2.762 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.762 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.763 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.763 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.764 * [backup-simplify]: Simplify (+ 0 0) into 0 2.764 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.765 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.766 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.767 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) 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 2.767 * [backup-simplify]: Simplify 0 into 0 2.767 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.768 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.770 * [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 2.770 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.770 * [backup-simplify]: Simplify (+ 0 0) into 0 2.771 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.772 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.773 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.774 * [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 2.774 * [taylor]: Taking taylor expansion of 0 in k 2.774 * [backup-simplify]: Simplify 0 into 0 2.774 * [backup-simplify]: Simplify 0 into 0 2.774 * [backup-simplify]: Simplify 0 into 0 2.774 * [backup-simplify]: Simplify 0 into 0 2.775 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.776 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.779 * [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 2.779 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.779 * [backup-simplify]: Simplify (+ 0 0) into 0 2.780 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.781 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.782 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.783 * [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 2.783 * [taylor]: Taking taylor expansion of 0 in k 2.783 * [backup-simplify]: Simplify 0 into 0 2.783 * [backup-simplify]: Simplify 0 into 0 2.784 * [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)))))) 2.784 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 2.785 * [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))) 2.785 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.785 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.785 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.785 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.785 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.785 * [taylor]: Taking taylor expansion of 0.25 in k 2.785 * [backup-simplify]: Simplify 0.25 into 0.25 2.785 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.785 * [taylor]: Taking taylor expansion of 1.0 in k 2.785 * [backup-simplify]: Simplify 1.0 into 1.0 2.785 * [taylor]: Taking taylor expansion of k in k 2.785 * [backup-simplify]: Simplify 0 into 0 2.785 * [backup-simplify]: Simplify 1 into 1 2.785 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.785 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.785 * [taylor]: Taking taylor expansion of 2.0 in k 2.785 * [backup-simplify]: Simplify 2.0 into 2.0 2.785 * [taylor]: Taking taylor expansion of (* n PI) in k 2.785 * [taylor]: Taking taylor expansion of n in k 2.785 * [backup-simplify]: Simplify n into n 2.785 * [taylor]: Taking taylor expansion of PI in k 2.785 * [backup-simplify]: Simplify PI into PI 2.785 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.785 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.785 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.785 * [backup-simplify]: Simplify (- 0) into 0 2.786 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.786 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.786 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.786 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.786 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.786 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.786 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.786 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.786 * [taylor]: Taking taylor expansion of 0.25 in n 2.786 * [backup-simplify]: Simplify 0.25 into 0.25 2.786 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.786 * [taylor]: Taking taylor expansion of 1.0 in n 2.786 * [backup-simplify]: Simplify 1.0 into 1.0 2.786 * [taylor]: Taking taylor expansion of k in n 2.786 * [backup-simplify]: Simplify k into k 2.786 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.786 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.786 * [taylor]: Taking taylor expansion of 2.0 in n 2.786 * [backup-simplify]: Simplify 2.0 into 2.0 2.786 * [taylor]: Taking taylor expansion of (* n PI) in n 2.786 * [taylor]: Taking taylor expansion of n in n 2.786 * [backup-simplify]: Simplify 0 into 0 2.786 * [backup-simplify]: Simplify 1 into 1 2.786 * [taylor]: Taking taylor expansion of PI in n 2.786 * [backup-simplify]: Simplify PI into PI 2.787 * [backup-simplify]: Simplify (* 0 PI) into 0 2.787 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.788 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.789 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.789 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.789 * [backup-simplify]: Simplify (- k) into (- k) 2.789 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.789 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.790 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.791 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.792 * [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))))) 2.792 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.792 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.792 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.792 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.792 * [taylor]: Taking taylor expansion of 0.25 in n 2.792 * [backup-simplify]: Simplify 0.25 into 0.25 2.792 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.792 * [taylor]: Taking taylor expansion of 1.0 in n 2.792 * [backup-simplify]: Simplify 1.0 into 1.0 2.792 * [taylor]: Taking taylor expansion of k in n 2.792 * [backup-simplify]: Simplify k into k 2.792 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.792 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.792 * [taylor]: Taking taylor expansion of 2.0 in n 2.792 * [backup-simplify]: Simplify 2.0 into 2.0 2.792 * [taylor]: Taking taylor expansion of (* n PI) in n 2.792 * [taylor]: Taking taylor expansion of n in n 2.792 * [backup-simplify]: Simplify 0 into 0 2.792 * [backup-simplify]: Simplify 1 into 1 2.792 * [taylor]: Taking taylor expansion of PI in n 2.792 * [backup-simplify]: Simplify PI into PI 2.792 * [backup-simplify]: Simplify (* 0 PI) into 0 2.792 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.793 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.794 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.795 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.795 * [backup-simplify]: Simplify (- k) into (- k) 2.795 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.795 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.796 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.796 * [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)))) 2.797 * [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))))) 2.797 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.797 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.797 * [taylor]: Taking taylor expansion of 0.25 in k 2.797 * [backup-simplify]: Simplify 0.25 into 0.25 2.797 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.797 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.797 * [taylor]: Taking taylor expansion of 1.0 in k 2.797 * [backup-simplify]: Simplify 1.0 into 1.0 2.797 * [taylor]: Taking taylor expansion of k in k 2.797 * [backup-simplify]: Simplify 0 into 0 2.797 * [backup-simplify]: Simplify 1 into 1 2.797 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.797 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.797 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.797 * [taylor]: Taking taylor expansion of 2.0 in k 2.797 * [backup-simplify]: Simplify 2.0 into 2.0 2.797 * [taylor]: Taking taylor expansion of PI in k 2.797 * [backup-simplify]: Simplify PI into PI 2.798 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.798 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.798 * [taylor]: Taking taylor expansion of (log n) in k 2.798 * [taylor]: Taking taylor expansion of n in k 2.798 * [backup-simplify]: Simplify n into n 2.798 * [backup-simplify]: Simplify (log n) into (log n) 2.799 * [backup-simplify]: Simplify (- 0) into 0 2.799 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.800 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.800 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.801 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.802 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.802 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.803 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.803 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.804 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.804 * [backup-simplify]: Simplify (- 0) into 0 2.805 * [backup-simplify]: Simplify (+ 0 0) into 0 2.805 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.806 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.806 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.808 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.808 * [taylor]: Taking taylor expansion of 0 in k 2.808 * [backup-simplify]: Simplify 0 into 0 2.808 * [backup-simplify]: Simplify 0 into 0 2.808 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.809 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.810 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.810 * [backup-simplify]: Simplify (+ 0 0) into 0 2.810 * [backup-simplify]: Simplify (- 1) into -1 2.810 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.811 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.813 * [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)))) 2.814 * [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)))))) 2.816 * [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)))))) 2.817 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.818 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.819 * [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 2.819 * [backup-simplify]: Simplify (- 0) into 0 2.820 * [backup-simplify]: Simplify (+ 0 0) into 0 2.825 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.827 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.827 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.829 * [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 2.829 * [taylor]: Taking taylor expansion of 0 in k 2.829 * [backup-simplify]: Simplify 0 into 0 2.829 * [backup-simplify]: Simplify 0 into 0 2.829 * [backup-simplify]: Simplify 0 into 0 2.830 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.831 * [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 2.832 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.833 * [backup-simplify]: Simplify (+ 0 0) into 0 2.833 * [backup-simplify]: Simplify (- 0) into 0 2.833 * [backup-simplify]: Simplify (+ 0 0) into 0 2.834 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.836 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.838 * [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))))) 2.841 * [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))))) 2.847 * [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)))))) 2.847 * [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)))) 2.847 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.847 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.847 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.847 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.847 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.847 * [taylor]: Taking taylor expansion of 0.25 in k 2.847 * [backup-simplify]: Simplify 0.25 into 0.25 2.847 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.847 * [taylor]: Taking taylor expansion of 1.0 in k 2.847 * [backup-simplify]: Simplify 1.0 into 1.0 2.847 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.847 * [taylor]: Taking taylor expansion of k in k 2.848 * [backup-simplify]: Simplify 0 into 0 2.848 * [backup-simplify]: Simplify 1 into 1 2.848 * [backup-simplify]: Simplify (/ 1 1) into 1 2.848 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.848 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.848 * [taylor]: Taking taylor expansion of 2.0 in k 2.848 * [backup-simplify]: Simplify 2.0 into 2.0 2.848 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.848 * [taylor]: Taking taylor expansion of PI in k 2.848 * [backup-simplify]: Simplify PI into PI 2.848 * [taylor]: Taking taylor expansion of n in k 2.848 * [backup-simplify]: Simplify n into n 2.848 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.848 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.848 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.848 * [backup-simplify]: Simplify (- 1) into -1 2.849 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.849 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.849 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.849 * [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))))) 2.849 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.849 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.849 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.849 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.849 * [taylor]: Taking taylor expansion of 0.25 in n 2.849 * [backup-simplify]: Simplify 0.25 into 0.25 2.849 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.849 * [taylor]: Taking taylor expansion of 1.0 in n 2.849 * [backup-simplify]: Simplify 1.0 into 1.0 2.849 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.849 * [taylor]: Taking taylor expansion of k in n 2.849 * [backup-simplify]: Simplify k into k 2.849 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.849 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.849 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.849 * [taylor]: Taking taylor expansion of 2.0 in n 2.849 * [backup-simplify]: Simplify 2.0 into 2.0 2.849 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.849 * [taylor]: Taking taylor expansion of PI in n 2.849 * [backup-simplify]: Simplify PI into PI 2.849 * [taylor]: Taking taylor expansion of n in n 2.849 * [backup-simplify]: Simplify 0 into 0 2.849 * [backup-simplify]: Simplify 1 into 1 2.850 * [backup-simplify]: Simplify (/ PI 1) into PI 2.850 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.851 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.851 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.851 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.851 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.852 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.852 * [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)))) 2.853 * [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))))) 2.853 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.853 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.853 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.853 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.853 * [taylor]: Taking taylor expansion of 0.25 in n 2.853 * [backup-simplify]: Simplify 0.25 into 0.25 2.853 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.853 * [taylor]: Taking taylor expansion of 1.0 in n 2.853 * [backup-simplify]: Simplify 1.0 into 1.0 2.853 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.853 * [taylor]: Taking taylor expansion of k in n 2.853 * [backup-simplify]: Simplify k into k 2.853 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.853 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.853 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.853 * [taylor]: Taking taylor expansion of 2.0 in n 2.853 * [backup-simplify]: Simplify 2.0 into 2.0 2.853 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.853 * [taylor]: Taking taylor expansion of PI in n 2.853 * [backup-simplify]: Simplify PI into PI 2.853 * [taylor]: Taking taylor expansion of n in n 2.853 * [backup-simplify]: Simplify 0 into 0 2.853 * [backup-simplify]: Simplify 1 into 1 2.854 * [backup-simplify]: Simplify (/ PI 1) into PI 2.854 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.855 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.855 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.855 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.855 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.856 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.856 * [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)))) 2.857 * [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))))) 2.857 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.857 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.857 * [taylor]: Taking taylor expansion of 0.25 in k 2.857 * [backup-simplify]: Simplify 0.25 into 0.25 2.857 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.857 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.857 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.857 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.857 * [taylor]: Taking taylor expansion of 2.0 in k 2.857 * [backup-simplify]: Simplify 2.0 into 2.0 2.857 * [taylor]: Taking taylor expansion of PI in k 2.857 * [backup-simplify]: Simplify PI into PI 2.858 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.858 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.858 * [taylor]: Taking taylor expansion of (log n) in k 2.858 * [taylor]: Taking taylor expansion of n in k 2.858 * [backup-simplify]: Simplify n into n 2.858 * [backup-simplify]: Simplify (log n) into (log n) 2.858 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.858 * [taylor]: Taking taylor expansion of 1.0 in k 2.858 * [backup-simplify]: Simplify 1.0 into 1.0 2.858 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.858 * [taylor]: Taking taylor expansion of k in k 2.858 * [backup-simplify]: Simplify 0 into 0 2.858 * [backup-simplify]: Simplify 1 into 1 2.859 * [backup-simplify]: Simplify (/ 1 1) into 1 2.859 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.859 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.860 * [backup-simplify]: Simplify (- 1) into -1 2.860 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.860 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.861 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.862 * [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))))) 2.863 * [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))))) 2.863 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.864 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.865 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.865 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.865 * [backup-simplify]: Simplify (- 0) into 0 2.865 * [backup-simplify]: Simplify (+ 0 0) into 0 2.865 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.866 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.867 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.868 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.868 * [taylor]: Taking taylor expansion of 0 in k 2.868 * [backup-simplify]: Simplify 0 into 0 2.868 * [backup-simplify]: Simplify 0 into 0 2.868 * [backup-simplify]: Simplify 0 into 0 2.869 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.870 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.871 * [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 2.872 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.872 * [backup-simplify]: Simplify (- 0) into 0 2.872 * [backup-simplify]: Simplify (+ 0 0) into 0 2.873 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.874 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.875 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.876 * [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 2.876 * [taylor]: Taking taylor expansion of 0 in k 2.876 * [backup-simplify]: Simplify 0 into 0 2.876 * [backup-simplify]: Simplify 0 into 0 2.876 * [backup-simplify]: Simplify 0 into 0 2.876 * [backup-simplify]: Simplify 0 into 0 2.877 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.877 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.880 * [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 2.880 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.881 * [backup-simplify]: Simplify (- 0) into 0 2.881 * [backup-simplify]: Simplify (+ 0 0) into 0 2.882 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.882 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.883 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.885 * [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 2.885 * [taylor]: Taking taylor expansion of 0 in k 2.885 * [backup-simplify]: Simplify 0 into 0 2.885 * [backup-simplify]: Simplify 0 into 0 2.886 * [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)))) 2.886 * [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))) 2.886 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.886 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.886 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.886 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.886 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.886 * [taylor]: Taking taylor expansion of 0.25 in k 2.886 * [backup-simplify]: Simplify 0.25 into 0.25 2.886 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.887 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.887 * [taylor]: Taking taylor expansion of k in k 2.887 * [backup-simplify]: Simplify 0 into 0 2.887 * [backup-simplify]: Simplify 1 into 1 2.887 * [backup-simplify]: Simplify (/ 1 1) into 1 2.887 * [taylor]: Taking taylor expansion of 1.0 in k 2.887 * [backup-simplify]: Simplify 1.0 into 1.0 2.887 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.887 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.887 * [taylor]: Taking taylor expansion of -2.0 in k 2.887 * [backup-simplify]: Simplify -2.0 into -2.0 2.887 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.887 * [taylor]: Taking taylor expansion of PI in k 2.887 * [backup-simplify]: Simplify PI into PI 2.887 * [taylor]: Taking taylor expansion of n in k 2.887 * [backup-simplify]: Simplify n into n 2.887 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.887 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.887 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.887 * [backup-simplify]: Simplify (+ 1 0) into 1 2.888 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.888 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.888 * [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)))))) 2.888 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.888 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.888 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.888 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.888 * [taylor]: Taking taylor expansion of 0.25 in n 2.888 * [backup-simplify]: Simplify 0.25 into 0.25 2.888 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.888 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.888 * [taylor]: Taking taylor expansion of k in n 2.888 * [backup-simplify]: Simplify k into k 2.888 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.888 * [taylor]: Taking taylor expansion of 1.0 in n 2.888 * [backup-simplify]: Simplify 1.0 into 1.0 2.888 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.888 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.888 * [taylor]: Taking taylor expansion of -2.0 in n 2.888 * [backup-simplify]: Simplify -2.0 into -2.0 2.888 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.888 * [taylor]: Taking taylor expansion of PI in n 2.888 * [backup-simplify]: Simplify PI into PI 2.888 * [taylor]: Taking taylor expansion of n in n 2.888 * [backup-simplify]: Simplify 0 into 0 2.888 * [backup-simplify]: Simplify 1 into 1 2.889 * [backup-simplify]: Simplify (/ PI 1) into PI 2.889 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.889 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.890 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.890 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.890 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.891 * [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)))) 2.892 * [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))))) 2.892 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.892 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.892 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.892 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.892 * [taylor]: Taking taylor expansion of 0.25 in n 2.892 * [backup-simplify]: Simplify 0.25 into 0.25 2.892 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.892 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.892 * [taylor]: Taking taylor expansion of k in n 2.892 * [backup-simplify]: Simplify k into k 2.892 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.892 * [taylor]: Taking taylor expansion of 1.0 in n 2.892 * [backup-simplify]: Simplify 1.0 into 1.0 2.892 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.892 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.892 * [taylor]: Taking taylor expansion of -2.0 in n 2.892 * [backup-simplify]: Simplify -2.0 into -2.0 2.892 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.892 * [taylor]: Taking taylor expansion of PI in n 2.892 * [backup-simplify]: Simplify PI into PI 2.892 * [taylor]: Taking taylor expansion of n in n 2.892 * [backup-simplify]: Simplify 0 into 0 2.892 * [backup-simplify]: Simplify 1 into 1 2.893 * [backup-simplify]: Simplify (/ PI 1) into PI 2.893 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.893 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.894 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.894 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.894 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.895 * [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)))) 2.896 * [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))))) 2.896 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.896 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.896 * [taylor]: Taking taylor expansion of 0.25 in k 2.896 * [backup-simplify]: Simplify 0.25 into 0.25 2.896 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.896 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.896 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.896 * [taylor]: Taking taylor expansion of k in k 2.896 * [backup-simplify]: Simplify 0 into 0 2.896 * [backup-simplify]: Simplify 1 into 1 2.896 * [backup-simplify]: Simplify (/ 1 1) into 1 2.896 * [taylor]: Taking taylor expansion of 1.0 in k 2.896 * [backup-simplify]: Simplify 1.0 into 1.0 2.896 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.896 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.896 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.896 * [taylor]: Taking taylor expansion of -2.0 in k 2.896 * [backup-simplify]: Simplify -2.0 into -2.0 2.896 * [taylor]: Taking taylor expansion of PI in k 2.896 * [backup-simplify]: Simplify PI into PI 2.897 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.897 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.897 * [taylor]: Taking taylor expansion of (log n) in k 2.897 * [taylor]: Taking taylor expansion of n in k 2.897 * [backup-simplify]: Simplify n into n 2.897 * [backup-simplify]: Simplify (log n) into (log n) 2.898 * [backup-simplify]: Simplify (+ 1 0) into 1 2.898 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.898 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.899 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.900 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.900 * [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))))) 2.901 * [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))))) 2.902 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.902 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.903 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.903 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.903 * [backup-simplify]: Simplify (+ 0 0) into 0 2.904 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.904 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.905 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.906 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.906 * [taylor]: Taking taylor expansion of 0 in k 2.906 * [backup-simplify]: Simplify 0 into 0 2.906 * [backup-simplify]: Simplify 0 into 0 2.906 * [backup-simplify]: Simplify 0 into 0 2.907 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.908 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.909 * [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 2.909 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.910 * [backup-simplify]: Simplify (+ 0 0) into 0 2.910 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.911 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.912 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.913 * [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 2.913 * [taylor]: Taking taylor expansion of 0 in k 2.913 * [backup-simplify]: Simplify 0 into 0 2.913 * [backup-simplify]: Simplify 0 into 0 2.913 * [backup-simplify]: Simplify 0 into 0 2.914 * [backup-simplify]: Simplify 0 into 0 2.914 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.915 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.924 * [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 2.924 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.924 * [backup-simplify]: Simplify (+ 0 0) into 0 2.925 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.926 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.927 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.928 * [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 2.928 * [taylor]: Taking taylor expansion of 0 in k 2.928 * [backup-simplify]: Simplify 0 into 0 2.928 * [backup-simplify]: Simplify 0 into 0 2.929 * [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)))))) 2.929 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 2.929 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 2.929 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.929 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.929 * [taylor]: Taking taylor expansion of 1.0 in k 2.930 * [backup-simplify]: Simplify 1.0 into 1.0 2.930 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.930 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.930 * [taylor]: Taking taylor expansion of k in k 2.930 * [backup-simplify]: Simplify 0 into 0 2.930 * [backup-simplify]: Simplify 1 into 1 2.930 * [backup-simplify]: Simplify (/ 1 1) into 1 2.930 * [backup-simplify]: Simplify (sqrt 0) into 0 2.931 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.931 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.931 * [taylor]: Taking taylor expansion of 1.0 in k 2.931 * [backup-simplify]: Simplify 1.0 into 1.0 2.931 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.931 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.931 * [taylor]: Taking taylor expansion of k in k 2.931 * [backup-simplify]: Simplify 0 into 0 2.931 * [backup-simplify]: Simplify 1 into 1 2.931 * [backup-simplify]: Simplify (/ 1 1) into 1 2.931 * [backup-simplify]: Simplify (sqrt 0) into 0 2.932 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.933 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.933 * [backup-simplify]: Simplify 0 into 0 2.933 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.934 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.934 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.936 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.937 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.937 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.937 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.940 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.941 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.941 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.942 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 2.942 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 2.942 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.942 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.942 * [taylor]: Taking taylor expansion of 1.0 in k 2.942 * [backup-simplify]: Simplify 1.0 into 1.0 2.942 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.942 * [taylor]: Taking taylor expansion of k in k 2.942 * [backup-simplify]: Simplify 0 into 0 2.942 * [backup-simplify]: Simplify 1 into 1 2.942 * [backup-simplify]: Simplify (sqrt 0) into 0 2.943 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.943 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.943 * [taylor]: Taking taylor expansion of 1.0 in k 2.943 * [backup-simplify]: Simplify 1.0 into 1.0 2.943 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.943 * [taylor]: Taking taylor expansion of k in k 2.943 * [backup-simplify]: Simplify 0 into 0 2.943 * [backup-simplify]: Simplify 1 into 1 2.943 * [backup-simplify]: Simplify (sqrt 0) into 0 2.944 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.944 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.944 * [backup-simplify]: Simplify 0 into 0 2.945 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.945 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.947 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.948 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.948 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.950 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.952 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.952 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.953 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 2.953 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 2.953 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.953 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.953 * [taylor]: Taking taylor expansion of 1.0 in k 2.953 * [backup-simplify]: Simplify 1.0 into 1.0 2.953 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.953 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.953 * [taylor]: Taking taylor expansion of -1 in k 2.953 * [backup-simplify]: Simplify -1 into -1 2.953 * [taylor]: Taking taylor expansion of k in k 2.953 * [backup-simplify]: Simplify 0 into 0 2.953 * [backup-simplify]: Simplify 1 into 1 2.953 * [backup-simplify]: Simplify (/ -1 1) into -1 2.954 * [backup-simplify]: Simplify (sqrt 0) into 0 2.954 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.955 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.955 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.955 * [taylor]: Taking taylor expansion of 1.0 in k 2.955 * [backup-simplify]: Simplify 1.0 into 1.0 2.955 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.955 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.955 * [taylor]: Taking taylor expansion of -1 in k 2.955 * [backup-simplify]: Simplify -1 into -1 2.955 * [taylor]: Taking taylor expansion of k in k 2.955 * [backup-simplify]: Simplify 0 into 0 2.955 * [backup-simplify]: Simplify 1 into 1 2.955 * [backup-simplify]: Simplify (/ -1 1) into -1 2.955 * [backup-simplify]: Simplify (sqrt 0) into 0 2.956 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.956 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.956 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.957 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.958 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.960 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 2.960 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.961 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.963 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.965 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 2.965 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.966 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 2.966 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 2.967 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.967 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.967 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.967 * [taylor]: Taking taylor expansion of 2.0 in n 2.967 * [backup-simplify]: Simplify 2.0 into 2.0 2.967 * [taylor]: Taking taylor expansion of (* n PI) in n 2.967 * [taylor]: Taking taylor expansion of n in n 2.967 * [backup-simplify]: Simplify 0 into 0 2.967 * [backup-simplify]: Simplify 1 into 1 2.967 * [taylor]: Taking taylor expansion of PI in n 2.967 * [backup-simplify]: Simplify PI into PI 2.967 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.967 * [taylor]: Taking taylor expansion of 2.0 in n 2.967 * [backup-simplify]: Simplify 2.0 into 2.0 2.967 * [taylor]: Taking taylor expansion of (* n PI) in n 2.967 * [taylor]: Taking taylor expansion of n in n 2.967 * [backup-simplify]: Simplify 0 into 0 2.967 * [backup-simplify]: Simplify 1 into 1 2.967 * [taylor]: Taking taylor expansion of PI in n 2.967 * [backup-simplify]: Simplify PI into PI 2.967 * [backup-simplify]: Simplify (* 0 PI) into 0 2.967 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.967 * [backup-simplify]: Simplify 0 into 0 2.968 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.969 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.970 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.970 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.971 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.971 * [backup-simplify]: Simplify 0 into 0 2.972 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.972 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.972 * [backup-simplify]: Simplify 0 into 0 2.973 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.974 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.974 * [backup-simplify]: Simplify 0 into 0 2.974 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.975 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.975 * [backup-simplify]: Simplify 0 into 0 2.976 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.977 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.977 * [backup-simplify]: Simplify 0 into 0 2.978 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.979 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.979 * [backup-simplify]: Simplify 0 into 0 2.979 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.980 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.980 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.980 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.980 * [taylor]: Taking taylor expansion of 2.0 in n 2.980 * [backup-simplify]: Simplify 2.0 into 2.0 2.980 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.980 * [taylor]: Taking taylor expansion of PI in n 2.980 * [backup-simplify]: Simplify PI into PI 2.980 * [taylor]: Taking taylor expansion of n in n 2.980 * [backup-simplify]: Simplify 0 into 0 2.980 * [backup-simplify]: Simplify 1 into 1 2.980 * [backup-simplify]: Simplify (/ PI 1) into PI 2.980 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.980 * [taylor]: Taking taylor expansion of 2.0 in n 2.980 * [backup-simplify]: Simplify 2.0 into 2.0 2.980 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.980 * [taylor]: Taking taylor expansion of PI in n 2.980 * [backup-simplify]: Simplify PI into PI 2.980 * [taylor]: Taking taylor expansion of n in n 2.980 * [backup-simplify]: Simplify 0 into 0 2.980 * [backup-simplify]: Simplify 1 into 1 2.980 * [backup-simplify]: Simplify (/ PI 1) into PI 2.981 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.981 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.982 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.982 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.982 * [backup-simplify]: Simplify 0 into 0 2.983 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.983 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.983 * [backup-simplify]: Simplify 0 into 0 2.984 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.984 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.984 * [backup-simplify]: Simplify 0 into 0 2.985 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.986 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.986 * [backup-simplify]: Simplify 0 into 0 2.986 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.987 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.987 * [backup-simplify]: Simplify 0 into 0 2.988 * [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 2.989 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.989 * [backup-simplify]: Simplify 0 into 0 2.989 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.989 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.989 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.989 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.989 * [taylor]: Taking taylor expansion of -2.0 in n 2.989 * [backup-simplify]: Simplify -2.0 into -2.0 2.989 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.989 * [taylor]: Taking taylor expansion of PI in n 2.989 * [backup-simplify]: Simplify PI into PI 2.989 * [taylor]: Taking taylor expansion of n in n 2.989 * [backup-simplify]: Simplify 0 into 0 2.989 * [backup-simplify]: Simplify 1 into 1 2.990 * [backup-simplify]: Simplify (/ PI 1) into PI 2.990 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.990 * [taylor]: Taking taylor expansion of -2.0 in n 2.990 * [backup-simplify]: Simplify -2.0 into -2.0 2.990 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.990 * [taylor]: Taking taylor expansion of PI in n 2.990 * [backup-simplify]: Simplify PI into PI 2.990 * [taylor]: Taking taylor expansion of n in n 2.990 * [backup-simplify]: Simplify 0 into 0 2.990 * [backup-simplify]: Simplify 1 into 1 2.990 * [backup-simplify]: Simplify (/ PI 1) into PI 2.990 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.991 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.991 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.992 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.992 * [backup-simplify]: Simplify 0 into 0 2.992 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.993 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.993 * [backup-simplify]: Simplify 0 into 0 2.993 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.994 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.994 * [backup-simplify]: Simplify 0 into 0 2.995 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.995 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.995 * [backup-simplify]: Simplify 0 into 0 2.996 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.997 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.997 * [backup-simplify]: Simplify 0 into 0 2.997 * [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 2.998 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.998 * [backup-simplify]: Simplify 0 into 0 2.998 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.999 * * * [progress]: simplifying candidates 3.002 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (+ (+ (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))) 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h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) 1)) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ 1 (sqrt 2))) (pow (* (* h0 h4) h3) (/ 1 1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (- h2 h1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (- h2 h1) 1)) (pow (* (* h0 h4) h3) 1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* h0 h4) (/ (/ (- h2 h1) h0) 2)) (pow h3 (/ (/ (- h2 h1) h0) 2)) (log (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (exp (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (- (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) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h9 h1) (- (+ (* h9 (pow h1 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- (* h9 (/ 1 (pow h1 3)))))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- h9))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) 3.018 * * [simplify]: iteration 0 : 859 enodes (cost 1848 ) 3.031 * * [simplify]: iteration 1 : 3384 enodes (cost 1776 ) 3.079 * * [simplify]: iteration 2 : 5001 enodes (cost 1766 ) 3.088 * * * [progress]: adding candidates to table 3.804 * * [progress]: iteration 4 / 4 3.804 * * * [progress]: picking best candidate 3.825 * * * * [pick]: Picked # 3.825 * * * [progress]: localizing error 3.846 * * * [progress]: generating rewritten candidates 3.846 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.874 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 2) 3.912 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2 1) 3.952 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 4.010 * * * [progress]: generating series expansions 4.010 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 4.011 * [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))) 4.011 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 4.011 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 4.011 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.011 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.011 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 4.011 * [taylor]: Taking taylor expansion of 0.25 in k 4.011 * [backup-simplify]: Simplify 0.25 into 0.25 4.011 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.011 * [taylor]: Taking taylor expansion of 1.0 in k 4.011 * [backup-simplify]: Simplify 1.0 into 1.0 4.011 * [taylor]: Taking taylor expansion of k in k 4.011 * [backup-simplify]: Simplify 0 into 0 4.011 * [backup-simplify]: Simplify 1 into 1 4.011 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.011 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.011 * [taylor]: Taking taylor expansion of 2.0 in k 4.011 * [backup-simplify]: Simplify 2.0 into 2.0 4.011 * [taylor]: Taking taylor expansion of (* n PI) in k 4.011 * [taylor]: Taking taylor expansion of n in k 4.011 * [backup-simplify]: Simplify n into n 4.011 * [taylor]: Taking taylor expansion of PI in k 4.011 * [backup-simplify]: Simplify PI into PI 4.011 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.011 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.012 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.012 * [backup-simplify]: Simplify (- 0) into 0 4.012 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.012 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 4.013 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 4.013 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 4.013 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.013 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.013 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.013 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.013 * [taylor]: Taking taylor expansion of 0.25 in n 4.013 * [backup-simplify]: Simplify 0.25 into 0.25 4.013 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.013 * [taylor]: Taking taylor expansion of 1.0 in n 4.013 * [backup-simplify]: Simplify 1.0 into 1.0 4.013 * [taylor]: Taking taylor expansion of k in n 4.013 * [backup-simplify]: Simplify k into k 4.013 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.013 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.013 * [taylor]: Taking taylor expansion of 2.0 in n 4.013 * [backup-simplify]: Simplify 2.0 into 2.0 4.013 * [taylor]: Taking taylor expansion of (* n PI) in n 4.013 * [taylor]: Taking taylor expansion of n in n 4.013 * [backup-simplify]: Simplify 0 into 0 4.013 * [backup-simplify]: Simplify 1 into 1 4.013 * [taylor]: Taking taylor expansion of PI in n 4.013 * [backup-simplify]: Simplify PI into PI 4.013 * [backup-simplify]: Simplify (* 0 PI) into 0 4.014 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.014 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.015 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.016 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.016 * [backup-simplify]: Simplify (- k) into (- k) 4.016 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.016 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.017 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.018 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.018 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.018 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.018 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.018 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.018 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.018 * [taylor]: Taking taylor expansion of 0.25 in n 4.018 * [backup-simplify]: Simplify 0.25 into 0.25 4.019 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.019 * [taylor]: Taking taylor expansion of 1.0 in n 4.019 * [backup-simplify]: Simplify 1.0 into 1.0 4.019 * [taylor]: Taking taylor expansion of k in n 4.019 * [backup-simplify]: Simplify k into k 4.019 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.019 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.019 * [taylor]: Taking taylor expansion of 2.0 in n 4.019 * [backup-simplify]: Simplify 2.0 into 2.0 4.019 * [taylor]: Taking taylor expansion of (* n PI) in n 4.019 * [taylor]: Taking taylor expansion of n in n 4.019 * [backup-simplify]: Simplify 0 into 0 4.019 * [backup-simplify]: Simplify 1 into 1 4.019 * [taylor]: Taking taylor expansion of PI in n 4.019 * [backup-simplify]: Simplify PI into PI 4.019 * [backup-simplify]: Simplify (* 0 PI) into 0 4.019 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.020 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.021 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.022 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.022 * [backup-simplify]: Simplify (- k) into (- k) 4.022 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.022 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.023 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.024 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.024 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.025 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.025 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.025 * [taylor]: Taking taylor expansion of 0.25 in k 4.025 * [backup-simplify]: Simplify 0.25 into 0.25 4.025 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.025 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.025 * [taylor]: Taking taylor expansion of 1.0 in k 4.025 * [backup-simplify]: Simplify 1.0 into 1.0 4.025 * [taylor]: Taking taylor expansion of k in k 4.025 * [backup-simplify]: Simplify 0 into 0 4.025 * [backup-simplify]: Simplify 1 into 1 4.025 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.025 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.025 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.025 * [taylor]: Taking taylor expansion of 2.0 in k 4.025 * [backup-simplify]: Simplify 2.0 into 2.0 4.025 * [taylor]: Taking taylor expansion of PI in k 4.025 * [backup-simplify]: Simplify PI into PI 4.025 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.026 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.026 * [taylor]: Taking taylor expansion of (log n) in k 4.026 * [taylor]: Taking taylor expansion of n in k 4.026 * [backup-simplify]: Simplify n into n 4.026 * [backup-simplify]: Simplify (log n) into (log n) 4.026 * [backup-simplify]: Simplify (- 0) into 0 4.026 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.027 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.028 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.028 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 4.029 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.030 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.030 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.031 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.032 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.032 * [backup-simplify]: Simplify (- 0) into 0 4.032 * [backup-simplify]: Simplify (+ 0 0) into 0 4.033 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 4.033 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.034 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.035 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.035 * [taylor]: Taking taylor expansion of 0 in k 4.035 * [backup-simplify]: Simplify 0 into 0 4.036 * [backup-simplify]: Simplify 0 into 0 4.036 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.037 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.037 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.038 * [backup-simplify]: Simplify (+ 0 0) into 0 4.038 * [backup-simplify]: Simplify (- 1) into -1 4.038 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.039 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.041 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 4.043 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 4.044 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 4.045 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.046 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.047 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.048 * [backup-simplify]: Simplify (- 0) into 0 4.048 * [backup-simplify]: Simplify (+ 0 0) into 0 4.048 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.049 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.050 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.051 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.051 * [taylor]: Taking taylor expansion of 0 in k 4.051 * [backup-simplify]: Simplify 0 into 0 4.051 * [backup-simplify]: Simplify 0 into 0 4.051 * [backup-simplify]: Simplify 0 into 0 4.052 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.054 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.055 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.055 * [backup-simplify]: Simplify (+ 0 0) into 0 4.055 * [backup-simplify]: Simplify (- 0) into 0 4.055 * [backup-simplify]: Simplify (+ 0 0) into 0 4.057 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.058 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.060 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 4.063 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 4.069 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 4.070 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 4.070 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 4.070 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 4.070 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.070 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.070 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 4.070 * [taylor]: Taking taylor expansion of 0.25 in k 4.070 * [backup-simplify]: Simplify 0.25 into 0.25 4.070 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.070 * [taylor]: Taking taylor expansion of 1.0 in k 4.070 * [backup-simplify]: Simplify 1.0 into 1.0 4.070 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.070 * [taylor]: Taking taylor expansion of k in k 4.070 * [backup-simplify]: Simplify 0 into 0 4.070 * [backup-simplify]: Simplify 1 into 1 4.070 * [backup-simplify]: Simplify (/ 1 1) into 1 4.070 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.070 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.070 * [taylor]: Taking taylor expansion of 2.0 in k 4.070 * [backup-simplify]: Simplify 2.0 into 2.0 4.070 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.070 * [taylor]: Taking taylor expansion of PI in k 4.070 * [backup-simplify]: Simplify PI into PI 4.070 * [taylor]: Taking taylor expansion of n in k 4.070 * [backup-simplify]: Simplify n into n 4.070 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.070 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.070 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.071 * [backup-simplify]: Simplify (- 1) into -1 4.071 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.071 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 4.071 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 4.071 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.071 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.071 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.071 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.071 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.072 * [taylor]: Taking taylor expansion of 0.25 in n 4.072 * [backup-simplify]: Simplify 0.25 into 0.25 4.072 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.072 * [taylor]: Taking taylor expansion of 1.0 in n 4.072 * [backup-simplify]: Simplify 1.0 into 1.0 4.072 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.072 * [taylor]: Taking taylor expansion of k in n 4.072 * [backup-simplify]: Simplify k into k 4.072 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.072 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.072 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.072 * [taylor]: Taking taylor expansion of 2.0 in n 4.072 * [backup-simplify]: Simplify 2.0 into 2.0 4.072 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.072 * [taylor]: Taking taylor expansion of PI in n 4.072 * [backup-simplify]: Simplify PI into PI 4.072 * [taylor]: Taking taylor expansion of n in n 4.072 * [backup-simplify]: Simplify 0 into 0 4.072 * [backup-simplify]: Simplify 1 into 1 4.072 * [backup-simplify]: Simplify (/ PI 1) into PI 4.072 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.073 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.073 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.073 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.073 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.074 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.075 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.075 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.075 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.075 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.075 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.076 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.076 * [taylor]: Taking taylor expansion of 0.25 in n 4.076 * [backup-simplify]: Simplify 0.25 into 0.25 4.076 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.076 * [taylor]: Taking taylor expansion of 1.0 in n 4.076 * [backup-simplify]: Simplify 1.0 into 1.0 4.076 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.076 * [taylor]: Taking taylor expansion of k in n 4.076 * [backup-simplify]: Simplify k into k 4.076 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.076 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.076 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.076 * [taylor]: Taking taylor expansion of 2.0 in n 4.076 * [backup-simplify]: Simplify 2.0 into 2.0 4.076 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.076 * [taylor]: Taking taylor expansion of PI in n 4.076 * [backup-simplify]: Simplify PI into PI 4.076 * [taylor]: Taking taylor expansion of n in n 4.076 * [backup-simplify]: Simplify 0 into 0 4.076 * [backup-simplify]: Simplify 1 into 1 4.076 * [backup-simplify]: Simplify (/ PI 1) into PI 4.076 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.077 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.077 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.077 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.077 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.078 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.079 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.079 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.080 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.080 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.080 * [taylor]: Taking taylor expansion of 0.25 in k 4.080 * [backup-simplify]: Simplify 0.25 into 0.25 4.080 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.080 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.080 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.080 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.080 * [taylor]: Taking taylor expansion of 2.0 in k 4.080 * [backup-simplify]: Simplify 2.0 into 2.0 4.080 * [taylor]: Taking taylor expansion of PI in k 4.080 * [backup-simplify]: Simplify PI into PI 4.080 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.088 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.088 * [taylor]: Taking taylor expansion of (log n) in k 4.088 * [taylor]: Taking taylor expansion of n in k 4.088 * [backup-simplify]: Simplify n into n 4.088 * [backup-simplify]: Simplify (log n) into (log n) 4.088 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.088 * [taylor]: Taking taylor expansion of 1.0 in k 4.088 * [backup-simplify]: Simplify 1.0 into 1.0 4.088 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.088 * [taylor]: Taking taylor expansion of k in k 4.088 * [backup-simplify]: Simplify 0 into 0 4.088 * [backup-simplify]: Simplify 1 into 1 4.088 * [backup-simplify]: Simplify (/ 1 1) into 1 4.088 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.089 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.089 * [backup-simplify]: Simplify (- 1) into -1 4.089 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.090 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.091 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 4.092 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.092 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.093 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.093 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.094 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.094 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.095 * [backup-simplify]: Simplify (- 0) into 0 4.095 * [backup-simplify]: Simplify (+ 0 0) into 0 4.095 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.096 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.097 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.098 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.098 * [taylor]: Taking taylor expansion of 0 in k 4.098 * [backup-simplify]: Simplify 0 into 0 4.098 * [backup-simplify]: Simplify 0 into 0 4.098 * [backup-simplify]: Simplify 0 into 0 4.098 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.099 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.101 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.101 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.101 * [backup-simplify]: Simplify (- 0) into 0 4.101 * [backup-simplify]: Simplify (+ 0 0) into 0 4.102 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.103 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.103 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.105 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.105 * [taylor]: Taking taylor expansion of 0 in k 4.105 * [backup-simplify]: Simplify 0 into 0 4.105 * [backup-simplify]: Simplify 0 into 0 4.105 * [backup-simplify]: Simplify 0 into 0 4.105 * [backup-simplify]: Simplify 0 into 0 4.106 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.106 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.109 * [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 4.109 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.109 * [backup-simplify]: Simplify (- 0) into 0 4.110 * [backup-simplify]: Simplify (+ 0 0) into 0 4.110 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.112 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.114 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.114 * [taylor]: Taking taylor expansion of 0 in k 4.114 * [backup-simplify]: Simplify 0 into 0 4.114 * [backup-simplify]: Simplify 0 into 0 4.115 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.115 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 4.115 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 4.115 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 4.115 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.115 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.115 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 4.115 * [taylor]: Taking taylor expansion of 0.25 in k 4.115 * [backup-simplify]: Simplify 0.25 into 0.25 4.115 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.115 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.115 * [taylor]: Taking taylor expansion of k in k 4.115 * [backup-simplify]: Simplify 0 into 0 4.115 * [backup-simplify]: Simplify 1 into 1 4.116 * [backup-simplify]: Simplify (/ 1 1) into 1 4.116 * [taylor]: Taking taylor expansion of 1.0 in k 4.116 * [backup-simplify]: Simplify 1.0 into 1.0 4.116 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.116 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.116 * [taylor]: Taking taylor expansion of -2.0 in k 4.116 * [backup-simplify]: Simplify -2.0 into -2.0 4.116 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.116 * [taylor]: Taking taylor expansion of PI in k 4.116 * [backup-simplify]: Simplify PI into PI 4.116 * [taylor]: Taking taylor expansion of n in k 4.116 * [backup-simplify]: Simplify n into n 4.116 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.116 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.116 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.116 * [backup-simplify]: Simplify (+ 1 0) into 1 4.117 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 4.117 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 4.117 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.117 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.117 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.117 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.117 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.117 * [taylor]: Taking taylor expansion of 0.25 in n 4.117 * [backup-simplify]: Simplify 0.25 into 0.25 4.117 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.117 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.117 * [taylor]: Taking taylor expansion of k in n 4.117 * [backup-simplify]: Simplify k into k 4.117 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.117 * [taylor]: Taking taylor expansion of 1.0 in n 4.117 * [backup-simplify]: Simplify 1.0 into 1.0 4.117 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.117 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.117 * [taylor]: Taking taylor expansion of -2.0 in n 4.117 * [backup-simplify]: Simplify -2.0 into -2.0 4.117 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.117 * [taylor]: Taking taylor expansion of PI in n 4.117 * [backup-simplify]: Simplify PI into PI 4.117 * [taylor]: Taking taylor expansion of n in n 4.117 * [backup-simplify]: Simplify 0 into 0 4.117 * [backup-simplify]: Simplify 1 into 1 4.117 * [backup-simplify]: Simplify (/ PI 1) into PI 4.118 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.118 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.118 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.118 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.119 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.120 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.121 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.121 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.121 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.121 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.121 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.121 * [taylor]: Taking taylor expansion of 0.25 in n 4.121 * [backup-simplify]: Simplify 0.25 into 0.25 4.121 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.121 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.121 * [taylor]: Taking taylor expansion of k in n 4.121 * [backup-simplify]: Simplify k into k 4.121 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.121 * [taylor]: Taking taylor expansion of 1.0 in n 4.121 * [backup-simplify]: Simplify 1.0 into 1.0 4.121 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.121 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.121 * [taylor]: Taking taylor expansion of -2.0 in n 4.121 * [backup-simplify]: Simplify -2.0 into -2.0 4.121 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.121 * [taylor]: Taking taylor expansion of PI in n 4.121 * [backup-simplify]: Simplify PI into PI 4.121 * [taylor]: Taking taylor expansion of n in n 4.121 * [backup-simplify]: Simplify 0 into 0 4.121 * [backup-simplify]: Simplify 1 into 1 4.121 * [backup-simplify]: Simplify (/ PI 1) into PI 4.122 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.122 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.122 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.123 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.124 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.124 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.125 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.125 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.125 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.125 * [taylor]: Taking taylor expansion of 0.25 in k 4.125 * [backup-simplify]: Simplify 0.25 into 0.25 4.125 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.125 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.125 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.125 * [taylor]: Taking taylor expansion of k in k 4.125 * [backup-simplify]: Simplify 0 into 0 4.125 * [backup-simplify]: Simplify 1 into 1 4.126 * [backup-simplify]: Simplify (/ 1 1) into 1 4.126 * [taylor]: Taking taylor expansion of 1.0 in k 4.126 * [backup-simplify]: Simplify 1.0 into 1.0 4.126 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.126 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.126 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.126 * [taylor]: Taking taylor expansion of -2.0 in k 4.126 * [backup-simplify]: Simplify -2.0 into -2.0 4.126 * [taylor]: Taking taylor expansion of PI in k 4.126 * [backup-simplify]: Simplify PI into PI 4.126 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.127 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.127 * [taylor]: Taking taylor expansion of (log n) in k 4.127 * [taylor]: Taking taylor expansion of n in k 4.127 * [backup-simplify]: Simplify n into n 4.127 * [backup-simplify]: Simplify (log n) into (log n) 4.127 * [backup-simplify]: Simplify (+ 1 0) into 1 4.127 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.128 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.128 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.129 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 4.130 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.130 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.131 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.132 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.133 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.133 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.133 * [backup-simplify]: Simplify (+ 0 0) into 0 4.133 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.134 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.135 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.136 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.136 * [taylor]: Taking taylor expansion of 0 in k 4.136 * [backup-simplify]: Simplify 0 into 0 4.136 * [backup-simplify]: Simplify 0 into 0 4.136 * [backup-simplify]: Simplify 0 into 0 4.137 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.137 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.139 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 4.139 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.139 * [backup-simplify]: Simplify (+ 0 0) into 0 4.140 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.141 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.141 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.143 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.143 * [taylor]: Taking taylor expansion of 0 in k 4.143 * [backup-simplify]: Simplify 0 into 0 4.143 * [backup-simplify]: Simplify 0 into 0 4.143 * [backup-simplify]: Simplify 0 into 0 4.143 * [backup-simplify]: Simplify 0 into 0 4.144 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.144 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.147 * [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 4.147 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.148 * [backup-simplify]: Simplify (+ 0 0) into 0 4.148 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.149 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.150 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.152 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.152 * [taylor]: Taking taylor expansion of 0 in k 4.152 * [backup-simplify]: Simplify 0 into 0 4.152 * [backup-simplify]: Simplify 0 into 0 4.153 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.153 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 2) 4.153 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) into (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 4.153 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in (n k) around 0 4.153 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in k 4.153 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.153 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.153 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in k 4.153 * [taylor]: Taking taylor expansion of 0.125 in k 4.153 * [backup-simplify]: Simplify 0.125 into 0.125 4.153 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.153 * [taylor]: Taking taylor expansion of 1.0 in k 4.153 * [backup-simplify]: Simplify 1.0 into 1.0 4.153 * [taylor]: Taking taylor expansion of k in k 4.153 * [backup-simplify]: Simplify 0 into 0 4.153 * [backup-simplify]: Simplify 1 into 1 4.153 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.153 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.153 * [taylor]: Taking taylor expansion of 2.0 in k 4.153 * [backup-simplify]: Simplify 2.0 into 2.0 4.154 * [taylor]: Taking taylor expansion of (* n PI) in k 4.154 * [taylor]: Taking taylor expansion of n in k 4.154 * [backup-simplify]: Simplify n into n 4.154 * [taylor]: Taking taylor expansion of PI in k 4.154 * [backup-simplify]: Simplify PI into PI 4.154 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.154 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.154 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.154 * [backup-simplify]: Simplify (- 0) into 0 4.154 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.154 * [backup-simplify]: Simplify (* 0.125 1.0) into 0.125 4.155 * [backup-simplify]: Simplify (* 0.125 (log (* 2.0 (* n PI)))) into (* 0.125 (log (* 2.0 (* n PI)))) 4.155 * [backup-simplify]: Simplify (exp (* 0.125 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.125) 4.155 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.155 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.155 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.155 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.155 * [taylor]: Taking taylor expansion of 0.125 in n 4.155 * [backup-simplify]: Simplify 0.125 into 0.125 4.155 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.155 * [taylor]: Taking taylor expansion of 1.0 in n 4.155 * [backup-simplify]: Simplify 1.0 into 1.0 4.155 * [taylor]: Taking taylor expansion of k in n 4.155 * [backup-simplify]: Simplify k into k 4.155 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.155 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.155 * [taylor]: Taking taylor expansion of 2.0 in n 4.155 * [backup-simplify]: Simplify 2.0 into 2.0 4.155 * [taylor]: Taking taylor expansion of (* n PI) in n 4.155 * [taylor]: Taking taylor expansion of n in n 4.155 * [backup-simplify]: Simplify 0 into 0 4.155 * [backup-simplify]: Simplify 1 into 1 4.155 * [taylor]: Taking taylor expansion of PI in n 4.155 * [backup-simplify]: Simplify PI into PI 4.155 * [backup-simplify]: Simplify (* 0 PI) into 0 4.155 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.156 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.157 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.158 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.158 * [backup-simplify]: Simplify (- k) into (- k) 4.158 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.158 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.159 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.159 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.160 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.160 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.160 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.160 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.160 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.160 * [taylor]: Taking taylor expansion of 0.125 in n 4.160 * [backup-simplify]: Simplify 0.125 into 0.125 4.160 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.160 * [taylor]: Taking taylor expansion of 1.0 in n 4.160 * [backup-simplify]: Simplify 1.0 into 1.0 4.160 * [taylor]: Taking taylor expansion of k in n 4.160 * [backup-simplify]: Simplify k into k 4.160 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.160 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.160 * [taylor]: Taking taylor expansion of 2.0 in n 4.160 * [backup-simplify]: Simplify 2.0 into 2.0 4.160 * [taylor]: Taking taylor expansion of (* n PI) in n 4.160 * [taylor]: Taking taylor expansion of n in n 4.160 * [backup-simplify]: Simplify 0 into 0 4.160 * [backup-simplify]: Simplify 1 into 1 4.160 * [taylor]: Taking taylor expansion of PI in n 4.161 * [backup-simplify]: Simplify PI into PI 4.161 * [backup-simplify]: Simplify (* 0 PI) into 0 4.161 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.162 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.163 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.163 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.163 * [backup-simplify]: Simplify (- k) into (- k) 4.163 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.163 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.164 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.165 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.166 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.166 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.166 * [taylor]: Taking taylor expansion of (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.166 * [taylor]: Taking taylor expansion of 0.125 in k 4.166 * [backup-simplify]: Simplify 0.125 into 0.125 4.166 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.166 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.166 * [taylor]: Taking taylor expansion of 1.0 in k 4.166 * [backup-simplify]: Simplify 1.0 into 1.0 4.166 * [taylor]: Taking taylor expansion of k in k 4.166 * [backup-simplify]: Simplify 0 into 0 4.166 * [backup-simplify]: Simplify 1 into 1 4.166 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.166 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.166 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.166 * [taylor]: Taking taylor expansion of 2.0 in k 4.166 * [backup-simplify]: Simplify 2.0 into 2.0 4.166 * [taylor]: Taking taylor expansion of PI in k 4.166 * [backup-simplify]: Simplify PI into PI 4.166 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.167 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.167 * [taylor]: Taking taylor expansion of (log n) in k 4.167 * [taylor]: Taking taylor expansion of n in k 4.167 * [backup-simplify]: Simplify n into n 4.167 * [backup-simplify]: Simplify (log n) into (log n) 4.167 * [backup-simplify]: Simplify (- 0) into 0 4.168 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.168 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.169 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.169 * [backup-simplify]: Simplify (* 0.125 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.125 (+ (log (* 2.0 PI)) (log n))) 4.170 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.171 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.171 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.172 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.173 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.173 * [backup-simplify]: Simplify (- 0) into 0 4.173 * [backup-simplify]: Simplify (+ 0 0) into 0 4.174 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 k))) into 0 4.174 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.175 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.176 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.176 * [taylor]: Taking taylor expansion of 0 in k 4.176 * [backup-simplify]: Simplify 0 into 0 4.176 * [backup-simplify]: Simplify 0 into 0 4.177 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.183 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.184 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.184 * [backup-simplify]: Simplify (+ 0 0) into 0 4.185 * [backup-simplify]: Simplify (- 1) into -1 4.185 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.186 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.187 * [backup-simplify]: Simplify (+ (* 0.125 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 4.189 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 1) 1)))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.191 * [backup-simplify]: Simplify (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.191 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.192 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.194 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.194 * [backup-simplify]: Simplify (- 0) into 0 4.194 * [backup-simplify]: Simplify (+ 0 0) into 0 4.195 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.195 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.197 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.198 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.198 * [taylor]: Taking taylor expansion of 0 in k 4.198 * [backup-simplify]: Simplify 0 into 0 4.198 * [backup-simplify]: Simplify 0 into 0 4.198 * [backup-simplify]: Simplify 0 into 0 4.199 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.200 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.201 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.202 * [backup-simplify]: Simplify (+ 0 0) into 0 4.202 * [backup-simplify]: Simplify (- 0) into 0 4.202 * [backup-simplify]: Simplify (+ 0 0) into 0 4.203 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.205 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.207 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.210 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.216 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) (* k 1)) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.0078125 (* (pow k 2) (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (* 0.015625 (* (pow k 2) (* (log (* 2.0 PI)) (* (log n) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))))))) (+ (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log (* 2.0 PI))))))) 4.216 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (/ (- 1.0 (/ 1 k)) 2.0) 2) 2)) into (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 4.216 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in (n k) around 0 4.216 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in k 4.216 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.216 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.216 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in k 4.216 * [taylor]: Taking taylor expansion of 0.125 in k 4.216 * [backup-simplify]: Simplify 0.125 into 0.125 4.216 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.216 * [taylor]: Taking taylor expansion of 1.0 in k 4.216 * [backup-simplify]: Simplify 1.0 into 1.0 4.216 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.216 * [taylor]: Taking taylor expansion of k in k 4.216 * [backup-simplify]: Simplify 0 into 0 4.217 * [backup-simplify]: Simplify 1 into 1 4.217 * [backup-simplify]: Simplify (/ 1 1) into 1 4.217 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.217 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.217 * [taylor]: Taking taylor expansion of 2.0 in k 4.217 * [backup-simplify]: Simplify 2.0 into 2.0 4.217 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.217 * [taylor]: Taking taylor expansion of PI in k 4.217 * [backup-simplify]: Simplify PI into PI 4.217 * [taylor]: Taking taylor expansion of n in k 4.217 * [backup-simplify]: Simplify n into n 4.217 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.217 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.217 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.217 * [backup-simplify]: Simplify (- 1) into -1 4.218 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.218 * [backup-simplify]: Simplify (* 0.125 -1) into -0.125 4.218 * [backup-simplify]: Simplify (* -0.125 (log (* 2.0 (/ PI n)))) into (* -0.125 (log (* 2.0 (/ PI n)))) 4.218 * [backup-simplify]: Simplify (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.125 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.218 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.218 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.218 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.218 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.218 * [taylor]: Taking taylor expansion of 0.125 in n 4.218 * [backup-simplify]: Simplify 0.125 into 0.125 4.218 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.218 * [taylor]: Taking taylor expansion of 1.0 in n 4.218 * [backup-simplify]: Simplify 1.0 into 1.0 4.218 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.218 * [taylor]: Taking taylor expansion of k in n 4.218 * [backup-simplify]: Simplify k into k 4.218 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.218 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.218 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.218 * [taylor]: Taking taylor expansion of 2.0 in n 4.218 * [backup-simplify]: Simplify 2.0 into 2.0 4.218 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.218 * [taylor]: Taking taylor expansion of PI in n 4.218 * [backup-simplify]: Simplify PI into PI 4.218 * [taylor]: Taking taylor expansion of n in n 4.218 * [backup-simplify]: Simplify 0 into 0 4.218 * [backup-simplify]: Simplify 1 into 1 4.219 * [backup-simplify]: Simplify (/ PI 1) into PI 4.219 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.220 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.220 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.220 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.220 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.221 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.221 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.222 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.222 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.222 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.222 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.222 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.222 * [taylor]: Taking taylor expansion of 0.125 in n 4.222 * [backup-simplify]: Simplify 0.125 into 0.125 4.222 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.222 * [taylor]: Taking taylor expansion of 1.0 in n 4.222 * [backup-simplify]: Simplify 1.0 into 1.0 4.222 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.222 * [taylor]: Taking taylor expansion of k in n 4.222 * [backup-simplify]: Simplify k into k 4.222 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.222 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.222 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.222 * [taylor]: Taking taylor expansion of 2.0 in n 4.222 * [backup-simplify]: Simplify 2.0 into 2.0 4.222 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.222 * [taylor]: Taking taylor expansion of PI in n 4.222 * [backup-simplify]: Simplify PI into PI 4.222 * [taylor]: Taking taylor expansion of n in n 4.222 * [backup-simplify]: Simplify 0 into 0 4.222 * [backup-simplify]: Simplify 1 into 1 4.223 * [backup-simplify]: Simplify (/ PI 1) into PI 4.223 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.224 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.224 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.224 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.224 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.225 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.225 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.226 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.226 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.226 * [taylor]: Taking taylor expansion of (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.226 * [taylor]: Taking taylor expansion of 0.125 in k 4.226 * [backup-simplify]: Simplify 0.125 into 0.125 4.226 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.226 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.226 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.226 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.226 * [taylor]: Taking taylor expansion of 2.0 in k 4.226 * [backup-simplify]: Simplify 2.0 into 2.0 4.226 * [taylor]: Taking taylor expansion of PI in k 4.226 * [backup-simplify]: Simplify PI into PI 4.227 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.227 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.227 * [taylor]: Taking taylor expansion of (log n) in k 4.227 * [taylor]: Taking taylor expansion of n in k 4.227 * [backup-simplify]: Simplify n into n 4.227 * [backup-simplify]: Simplify (log n) into (log n) 4.227 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.227 * [taylor]: Taking taylor expansion of 1.0 in k 4.227 * [backup-simplify]: Simplify 1.0 into 1.0 4.227 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.227 * [taylor]: Taking taylor expansion of k in k 4.227 * [backup-simplify]: Simplify 0 into 0 4.227 * [backup-simplify]: Simplify 1 into 1 4.228 * [backup-simplify]: Simplify (/ 1 1) into 1 4.228 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.228 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.229 * [backup-simplify]: Simplify (- 1) into -1 4.229 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.229 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.230 * [backup-simplify]: Simplify (* 0.125 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.125 (- (log (* 2.0 PI)) (log n))) 4.231 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.232 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.232 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.233 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.233 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.234 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.234 * [backup-simplify]: Simplify (- 0) into 0 4.234 * [backup-simplify]: Simplify (+ 0 0) into 0 4.235 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.235 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.236 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.237 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.237 * [taylor]: Taking taylor expansion of 0 in k 4.237 * [backup-simplify]: Simplify 0 into 0 4.237 * [backup-simplify]: Simplify 0 into 0 4.237 * [backup-simplify]: Simplify 0 into 0 4.238 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.239 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.240 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.240 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.240 * [backup-simplify]: Simplify (- 0) into 0 4.241 * [backup-simplify]: Simplify (+ 0 0) into 0 4.241 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.242 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.243 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.244 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.244 * [taylor]: Taking taylor expansion of 0 in k 4.244 * [backup-simplify]: Simplify 0 into 0 4.244 * [backup-simplify]: Simplify 0 into 0 4.244 * [backup-simplify]: Simplify 0 into 0 4.244 * [backup-simplify]: Simplify 0 into 0 4.245 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.246 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.249 * [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 4.249 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.249 * [backup-simplify]: Simplify (- 0) into 0 4.250 * [backup-simplify]: Simplify (+ 0 0) into 0 4.250 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.251 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.253 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.254 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.254 * [taylor]: Taking taylor expansion of 0 in k 4.254 * [backup-simplify]: Simplify 0 into 0 4.254 * [backup-simplify]: Simplify 0 into 0 4.255 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.255 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2) 2)) into (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 4.255 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in (n k) around 0 4.255 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in k 4.255 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.256 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.256 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in k 4.256 * [taylor]: Taking taylor expansion of 0.125 in k 4.256 * [backup-simplify]: Simplify 0.125 into 0.125 4.256 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.256 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.256 * [taylor]: Taking taylor expansion of k in k 4.256 * [backup-simplify]: Simplify 0 into 0 4.256 * [backup-simplify]: Simplify 1 into 1 4.256 * [backup-simplify]: Simplify (/ 1 1) into 1 4.256 * [taylor]: Taking taylor expansion of 1.0 in k 4.256 * [backup-simplify]: Simplify 1.0 into 1.0 4.256 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.256 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.256 * [taylor]: Taking taylor expansion of -2.0 in k 4.256 * [backup-simplify]: Simplify -2.0 into -2.0 4.256 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.256 * [taylor]: Taking taylor expansion of PI in k 4.256 * [backup-simplify]: Simplify PI into PI 4.256 * [taylor]: Taking taylor expansion of n in k 4.256 * [backup-simplify]: Simplify n into n 4.256 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.256 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.256 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.256 * [backup-simplify]: Simplify (+ 1 0) into 1 4.257 * [backup-simplify]: Simplify (* 0.125 1) into 0.125 4.257 * [backup-simplify]: Simplify (* 0.125 (log (* -2.0 (/ PI n)))) into (* 0.125 (log (* -2.0 (/ PI n)))) 4.257 * [backup-simplify]: Simplify (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.257 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.257 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.257 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.257 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.257 * [taylor]: Taking taylor expansion of 0.125 in n 4.257 * [backup-simplify]: Simplify 0.125 into 0.125 4.257 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.257 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.257 * [taylor]: Taking taylor expansion of k in n 4.257 * [backup-simplify]: Simplify k into k 4.257 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.257 * [taylor]: Taking taylor expansion of 1.0 in n 4.257 * [backup-simplify]: Simplify 1.0 into 1.0 4.257 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.257 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.257 * [taylor]: Taking taylor expansion of -2.0 in n 4.257 * [backup-simplify]: Simplify -2.0 into -2.0 4.257 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.257 * [taylor]: Taking taylor expansion of PI in n 4.257 * [backup-simplify]: Simplify PI into PI 4.257 * [taylor]: Taking taylor expansion of n in n 4.257 * [backup-simplify]: Simplify 0 into 0 4.257 * [backup-simplify]: Simplify 1 into 1 4.258 * [backup-simplify]: Simplify (/ PI 1) into PI 4.258 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.259 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.259 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.259 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.260 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.260 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.261 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.261 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.261 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.261 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.261 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.261 * [taylor]: Taking taylor expansion of 0.125 in n 4.261 * [backup-simplify]: Simplify 0.125 into 0.125 4.261 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.261 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.261 * [taylor]: Taking taylor expansion of k in n 4.261 * [backup-simplify]: Simplify k into k 4.261 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.261 * [taylor]: Taking taylor expansion of 1.0 in n 4.261 * [backup-simplify]: Simplify 1.0 into 1.0 4.261 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.261 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.261 * [taylor]: Taking taylor expansion of -2.0 in n 4.261 * [backup-simplify]: Simplify -2.0 into -2.0 4.261 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.261 * [taylor]: Taking taylor expansion of PI in n 4.261 * [backup-simplify]: Simplify PI into PI 4.261 * [taylor]: Taking taylor expansion of n in n 4.261 * [backup-simplify]: Simplify 0 into 0 4.261 * [backup-simplify]: Simplify 1 into 1 4.262 * [backup-simplify]: Simplify (/ PI 1) into PI 4.262 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.263 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.263 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.263 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.263 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.264 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.265 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.265 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.265 * [taylor]: Taking taylor expansion of (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.265 * [taylor]: Taking taylor expansion of 0.125 in k 4.265 * [backup-simplify]: Simplify 0.125 into 0.125 4.265 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.265 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.265 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.265 * [taylor]: Taking taylor expansion of k in k 4.265 * [backup-simplify]: Simplify 0 into 0 4.265 * [backup-simplify]: Simplify 1 into 1 4.265 * [backup-simplify]: Simplify (/ 1 1) into 1 4.265 * [taylor]: Taking taylor expansion of 1.0 in k 4.265 * [backup-simplify]: Simplify 1.0 into 1.0 4.265 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.265 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.265 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.265 * [taylor]: Taking taylor expansion of -2.0 in k 4.265 * [backup-simplify]: Simplify -2.0 into -2.0 4.266 * [taylor]: Taking taylor expansion of PI in k 4.266 * [backup-simplify]: Simplify PI into PI 4.266 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.266 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.266 * [taylor]: Taking taylor expansion of (log n) in k 4.266 * [taylor]: Taking taylor expansion of n in k 4.266 * [backup-simplify]: Simplify n into n 4.267 * [backup-simplify]: Simplify (log n) into (log n) 4.267 * [backup-simplify]: Simplify (+ 1 0) into 1 4.267 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.267 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.268 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.269 * [backup-simplify]: Simplify (* 0.125 (- (log (* -2.0 PI)) (log n))) into (* 0.125 (- (log (* -2.0 PI)) (log n))) 4.269 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.270 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.271 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.271 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.272 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.272 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.273 * [backup-simplify]: Simplify (+ 0 0) into 0 4.273 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.280 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.280 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.282 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.282 * [taylor]: Taking taylor expansion of 0 in k 4.282 * [backup-simplify]: Simplify 0 into 0 4.282 * [backup-simplify]: Simplify 0 into 0 4.282 * [backup-simplify]: Simplify 0 into 0 4.282 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.283 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.285 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 4.285 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.285 * [backup-simplify]: Simplify (+ 0 0) into 0 4.285 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.286 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.287 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.289 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.289 * [taylor]: Taking taylor expansion of 0 in k 4.289 * [backup-simplify]: Simplify 0 into 0 4.289 * [backup-simplify]: Simplify 0 into 0 4.289 * [backup-simplify]: Simplify 0 into 0 4.289 * [backup-simplify]: Simplify 0 into 0 4.289 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.290 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.293 * [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 4.293 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.293 * [backup-simplify]: Simplify (+ 0 0) into 0 4.294 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.295 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.296 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.298 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.298 * [taylor]: Taking taylor expansion of 0 in k 4.298 * [backup-simplify]: Simplify 0 into 0 4.298 * [backup-simplify]: Simplify 0 into 0 4.298 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.125 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.298 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2 1) 4.299 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) into (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 4.299 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in (n k) around 0 4.299 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in k 4.299 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.299 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.299 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in k 4.299 * [taylor]: Taking taylor expansion of 0.125 in k 4.299 * [backup-simplify]: Simplify 0.125 into 0.125 4.299 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.299 * [taylor]: Taking taylor expansion of 1.0 in k 4.299 * [backup-simplify]: Simplify 1.0 into 1.0 4.299 * [taylor]: Taking taylor expansion of k in k 4.299 * [backup-simplify]: Simplify 0 into 0 4.299 * [backup-simplify]: Simplify 1 into 1 4.299 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.299 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.299 * [taylor]: Taking taylor expansion of 2.0 in k 4.299 * [backup-simplify]: Simplify 2.0 into 2.0 4.299 * [taylor]: Taking taylor expansion of (* n PI) in k 4.299 * [taylor]: Taking taylor expansion of n in k 4.299 * [backup-simplify]: Simplify n into n 4.299 * [taylor]: Taking taylor expansion of PI in k 4.299 * [backup-simplify]: Simplify PI into PI 4.299 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.299 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.299 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.300 * [backup-simplify]: Simplify (- 0) into 0 4.300 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.300 * [backup-simplify]: Simplify (* 0.125 1.0) into 0.125 4.300 * [backup-simplify]: Simplify (* 0.125 (log (* 2.0 (* n PI)))) into (* 0.125 (log (* 2.0 (* n PI)))) 4.300 * [backup-simplify]: Simplify (exp (* 0.125 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.125) 4.300 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.300 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.300 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.300 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.300 * [taylor]: Taking taylor expansion of 0.125 in n 4.300 * [backup-simplify]: Simplify 0.125 into 0.125 4.301 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.301 * [taylor]: Taking taylor expansion of 1.0 in n 4.301 * [backup-simplify]: Simplify 1.0 into 1.0 4.301 * [taylor]: Taking taylor expansion of k in n 4.301 * [backup-simplify]: Simplify k into k 4.301 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.301 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.301 * [taylor]: Taking taylor expansion of 2.0 in n 4.301 * [backup-simplify]: Simplify 2.0 into 2.0 4.301 * [taylor]: Taking taylor expansion of (* n PI) in n 4.301 * [taylor]: Taking taylor expansion of n in n 4.301 * [backup-simplify]: Simplify 0 into 0 4.301 * [backup-simplify]: Simplify 1 into 1 4.301 * [taylor]: Taking taylor expansion of PI in n 4.301 * [backup-simplify]: Simplify PI into PI 4.301 * [backup-simplify]: Simplify (* 0 PI) into 0 4.301 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.302 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.303 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.304 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.304 * [backup-simplify]: Simplify (- k) into (- k) 4.304 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.304 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.305 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.305 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.306 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.306 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.306 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.306 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.306 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.306 * [taylor]: Taking taylor expansion of 0.125 in n 4.306 * [backup-simplify]: Simplify 0.125 into 0.125 4.306 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.306 * [taylor]: Taking taylor expansion of 1.0 in n 4.306 * [backup-simplify]: Simplify 1.0 into 1.0 4.306 * [taylor]: Taking taylor expansion of k in n 4.306 * [backup-simplify]: Simplify k into k 4.306 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.306 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.306 * [taylor]: Taking taylor expansion of 2.0 in n 4.306 * [backup-simplify]: Simplify 2.0 into 2.0 4.306 * [taylor]: Taking taylor expansion of (* n PI) in n 4.306 * [taylor]: Taking taylor expansion of n in n 4.306 * [backup-simplify]: Simplify 0 into 0 4.306 * [backup-simplify]: Simplify 1 into 1 4.306 * [taylor]: Taking taylor expansion of PI in n 4.306 * [backup-simplify]: Simplify PI into PI 4.307 * [backup-simplify]: Simplify (* 0 PI) into 0 4.307 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.308 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.309 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.309 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.309 * [backup-simplify]: Simplify (- k) into (- k) 4.309 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.309 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.310 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.311 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.311 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.312 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.312 * [taylor]: Taking taylor expansion of (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.312 * [taylor]: Taking taylor expansion of 0.125 in k 4.312 * [backup-simplify]: Simplify 0.125 into 0.125 4.312 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.312 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.312 * [taylor]: Taking taylor expansion of 1.0 in k 4.312 * [backup-simplify]: Simplify 1.0 into 1.0 4.312 * [taylor]: Taking taylor expansion of k in k 4.312 * [backup-simplify]: Simplify 0 into 0 4.312 * [backup-simplify]: Simplify 1 into 1 4.312 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.312 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.312 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.312 * [taylor]: Taking taylor expansion of 2.0 in k 4.312 * [backup-simplify]: Simplify 2.0 into 2.0 4.312 * [taylor]: Taking taylor expansion of PI in k 4.312 * [backup-simplify]: Simplify PI into PI 4.312 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.313 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.313 * [taylor]: Taking taylor expansion of (log n) in k 4.313 * [taylor]: Taking taylor expansion of n in k 4.313 * [backup-simplify]: Simplify n into n 4.313 * [backup-simplify]: Simplify (log n) into (log n) 4.313 * [backup-simplify]: Simplify (- 0) into 0 4.313 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.314 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.315 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.315 * [backup-simplify]: Simplify (* 0.125 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.125 (+ (log (* 2.0 PI)) (log n))) 4.316 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.317 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.317 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.318 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.319 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.319 * [backup-simplify]: Simplify (- 0) into 0 4.319 * [backup-simplify]: Simplify (+ 0 0) into 0 4.319 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 k))) into 0 4.320 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.321 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.322 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.322 * [taylor]: Taking taylor expansion of 0 in k 4.322 * [backup-simplify]: Simplify 0 into 0 4.322 * [backup-simplify]: Simplify 0 into 0 4.322 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.323 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.324 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.324 * [backup-simplify]: Simplify (+ 0 0) into 0 4.324 * [backup-simplify]: Simplify (- 1) into -1 4.325 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.326 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.327 * [backup-simplify]: Simplify (+ (* 0.125 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 4.329 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 1) 1)))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.331 * [backup-simplify]: Simplify (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.332 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.332 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.334 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.334 * [backup-simplify]: Simplify (- 0) into 0 4.334 * [backup-simplify]: Simplify (+ 0 0) into 0 4.335 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.336 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.337 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.338 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.338 * [taylor]: Taking taylor expansion of 0 in k 4.338 * [backup-simplify]: Simplify 0 into 0 4.338 * [backup-simplify]: Simplify 0 into 0 4.338 * [backup-simplify]: Simplify 0 into 0 4.339 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.340 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.341 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.342 * [backup-simplify]: Simplify (+ 0 0) into 0 4.342 * [backup-simplify]: Simplify (- 0) into 0 4.342 * [backup-simplify]: Simplify (+ 0 0) into 0 4.343 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.345 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.347 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.350 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.356 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) (* k 1)) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.0078125 (* (pow k 2) (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (* 0.015625 (* (pow k 2) (* (log (* 2.0 PI)) (* (log n) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))))))) (+ (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log (* 2.0 PI))))))) 4.356 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (/ (- 1.0 (/ 1 k)) 2.0) 2) 2)) into (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 4.356 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in (n k) around 0 4.356 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in k 4.356 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.356 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.356 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in k 4.356 * [taylor]: Taking taylor expansion of 0.125 in k 4.356 * [backup-simplify]: Simplify 0.125 into 0.125 4.356 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.356 * [taylor]: Taking taylor expansion of 1.0 in k 4.356 * [backup-simplify]: Simplify 1.0 into 1.0 4.356 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.356 * [taylor]: Taking taylor expansion of k in k 4.356 * [backup-simplify]: Simplify 0 into 0 4.356 * [backup-simplify]: Simplify 1 into 1 4.357 * [backup-simplify]: Simplify (/ 1 1) into 1 4.357 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.357 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.357 * [taylor]: Taking taylor expansion of 2.0 in k 4.357 * [backup-simplify]: Simplify 2.0 into 2.0 4.357 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.357 * [taylor]: Taking taylor expansion of PI in k 4.357 * [backup-simplify]: Simplify PI into PI 4.357 * [taylor]: Taking taylor expansion of n in k 4.357 * [backup-simplify]: Simplify n into n 4.357 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.357 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.357 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.357 * [backup-simplify]: Simplify (- 1) into -1 4.357 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.358 * [backup-simplify]: Simplify (* 0.125 -1) into -0.125 4.358 * [backup-simplify]: Simplify (* -0.125 (log (* 2.0 (/ PI n)))) into (* -0.125 (log (* 2.0 (/ PI n)))) 4.358 * [backup-simplify]: Simplify (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.125 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.358 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.358 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.358 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.358 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.358 * [taylor]: Taking taylor expansion of 0.125 in n 4.358 * [backup-simplify]: Simplify 0.125 into 0.125 4.358 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.358 * [taylor]: Taking taylor expansion of 1.0 in n 4.358 * [backup-simplify]: Simplify 1.0 into 1.0 4.358 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.358 * [taylor]: Taking taylor expansion of k in n 4.358 * [backup-simplify]: Simplify k into k 4.358 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.358 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.358 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.358 * [taylor]: Taking taylor expansion of 2.0 in n 4.358 * [backup-simplify]: Simplify 2.0 into 2.0 4.358 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.358 * [taylor]: Taking taylor expansion of PI in n 4.358 * [backup-simplify]: Simplify PI into PI 4.358 * [taylor]: Taking taylor expansion of n in n 4.358 * [backup-simplify]: Simplify 0 into 0 4.358 * [backup-simplify]: Simplify 1 into 1 4.359 * [backup-simplify]: Simplify (/ PI 1) into PI 4.359 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.360 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.360 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.360 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.360 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.361 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.361 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.362 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.362 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.362 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.362 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.362 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.362 * [taylor]: Taking taylor expansion of 0.125 in n 4.362 * [backup-simplify]: Simplify 0.125 into 0.125 4.362 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.362 * [taylor]: Taking taylor expansion of 1.0 in n 4.362 * [backup-simplify]: Simplify 1.0 into 1.0 4.362 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.362 * [taylor]: Taking taylor expansion of k in n 4.362 * [backup-simplify]: Simplify k into k 4.362 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.362 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.362 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.362 * [taylor]: Taking taylor expansion of 2.0 in n 4.362 * [backup-simplify]: Simplify 2.0 into 2.0 4.362 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.362 * [taylor]: Taking taylor expansion of PI in n 4.362 * [backup-simplify]: Simplify PI into PI 4.362 * [taylor]: Taking taylor expansion of n in n 4.362 * [backup-simplify]: Simplify 0 into 0 4.362 * [backup-simplify]: Simplify 1 into 1 4.363 * [backup-simplify]: Simplify (/ PI 1) into PI 4.363 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.364 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.364 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.364 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.364 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.365 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.365 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.366 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.366 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.366 * [taylor]: Taking taylor expansion of (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.366 * [taylor]: Taking taylor expansion of 0.125 in k 4.366 * [backup-simplify]: Simplify 0.125 into 0.125 4.366 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.366 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.366 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.366 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.366 * [taylor]: Taking taylor expansion of 2.0 in k 4.366 * [backup-simplify]: Simplify 2.0 into 2.0 4.366 * [taylor]: Taking taylor expansion of PI in k 4.366 * [backup-simplify]: Simplify PI into PI 4.367 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.367 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.367 * [taylor]: Taking taylor expansion of (log n) in k 4.367 * [taylor]: Taking taylor expansion of n in k 4.367 * [backup-simplify]: Simplify n into n 4.367 * [backup-simplify]: Simplify (log n) into (log n) 4.367 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.367 * [taylor]: Taking taylor expansion of 1.0 in k 4.367 * [backup-simplify]: Simplify 1.0 into 1.0 4.367 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.367 * [taylor]: Taking taylor expansion of k in k 4.367 * [backup-simplify]: Simplify 0 into 0 4.367 * [backup-simplify]: Simplify 1 into 1 4.368 * [backup-simplify]: Simplify (/ 1 1) into 1 4.368 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.368 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.369 * [backup-simplify]: Simplify (- 1) into -1 4.374 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.375 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.376 * [backup-simplify]: Simplify (* 0.125 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.125 (- (log (* 2.0 PI)) (log n))) 4.377 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.377 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.378 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.378 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.379 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.379 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.380 * [backup-simplify]: Simplify (- 0) into 0 4.380 * [backup-simplify]: Simplify (+ 0 0) into 0 4.380 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.381 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.382 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.383 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.383 * [taylor]: Taking taylor expansion of 0 in k 4.383 * [backup-simplify]: Simplify 0 into 0 4.383 * [backup-simplify]: Simplify 0 into 0 4.383 * [backup-simplify]: Simplify 0 into 0 4.384 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.384 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.386 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.386 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.386 * [backup-simplify]: Simplify (- 0) into 0 4.386 * [backup-simplify]: Simplify (+ 0 0) into 0 4.387 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.388 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.389 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.390 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.390 * [taylor]: Taking taylor expansion of 0 in k 4.390 * [backup-simplify]: Simplify 0 into 0 4.390 * [backup-simplify]: Simplify 0 into 0 4.390 * [backup-simplify]: Simplify 0 into 0 4.390 * [backup-simplify]: Simplify 0 into 0 4.391 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.391 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.394 * [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 4.394 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.395 * [backup-simplify]: Simplify (- 0) into 0 4.395 * [backup-simplify]: Simplify (+ 0 0) into 0 4.395 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.396 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.398 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.399 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.399 * [taylor]: Taking taylor expansion of 0 in k 4.399 * [backup-simplify]: Simplify 0 into 0 4.399 * [backup-simplify]: Simplify 0 into 0 4.400 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.401 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2) 2)) into (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 4.401 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in (n k) around 0 4.401 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in k 4.401 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.401 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.401 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in k 4.401 * [taylor]: Taking taylor expansion of 0.125 in k 4.401 * [backup-simplify]: Simplify 0.125 into 0.125 4.401 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.401 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.401 * [taylor]: Taking taylor expansion of k in k 4.401 * [backup-simplify]: Simplify 0 into 0 4.401 * [backup-simplify]: Simplify 1 into 1 4.401 * [backup-simplify]: Simplify (/ 1 1) into 1 4.401 * [taylor]: Taking taylor expansion of 1.0 in k 4.401 * [backup-simplify]: Simplify 1.0 into 1.0 4.401 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.401 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.401 * [taylor]: Taking taylor expansion of -2.0 in k 4.401 * [backup-simplify]: Simplify -2.0 into -2.0 4.401 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.401 * [taylor]: Taking taylor expansion of PI in k 4.401 * [backup-simplify]: Simplify PI into PI 4.401 * [taylor]: Taking taylor expansion of n in k 4.401 * [backup-simplify]: Simplify n into n 4.401 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.401 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.401 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.402 * [backup-simplify]: Simplify (+ 1 0) into 1 4.402 * [backup-simplify]: Simplify (* 0.125 1) into 0.125 4.402 * [backup-simplify]: Simplify (* 0.125 (log (* -2.0 (/ PI n)))) into (* 0.125 (log (* -2.0 (/ PI n)))) 4.402 * [backup-simplify]: Simplify (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.402 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.402 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.402 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.402 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.402 * [taylor]: Taking taylor expansion of 0.125 in n 4.402 * [backup-simplify]: Simplify 0.125 into 0.125 4.402 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.402 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.402 * [taylor]: Taking taylor expansion of k in n 4.402 * [backup-simplify]: Simplify k into k 4.402 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.402 * [taylor]: Taking taylor expansion of 1.0 in n 4.402 * [backup-simplify]: Simplify 1.0 into 1.0 4.402 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.402 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.402 * [taylor]: Taking taylor expansion of -2.0 in n 4.402 * [backup-simplify]: Simplify -2.0 into -2.0 4.402 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.402 * [taylor]: Taking taylor expansion of PI in n 4.402 * [backup-simplify]: Simplify PI into PI 4.402 * [taylor]: Taking taylor expansion of n in n 4.402 * [backup-simplify]: Simplify 0 into 0 4.402 * [backup-simplify]: Simplify 1 into 1 4.403 * [backup-simplify]: Simplify (/ PI 1) into PI 4.403 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.404 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.404 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.404 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.405 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.405 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.406 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.406 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.406 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.406 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.406 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.406 * [taylor]: Taking taylor expansion of 0.125 in n 4.406 * [backup-simplify]: Simplify 0.125 into 0.125 4.406 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.406 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.406 * [taylor]: Taking taylor expansion of k in n 4.406 * [backup-simplify]: Simplify k into k 4.406 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.406 * [taylor]: Taking taylor expansion of 1.0 in n 4.406 * [backup-simplify]: Simplify 1.0 into 1.0 4.406 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.406 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.406 * [taylor]: Taking taylor expansion of -2.0 in n 4.406 * [backup-simplify]: Simplify -2.0 into -2.0 4.406 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.406 * [taylor]: Taking taylor expansion of PI in n 4.406 * [backup-simplify]: Simplify PI into PI 4.406 * [taylor]: Taking taylor expansion of n in n 4.406 * [backup-simplify]: Simplify 0 into 0 4.406 * [backup-simplify]: Simplify 1 into 1 4.407 * [backup-simplify]: Simplify (/ PI 1) into PI 4.407 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.408 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.408 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.408 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.409 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.409 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.410 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.410 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.410 * [taylor]: Taking taylor expansion of (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.410 * [taylor]: Taking taylor expansion of 0.125 in k 4.410 * [backup-simplify]: Simplify 0.125 into 0.125 4.410 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.410 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.410 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.410 * [taylor]: Taking taylor expansion of k in k 4.410 * [backup-simplify]: Simplify 0 into 0 4.410 * [backup-simplify]: Simplify 1 into 1 4.411 * [backup-simplify]: Simplify (/ 1 1) into 1 4.411 * [taylor]: Taking taylor expansion of 1.0 in k 4.411 * [backup-simplify]: Simplify 1.0 into 1.0 4.411 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.411 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.411 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.411 * [taylor]: Taking taylor expansion of -2.0 in k 4.411 * [backup-simplify]: Simplify -2.0 into -2.0 4.411 * [taylor]: Taking taylor expansion of PI in k 4.411 * [backup-simplify]: Simplify PI into PI 4.411 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.412 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.412 * [taylor]: Taking taylor expansion of (log n) in k 4.412 * [taylor]: Taking taylor expansion of n in k 4.412 * [backup-simplify]: Simplify n into n 4.412 * [backup-simplify]: Simplify (log n) into (log n) 4.412 * [backup-simplify]: Simplify (+ 1 0) into 1 4.412 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.413 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.413 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.414 * [backup-simplify]: Simplify (* 0.125 (- (log (* -2.0 PI)) (log n))) into (* 0.125 (- (log (* -2.0 PI)) (log n))) 4.415 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.415 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.416 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.416 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.417 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.417 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.418 * [backup-simplify]: Simplify (+ 0 0) into 0 4.418 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.419 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.419 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.421 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.421 * [taylor]: Taking taylor expansion of 0 in k 4.421 * [backup-simplify]: Simplify 0 into 0 4.421 * [backup-simplify]: Simplify 0 into 0 4.421 * [backup-simplify]: Simplify 0 into 0 4.421 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.422 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.424 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 4.424 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.424 * [backup-simplify]: Simplify (+ 0 0) into 0 4.425 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.425 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.426 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.428 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.428 * [taylor]: Taking taylor expansion of 0 in k 4.428 * [backup-simplify]: Simplify 0 into 0 4.428 * [backup-simplify]: Simplify 0 into 0 4.428 * [backup-simplify]: Simplify 0 into 0 4.428 * [backup-simplify]: Simplify 0 into 0 4.429 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.430 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.432 * [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 4.432 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.433 * [backup-simplify]: Simplify (+ 0 0) into 0 4.435 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.436 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.437 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.439 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.439 * [taylor]: Taking taylor expansion of 0 in k 4.439 * [backup-simplify]: Simplify 0 into 0 4.439 * [backup-simplify]: Simplify 0 into 0 4.440 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.125 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.440 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 4.440 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.440 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.440 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.440 * [taylor]: Taking taylor expansion of 1.0 in k 4.440 * [backup-simplify]: Simplify 1.0 into 1.0 4.440 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.440 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.440 * [taylor]: Taking taylor expansion of k in k 4.440 * [backup-simplify]: Simplify 0 into 0 4.440 * [backup-simplify]: Simplify 1 into 1 4.440 * [backup-simplify]: Simplify (/ 1 1) into 1 4.440 * [backup-simplify]: Simplify (sqrt 0) into 0 4.441 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.441 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.441 * [taylor]: Taking taylor expansion of 1.0 in k 4.441 * [backup-simplify]: Simplify 1.0 into 1.0 4.441 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.441 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.441 * [taylor]: Taking taylor expansion of k in k 4.441 * [backup-simplify]: Simplify 0 into 0 4.441 * [backup-simplify]: Simplify 1 into 1 4.441 * [backup-simplify]: Simplify (/ 1 1) into 1 4.442 * [backup-simplify]: Simplify (sqrt 0) into 0 4.442 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.443 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.443 * [backup-simplify]: Simplify 0 into 0 4.444 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.444 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.444 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.446 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.447 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.447 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.448 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.450 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.451 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.451 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.452 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.452 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.452 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.452 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.452 * [taylor]: Taking taylor expansion of 1.0 in k 4.452 * [backup-simplify]: Simplify 1.0 into 1.0 4.452 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.452 * [taylor]: Taking taylor expansion of k in k 4.453 * [backup-simplify]: Simplify 0 into 0 4.453 * [backup-simplify]: Simplify 1 into 1 4.453 * [backup-simplify]: Simplify (sqrt 0) into 0 4.453 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.454 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.454 * [taylor]: Taking taylor expansion of 1.0 in k 4.454 * [backup-simplify]: Simplify 1.0 into 1.0 4.454 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.454 * [taylor]: Taking taylor expansion of k in k 4.454 * [backup-simplify]: Simplify 0 into 0 4.454 * [backup-simplify]: Simplify 1 into 1 4.454 * [backup-simplify]: Simplify (sqrt 0) into 0 4.455 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.455 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.455 * [backup-simplify]: Simplify 0 into 0 4.456 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.456 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.458 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.459 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.459 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.461 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.462 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.462 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.463 * [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)))))))) 4.463 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.463 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.463 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.463 * [taylor]: Taking taylor expansion of 1.0 in k 4.464 * [backup-simplify]: Simplify 1.0 into 1.0 4.464 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.464 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.464 * [taylor]: Taking taylor expansion of -1 in k 4.464 * [backup-simplify]: Simplify -1 into -1 4.464 * [taylor]: Taking taylor expansion of k in k 4.464 * [backup-simplify]: Simplify 0 into 0 4.464 * [backup-simplify]: Simplify 1 into 1 4.464 * [backup-simplify]: Simplify (/ -1 1) into -1 4.464 * [backup-simplify]: Simplify (sqrt 0) into 0 4.472 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.472 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.472 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.472 * [taylor]: Taking taylor expansion of 1.0 in k 4.472 * [backup-simplify]: Simplify 1.0 into 1.0 4.472 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.472 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.472 * [taylor]: Taking taylor expansion of -1 in k 4.472 * [backup-simplify]: Simplify -1 into -1 4.472 * [taylor]: Taking taylor expansion of k in k 4.472 * [backup-simplify]: Simplify 0 into 0 4.472 * [backup-simplify]: Simplify 1 into 1 4.472 * [backup-simplify]: Simplify (/ -1 1) into -1 4.473 * [backup-simplify]: Simplify (sqrt 0) into 0 4.473 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.474 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.474 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.474 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.476 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.477 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.477 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.478 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.480 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.482 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.483 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.483 * [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))))) 4.483 * * * [progress]: simplifying candidates 4.492 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* 1 (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* 1 (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* 1 (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ 1.0 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ k 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (cbrt (/ (/ (/ (- 1.0 k) 2.0) 2) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (/ (- 1.0 k) 2.0) 2) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 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(log (* h0 h4)) 2) (exp (* h9 (+ (log (* h0 h4)) (log h3))))))) (+ (* h11 (* (pow h1 2) (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (* h10 (* (pow h1 2) (* (log (* h0 h4)) (* (log h3) (exp (* h9 (+ (log (* h0 h4)) (log h3))))))))))) (+ (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log h3)))) (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log (* h0 h4))))))) (exp (* h9 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h9 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (+ (* h11 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h9 (+ (log (* h0 h4)) (log h3))))))) (+ (* h11 (* (pow h1 2) (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (* h10 (* (pow h1 2) (* (log (* h0 h4)) (* (log h3) (exp (* h9 (+ (log (* h0 h4)) (log h3))))))))))) (+ (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log h3)))) (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log (* h0 h4))))))) (exp (* h9 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h9 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h12 h1) (- (+ (* h12 (pow h1 2)) (- h12))))) (- (+ (* h12 (/ 1 (pow h1 2))) (- (+ (* h12 (/ 1 h1)) (- (* h12 (/ 1 (pow h1 3)))))))) (- (+ (* h12 (/ 1 (pow h1 2))) (- (+ (* h12 (/ 1 h1)) (- h12))))) 4.516 * * [simplify]: iteration 0 : 1941 enodes (cost 5499 ) 4.537 * * [simplify]: iteration 1 : 5002 enodes (cost 5298 ) 4.560 * * * [progress]: adding candidates to table 6.806 * [progress]: [Phase 3 of 3] Extracting. 6.806 * * [regime]: Finding splitpoints for: (# # # # # # # #) 6.811 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 6.811 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 6.849 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 6.887 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 6.925 * * * [regime]: Found split indices: #