12.060 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.086 * * * [progress]: [2/2] Setting up program. 0.088 * [progress]: [Phase 2 of 3] Improving. 0.088 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.089 * [simplify]: Sending expressions to egg_math: (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) 0.090 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.092 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.093 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.096 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.102 * * [simplify]: iteration 4 : 1044 enodes (cost 8 ) 0.124 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.125 * * [progress]: iteration 1 / 4 0.125 * * * [progress]: picking best candidate 0.127 * * * * [pick]: Picked # 0.127 * * * [progress]: localizing error 0.140 * * * [progress]: generating rewritten candidates 0.140 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.161 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.170 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 0.187 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.231 * * * [progress]: generating series expansions 0.232 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.232 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 0.232 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.232 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.232 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.232 * [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 0.233 * [backup-simplify]: Simplify 0.5 into 0.5 0.233 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.233 * [taylor]: Taking taylor expansion of 1.0 in k 0.233 * [backup-simplify]: Simplify 1.0 into 1.0 0.233 * [taylor]: Taking taylor expansion of k in k 0.233 * [backup-simplify]: Simplify 0 into 0 0.233 * [backup-simplify]: Simplify 1 into 1 0.233 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.233 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.233 * [taylor]: Taking taylor expansion of 2.0 in k 0.233 * [backup-simplify]: Simplify 2.0 into 2.0 0.233 * [taylor]: Taking taylor expansion of (* n PI) in k 0.233 * [taylor]: Taking taylor expansion of n in k 0.233 * [backup-simplify]: Simplify n into n 0.233 * [taylor]: Taking taylor expansion of PI in k 0.233 * [backup-simplify]: Simplify PI into PI 0.233 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.233 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.233 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.233 * [backup-simplify]: Simplify (- 0) into 0 0.233 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.234 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.234 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.234 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.234 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.234 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.234 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.234 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.234 * [taylor]: Taking taylor expansion of 0.5 in n 0.234 * [backup-simplify]: Simplify 0.5 into 0.5 0.234 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.234 * [taylor]: Taking taylor expansion of 1.0 in n 0.234 * [backup-simplify]: Simplify 1.0 into 1.0 0.234 * [taylor]: Taking taylor expansion of k in n 0.234 * [backup-simplify]: Simplify k into k 0.234 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.234 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.234 * [taylor]: Taking taylor expansion of 2.0 in n 0.234 * [backup-simplify]: Simplify 2.0 into 2.0 0.234 * [taylor]: Taking taylor expansion of (* n PI) in n 0.234 * [taylor]: Taking taylor expansion of n in n 0.234 * [backup-simplify]: Simplify 0 into 0 0.234 * [backup-simplify]: Simplify 1 into 1 0.234 * [taylor]: Taking taylor expansion of PI in n 0.234 * [backup-simplify]: Simplify PI into PI 0.235 * [backup-simplify]: Simplify (* 0 PI) into 0 0.235 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.236 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.237 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.237 * [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) 0.238 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.238 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.239 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.240 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.240 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.240 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.240 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.240 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.240 * [taylor]: Taking taylor expansion of 0.5 in n 0.240 * [backup-simplify]: Simplify 0.5 into 0.5 0.240 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.240 * [taylor]: Taking taylor expansion of 1.0 in n 0.240 * [backup-simplify]: Simplify 1.0 into 1.0 0.240 * [taylor]: Taking taylor expansion of k in n 0.240 * [backup-simplify]: Simplify k into k 0.240 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.240 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.240 * [taylor]: Taking taylor expansion of 2.0 in n 0.240 * [backup-simplify]: Simplify 2.0 into 2.0 0.240 * [taylor]: Taking taylor expansion of (* n PI) in n 0.240 * [taylor]: Taking taylor expansion of n in n 0.240 * [backup-simplify]: Simplify 0 into 0 0.240 * [backup-simplify]: Simplify 1 into 1 0.240 * [taylor]: Taking taylor expansion of PI in n 0.240 * [backup-simplify]: Simplify PI into PI 0.240 * [backup-simplify]: Simplify (* 0 PI) into 0 0.241 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.242 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.242 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.243 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.243 * [backup-simplify]: Simplify (- k) into (- k) 0.243 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.243 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.244 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.245 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.245 * [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))))) 0.246 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.246 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.246 * [taylor]: Taking taylor expansion of 0.5 in k 0.246 * [backup-simplify]: Simplify 0.5 into 0.5 0.246 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.246 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.246 * [taylor]: Taking taylor expansion of 1.0 in k 0.246 * [backup-simplify]: Simplify 1.0 into 1.0 0.246 * [taylor]: Taking taylor expansion of k in k 0.246 * [backup-simplify]: Simplify 0 into 0 0.246 * [backup-simplify]: Simplify 1 into 1 0.246 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.246 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.246 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.246 * [taylor]: Taking taylor expansion of 2.0 in k 0.246 * [backup-simplify]: Simplify 2.0 into 2.0 0.246 * [taylor]: Taking taylor expansion of PI in k 0.246 * [backup-simplify]: Simplify PI into PI 0.246 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.247 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.247 * [taylor]: Taking taylor expansion of (log n) in k 0.247 * [taylor]: Taking taylor expansion of n in k 0.247 * [backup-simplify]: Simplify n into n 0.247 * [backup-simplify]: Simplify (log n) into (log n) 0.247 * [backup-simplify]: Simplify (- 0) into 0 0.247 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.248 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.249 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.249 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.250 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.251 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.251 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.252 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.253 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.253 * [backup-simplify]: Simplify (- 0) into 0 0.253 * [backup-simplify]: Simplify (+ 0 0) into 0 0.253 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 0.254 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.255 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.256 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.256 * [taylor]: Taking taylor expansion of 0 in k 0.256 * [backup-simplify]: Simplify 0 into 0 0.256 * [backup-simplify]: Simplify 0 into 0 0.257 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.258 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.258 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.259 * [backup-simplify]: Simplify (+ 0 0) into 0 0.259 * [backup-simplify]: Simplify (- 1) into -1 0.259 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.260 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.261 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 0.263 * [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)))))) 0.265 * [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)))))) 0.266 * [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 0.268 * [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 0.269 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 0.270 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.271 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.272 * [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 0.272 * [taylor]: Taking taylor expansion of 0 in k 0.272 * [backup-simplify]: Simplify 0 into 0 0.272 * [backup-simplify]: Simplify 0 into 0 0.272 * [backup-simplify]: Simplify 0 into 0 0.273 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.275 * [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 0.276 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 0.276 * [backup-simplify]: Simplify (+ 0 0) into 0 0.276 * [backup-simplify]: Simplify (- 0) into 0 0.276 * [backup-simplify]: Simplify (+ 0 0) into 0 0.277 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.279 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 0.281 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0.284 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0.290 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 0.291 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 0.291 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.291 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.291 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.291 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.291 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.291 * [taylor]: Taking taylor expansion of 0.5 in k 0.291 * [backup-simplify]: Simplify 0.5 into 0.5 0.291 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.291 * [taylor]: Taking taylor expansion of 1.0 in k 0.291 * [backup-simplify]: Simplify 1.0 into 1.0 0.291 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.291 * [taylor]: Taking taylor expansion of k in k 0.291 * [backup-simplify]: Simplify 0 into 0 0.291 * [backup-simplify]: Simplify 1 into 1 0.291 * [backup-simplify]: Simplify (/ 1 1) into 1 0.291 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.291 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.291 * [taylor]: Taking taylor expansion of 2.0 in k 0.291 * [backup-simplify]: Simplify 2.0 into 2.0 0.291 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.291 * [taylor]: Taking taylor expansion of PI in k 0.291 * [backup-simplify]: Simplify PI into PI 0.292 * [taylor]: Taking taylor expansion of n in k 0.292 * [backup-simplify]: Simplify n into n 0.292 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.292 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.292 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.292 * [backup-simplify]: Simplify (- 1) into -1 0.292 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.292 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.292 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.293 * [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))))) 0.293 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.293 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.293 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.293 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.293 * [taylor]: Taking taylor expansion of 0.5 in n 0.293 * [backup-simplify]: Simplify 0.5 into 0.5 0.293 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.293 * [taylor]: Taking taylor expansion of 1.0 in n 0.293 * [backup-simplify]: Simplify 1.0 into 1.0 0.293 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.293 * [taylor]: Taking taylor expansion of k in n 0.293 * [backup-simplify]: Simplify k into k 0.293 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.293 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.293 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.293 * [taylor]: Taking taylor expansion of 2.0 in n 0.293 * [backup-simplify]: Simplify 2.0 into 2.0 0.293 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.293 * [taylor]: Taking taylor expansion of PI in n 0.293 * [backup-simplify]: Simplify PI into PI 0.293 * [taylor]: Taking taylor expansion of n in n 0.293 * [backup-simplify]: Simplify 0 into 0 0.293 * [backup-simplify]: Simplify 1 into 1 0.293 * [backup-simplify]: Simplify (/ PI 1) into PI 0.294 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.294 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.294 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.294 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.294 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.295 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.296 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.297 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.297 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.297 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.297 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.297 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.297 * [taylor]: Taking taylor expansion of 0.5 in n 0.297 * [backup-simplify]: Simplify 0.5 into 0.5 0.297 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.297 * [taylor]: Taking taylor expansion of 1.0 in n 0.297 * [backup-simplify]: Simplify 1.0 into 1.0 0.297 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.297 * [taylor]: Taking taylor expansion of k in n 0.297 * [backup-simplify]: Simplify k into k 0.297 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.297 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.297 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.297 * [taylor]: Taking taylor expansion of 2.0 in n 0.297 * [backup-simplify]: Simplify 2.0 into 2.0 0.297 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.297 * [taylor]: Taking taylor expansion of PI in n 0.297 * [backup-simplify]: Simplify PI into PI 0.297 * [taylor]: Taking taylor expansion of n in n 0.297 * [backup-simplify]: Simplify 0 into 0 0.297 * [backup-simplify]: Simplify 1 into 1 0.298 * [backup-simplify]: Simplify (/ PI 1) into PI 0.298 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.299 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.299 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.299 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.299 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.300 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.300 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.301 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.301 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.301 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.301 * [taylor]: Taking taylor expansion of 0.5 in k 0.301 * [backup-simplify]: Simplify 0.5 into 0.5 0.301 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.301 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.301 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.301 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.301 * [taylor]: Taking taylor expansion of 2.0 in k 0.301 * [backup-simplify]: Simplify 2.0 into 2.0 0.301 * [taylor]: Taking taylor expansion of PI in k 0.301 * [backup-simplify]: Simplify PI into PI 0.302 * [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 * [taylor]: Taking taylor expansion of (log n) in k 0.302 * [taylor]: Taking taylor expansion of n in k 0.302 * [backup-simplify]: Simplify n into n 0.302 * [backup-simplify]: Simplify (log n) into (log n) 0.302 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.302 * [taylor]: Taking taylor expansion of 1.0 in k 0.302 * [backup-simplify]: Simplify 1.0 into 1.0 0.302 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.302 * [taylor]: Taking taylor expansion of k in k 0.302 * [backup-simplify]: Simplify 0 into 0 0.302 * [backup-simplify]: Simplify 1 into 1 0.303 * [backup-simplify]: Simplify (/ 1 1) into 1 0.303 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.303 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.304 * [backup-simplify]: Simplify (- 1) into -1 0.304 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.304 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.305 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 0.306 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.307 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.307 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.308 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.309 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.309 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.309 * [backup-simplify]: Simplify (- 0) into 0 0.309 * [backup-simplify]: Simplify (+ 0 0) into 0 0.310 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.311 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.311 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.312 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.312 * [taylor]: Taking taylor expansion of 0 in k 0.312 * [backup-simplify]: Simplify 0 into 0 0.312 * [backup-simplify]: Simplify 0 into 0 0.313 * [backup-simplify]: Simplify 0 into 0 0.313 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.314 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.315 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.316 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.316 * [backup-simplify]: Simplify (- 0) into 0 0.316 * [backup-simplify]: Simplify (+ 0 0) into 0 0.317 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 0.323 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.324 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 0.326 * [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 0.326 * [taylor]: Taking taylor expansion of 0 in k 0.326 * [backup-simplify]: Simplify 0 into 0 0.326 * [backup-simplify]: Simplify 0 into 0 0.326 * [backup-simplify]: Simplify 0 into 0 0.326 * [backup-simplify]: Simplify 0 into 0 0.326 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.327 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.330 * [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 0.330 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.330 * [backup-simplify]: Simplify (- 0) into 0 0.331 * [backup-simplify]: Simplify (+ 0 0) into 0 0.331 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 0.332 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.333 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 0.335 * [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 0.335 * [taylor]: Taking taylor expansion of 0 in k 0.335 * [backup-simplify]: Simplify 0 into 0 0.335 * [backup-simplify]: Simplify 0 into 0 0.336 * [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)))) 0.336 * [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))) 0.336 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.336 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.336 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.336 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.336 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.336 * [taylor]: Taking taylor expansion of 0.5 in k 0.336 * [backup-simplify]: Simplify 0.5 into 0.5 0.336 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.336 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.336 * [taylor]: Taking taylor expansion of k in k 0.336 * [backup-simplify]: Simplify 0 into 0 0.336 * [backup-simplify]: Simplify 1 into 1 0.337 * [backup-simplify]: Simplify (/ 1 1) into 1 0.337 * [taylor]: Taking taylor expansion of 1.0 in k 0.337 * [backup-simplify]: Simplify 1.0 into 1.0 0.337 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.337 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.337 * [taylor]: Taking taylor expansion of -2.0 in k 0.337 * [backup-simplify]: Simplify -2.0 into -2.0 0.337 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.337 * [taylor]: Taking taylor expansion of PI in k 0.337 * [backup-simplify]: Simplify PI into PI 0.337 * [taylor]: Taking taylor expansion of n in k 0.337 * [backup-simplify]: Simplify n into n 0.337 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.337 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.337 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.337 * [backup-simplify]: Simplify (+ 1 0) into 1 0.338 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.338 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.338 * [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)))))) 0.338 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.338 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.338 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.338 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.338 * [taylor]: Taking taylor expansion of 0.5 in n 0.338 * [backup-simplify]: Simplify 0.5 into 0.5 0.338 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.338 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.338 * [taylor]: Taking taylor expansion of k in n 0.338 * [backup-simplify]: Simplify k into k 0.338 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.338 * [taylor]: Taking taylor expansion of 1.0 in n 0.338 * [backup-simplify]: Simplify 1.0 into 1.0 0.338 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.338 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.338 * [taylor]: Taking taylor expansion of -2.0 in n 0.338 * [backup-simplify]: Simplify -2.0 into -2.0 0.338 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.338 * [taylor]: Taking taylor expansion of PI in n 0.338 * [backup-simplify]: Simplify PI into PI 0.338 * [taylor]: Taking taylor expansion of n in n 0.338 * [backup-simplify]: Simplify 0 into 0 0.338 * [backup-simplify]: Simplify 1 into 1 0.338 * [backup-simplify]: Simplify (/ PI 1) into PI 0.339 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.339 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.339 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.339 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.340 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.341 * [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)))) 0.342 * [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))))) 0.342 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.342 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.342 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.342 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.342 * [taylor]: Taking taylor expansion of 0.5 in n 0.342 * [backup-simplify]: Simplify 0.5 into 0.5 0.342 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.342 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.342 * [taylor]: Taking taylor expansion of k in n 0.342 * [backup-simplify]: Simplify k into k 0.342 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.342 * [taylor]: Taking taylor expansion of 1.0 in n 0.342 * [backup-simplify]: Simplify 1.0 into 1.0 0.342 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.342 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.342 * [taylor]: Taking taylor expansion of -2.0 in n 0.342 * [backup-simplify]: Simplify -2.0 into -2.0 0.342 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.342 * [taylor]: Taking taylor expansion of PI in n 0.342 * [backup-simplify]: Simplify PI into PI 0.342 * [taylor]: Taking taylor expansion of n in n 0.342 * [backup-simplify]: Simplify 0 into 0 0.342 * [backup-simplify]: Simplify 1 into 1 0.343 * [backup-simplify]: Simplify (/ PI 1) into PI 0.343 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.344 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.344 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.344 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.344 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.345 * [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)))) 0.346 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.346 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.346 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.346 * [taylor]: Taking taylor expansion of 0.5 in k 0.346 * [backup-simplify]: Simplify 0.5 into 0.5 0.346 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.346 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.346 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.346 * [taylor]: Taking taylor expansion of k in k 0.346 * [backup-simplify]: Simplify 0 into 0 0.346 * [backup-simplify]: Simplify 1 into 1 0.346 * [backup-simplify]: Simplify (/ 1 1) into 1 0.346 * [taylor]: Taking taylor expansion of 1.0 in k 0.346 * [backup-simplify]: Simplify 1.0 into 1.0 0.346 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.346 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.346 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.347 * [taylor]: Taking taylor expansion of -2.0 in k 0.347 * [backup-simplify]: Simplify -2.0 into -2.0 0.347 * [taylor]: Taking taylor expansion of PI in k 0.347 * [backup-simplify]: Simplify PI into PI 0.347 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.347 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.347 * [taylor]: Taking taylor expansion of (log n) in k 0.347 * [taylor]: Taking taylor expansion of n in k 0.348 * [backup-simplify]: Simplify n into n 0.348 * [backup-simplify]: Simplify (log n) into (log n) 0.348 * [backup-simplify]: Simplify (+ 1 0) into 1 0.348 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.348 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 0.349 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 0.350 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 0.351 * [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))))) 0.351 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.352 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.353 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.353 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.353 * [backup-simplify]: Simplify (+ 0 0) into 0 0.354 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 0.355 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.355 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.357 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.357 * [taylor]: Taking taylor expansion of 0 in k 0.357 * [backup-simplify]: Simplify 0 into 0 0.357 * [backup-simplify]: Simplify 0 into 0 0.357 * [backup-simplify]: Simplify 0 into 0 0.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.358 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.360 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 0.360 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.360 * [backup-simplify]: Simplify (+ 0 0) into 0 0.361 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 0.362 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.362 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 0.364 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.364 * [taylor]: Taking taylor expansion of 0 in k 0.364 * [backup-simplify]: Simplify 0 into 0 0.364 * [backup-simplify]: Simplify 0 into 0 0.364 * [backup-simplify]: Simplify 0 into 0 0.364 * [backup-simplify]: Simplify 0 into 0 0.365 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.365 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.368 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 0.368 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.369 * [backup-simplify]: Simplify (+ 0 0) into 0 0.369 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.370 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.371 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 0.373 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 0.373 * [taylor]: Taking taylor expansion of 0 in k 0.373 * [backup-simplify]: Simplify 0 into 0 0.373 * [backup-simplify]: Simplify 0 into 0 0.374 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 0.374 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.374 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.374 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.374 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.374 * [taylor]: Taking taylor expansion of 1.0 in k 0.374 * [backup-simplify]: Simplify 1.0 into 1.0 0.374 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.374 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.374 * [taylor]: Taking taylor expansion of k in k 0.374 * [backup-simplify]: Simplify 0 into 0 0.374 * [backup-simplify]: Simplify 1 into 1 0.374 * [backup-simplify]: Simplify (/ 1 1) into 1 0.374 * [backup-simplify]: Simplify (sqrt 0) into 0 0.375 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.375 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.375 * [taylor]: Taking taylor expansion of 1.0 in k 0.375 * [backup-simplify]: Simplify 1.0 into 1.0 0.375 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.375 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.375 * [taylor]: Taking taylor expansion of k in k 0.375 * [backup-simplify]: Simplify 0 into 0 0.375 * [backup-simplify]: Simplify 1 into 1 0.376 * [backup-simplify]: Simplify (/ 1 1) into 1 0.376 * [backup-simplify]: Simplify (sqrt 0) into 0 0.376 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.377 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.377 * [backup-simplify]: Simplify 0 into 0 0.378 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.378 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.378 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.380 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.381 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.381 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.382 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.384 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.385 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.385 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.386 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 0.387 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 0.387 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.387 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.387 * [taylor]: Taking taylor expansion of 1.0 in k 0.387 * [backup-simplify]: Simplify 1.0 into 1.0 0.387 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.387 * [taylor]: Taking taylor expansion of k in k 0.387 * [backup-simplify]: Simplify 0 into 0 0.387 * [backup-simplify]: Simplify 1 into 1 0.387 * [backup-simplify]: Simplify (sqrt 0) into 0 0.388 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.388 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.388 * [taylor]: Taking taylor expansion of 1.0 in k 0.388 * [backup-simplify]: Simplify 1.0 into 1.0 0.388 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.388 * [taylor]: Taking taylor expansion of k in k 0.388 * [backup-simplify]: Simplify 0 into 0 0.388 * [backup-simplify]: Simplify 1 into 1 0.388 * [backup-simplify]: Simplify (sqrt 0) into 0 0.389 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.389 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.389 * [backup-simplify]: Simplify 0 into 0 0.390 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.390 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.392 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.393 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.393 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.395 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.396 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.397 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.398 * [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)))))))) 0.398 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.398 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.398 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.398 * [taylor]: Taking taylor expansion of 1.0 in k 0.398 * [backup-simplify]: Simplify 1.0 into 1.0 0.398 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.398 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.398 * [taylor]: Taking taylor expansion of -1 in k 0.398 * [backup-simplify]: Simplify -1 into -1 0.398 * [taylor]: Taking taylor expansion of k in k 0.398 * [backup-simplify]: Simplify 0 into 0 0.398 * [backup-simplify]: Simplify 1 into 1 0.398 * [backup-simplify]: Simplify (/ -1 1) into -1 0.398 * [backup-simplify]: Simplify (sqrt 0) into 0 0.399 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.399 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.399 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.399 * [taylor]: Taking taylor expansion of 1.0 in k 0.399 * [backup-simplify]: Simplify 1.0 into 1.0 0.400 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.400 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.400 * [taylor]: Taking taylor expansion of -1 in k 0.400 * [backup-simplify]: Simplify -1 into -1 0.400 * [taylor]: Taking taylor expansion of k in k 0.400 * [backup-simplify]: Simplify 0 into 0 0.400 * [backup-simplify]: Simplify 1 into 1 0.400 * [backup-simplify]: Simplify (/ -1 1) into -1 0.400 * [backup-simplify]: Simplify (sqrt 0) into 0 0.401 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.401 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.401 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.402 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.403 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.405 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 0.405 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.408 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.410 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 0.410 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.411 * [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))))) 0.411 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 0.411 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.411 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.411 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.411 * [taylor]: Taking taylor expansion of 2.0 in n 0.411 * [backup-simplify]: Simplify 2.0 into 2.0 0.411 * [taylor]: Taking taylor expansion of (* n PI) in n 0.411 * [taylor]: Taking taylor expansion of n in n 0.411 * [backup-simplify]: Simplify 0 into 0 0.411 * [backup-simplify]: Simplify 1 into 1 0.411 * [taylor]: Taking taylor expansion of PI in n 0.412 * [backup-simplify]: Simplify PI into PI 0.412 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.412 * [taylor]: Taking taylor expansion of 2.0 in n 0.412 * [backup-simplify]: Simplify 2.0 into 2.0 0.412 * [taylor]: Taking taylor expansion of (* n PI) in n 0.412 * [taylor]: Taking taylor expansion of n in n 0.412 * [backup-simplify]: Simplify 0 into 0 0.412 * [backup-simplify]: Simplify 1 into 1 0.412 * [taylor]: Taking taylor expansion of PI in n 0.412 * [backup-simplify]: Simplify PI into PI 0.412 * [backup-simplify]: Simplify (* 0 PI) into 0 0.412 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.412 * [backup-simplify]: Simplify 0 into 0 0.418 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.419 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.420 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.420 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.421 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.421 * [backup-simplify]: Simplify 0 into 0 0.421 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.422 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.422 * [backup-simplify]: Simplify 0 into 0 0.423 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.423 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.423 * [backup-simplify]: Simplify 0 into 0 0.424 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.425 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 0.425 * [backup-simplify]: Simplify 0 into 0 0.426 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.427 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.427 * [backup-simplify]: Simplify 0 into 0 0.428 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.429 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.429 * [backup-simplify]: Simplify 0 into 0 0.429 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.430 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 0.430 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.430 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.430 * [taylor]: Taking taylor expansion of 2.0 in n 0.430 * [backup-simplify]: Simplify 2.0 into 2.0 0.430 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.430 * [taylor]: Taking taylor expansion of PI in n 0.430 * [backup-simplify]: Simplify PI into PI 0.430 * [taylor]: Taking taylor expansion of n in n 0.430 * [backup-simplify]: Simplify 0 into 0 0.430 * [backup-simplify]: Simplify 1 into 1 0.430 * [backup-simplify]: Simplify (/ PI 1) into PI 0.430 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.430 * [taylor]: Taking taylor expansion of 2.0 in n 0.430 * [backup-simplify]: Simplify 2.0 into 2.0 0.430 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.430 * [taylor]: Taking taylor expansion of PI in n 0.430 * [backup-simplify]: Simplify PI into PI 0.430 * [taylor]: Taking taylor expansion of n in n 0.430 * [backup-simplify]: Simplify 0 into 0 0.430 * [backup-simplify]: Simplify 1 into 1 0.431 * [backup-simplify]: Simplify (/ PI 1) into PI 0.431 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.431 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.432 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.432 * [backup-simplify]: Simplify 0 into 0 0.433 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.433 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.433 * [backup-simplify]: Simplify 0 into 0 0.434 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.434 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.434 * [backup-simplify]: Simplify 0 into 0 0.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.436 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.436 * [backup-simplify]: Simplify 0 into 0 0.437 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.437 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.437 * [backup-simplify]: Simplify 0 into 0 0.438 * [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 0.439 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.439 * [backup-simplify]: Simplify 0 into 0 0.439 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.440 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.440 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.440 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.440 * [taylor]: Taking taylor expansion of -2.0 in n 0.440 * [backup-simplify]: Simplify -2.0 into -2.0 0.440 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.440 * [taylor]: Taking taylor expansion of PI in n 0.440 * [backup-simplify]: Simplify PI into PI 0.440 * [taylor]: Taking taylor expansion of n in n 0.440 * [backup-simplify]: Simplify 0 into 0 0.440 * [backup-simplify]: Simplify 1 into 1 0.440 * [backup-simplify]: Simplify (/ PI 1) into PI 0.440 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.440 * [taylor]: Taking taylor expansion of -2.0 in n 0.440 * [backup-simplify]: Simplify -2.0 into -2.0 0.440 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.440 * [taylor]: Taking taylor expansion of PI in n 0.440 * [backup-simplify]: Simplify PI into PI 0.440 * [taylor]: Taking taylor expansion of n in n 0.440 * [backup-simplify]: Simplify 0 into 0 0.440 * [backup-simplify]: Simplify 1 into 1 0.440 * [backup-simplify]: Simplify (/ PI 1) into PI 0.441 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.441 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.442 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.442 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.442 * [backup-simplify]: Simplify 0 into 0 0.443 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.443 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.443 * [backup-simplify]: Simplify 0 into 0 0.444 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.444 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.444 * [backup-simplify]: Simplify 0 into 0 0.445 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.446 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.446 * [backup-simplify]: Simplify 0 into 0 0.446 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.447 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.447 * [backup-simplify]: Simplify 0 into 0 0.448 * [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 0.449 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.449 * [backup-simplify]: Simplify 0 into 0 0.449 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.449 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.450 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 0.450 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 0.450 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.450 * [taylor]: Taking taylor expansion of 1.0 in n 0.450 * [backup-simplify]: Simplify 1.0 into 1.0 0.450 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.450 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.450 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.450 * [taylor]: Taking taylor expansion of k in n 0.450 * [backup-simplify]: Simplify k into k 0.450 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.450 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 0.450 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.450 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 0.450 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.450 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.450 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.450 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.450 * [taylor]: Taking taylor expansion of 0.5 in n 0.450 * [backup-simplify]: Simplify 0.5 into 0.5 0.450 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.450 * [taylor]: Taking taylor expansion of 1.0 in n 0.450 * [backup-simplify]: Simplify 1.0 into 1.0 0.450 * [taylor]: Taking taylor expansion of k in n 0.450 * [backup-simplify]: Simplify k into k 0.450 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.450 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.450 * [taylor]: Taking taylor expansion of 2.0 in n 0.450 * [backup-simplify]: Simplify 2.0 into 2.0 0.450 * [taylor]: Taking taylor expansion of (* n PI) in n 0.450 * [taylor]: Taking taylor expansion of n in n 0.450 * [backup-simplify]: Simplify 0 into 0 0.450 * [backup-simplify]: Simplify 1 into 1 0.450 * [taylor]: Taking taylor expansion of PI in n 0.450 * [backup-simplify]: Simplify PI into PI 0.451 * [backup-simplify]: Simplify (* 0 PI) into 0 0.451 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.452 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.453 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.453 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.453 * [backup-simplify]: Simplify (- k) into (- k) 0.453 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.453 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.454 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.455 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.455 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.456 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.456 * [taylor]: Taking taylor expansion of 1.0 in k 0.456 * [backup-simplify]: Simplify 1.0 into 1.0 0.456 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.456 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.456 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.456 * [taylor]: Taking taylor expansion of k in k 0.456 * [backup-simplify]: Simplify 0 into 0 0.456 * [backup-simplify]: Simplify 1 into 1 0.456 * [backup-simplify]: Simplify (/ 1 1) into 1 0.456 * [backup-simplify]: Simplify (sqrt 0) into 0 0.457 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.457 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.457 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.457 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.457 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.457 * [taylor]: Taking taylor expansion of 0.5 in k 0.457 * [backup-simplify]: Simplify 0.5 into 0.5 0.457 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.457 * [taylor]: Taking taylor expansion of 1.0 in k 0.457 * [backup-simplify]: Simplify 1.0 into 1.0 0.457 * [taylor]: Taking taylor expansion of k in k 0.457 * [backup-simplify]: Simplify 0 into 0 0.457 * [backup-simplify]: Simplify 1 into 1 0.457 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.457 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.457 * [taylor]: Taking taylor expansion of 2.0 in k 0.457 * [backup-simplify]: Simplify 2.0 into 2.0 0.457 * [taylor]: Taking taylor expansion of (* n PI) in k 0.457 * [taylor]: Taking taylor expansion of n in k 0.457 * [backup-simplify]: Simplify n into n 0.457 * [taylor]: Taking taylor expansion of PI in k 0.457 * [backup-simplify]: Simplify PI into PI 0.457 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.457 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.457 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.458 * [backup-simplify]: Simplify (- 0) into 0 0.458 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.458 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.458 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.458 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.458 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.458 * [taylor]: Taking taylor expansion of 1.0 in k 0.458 * [backup-simplify]: Simplify 1.0 into 1.0 0.458 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.458 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.458 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.458 * [taylor]: Taking taylor expansion of k in k 0.458 * [backup-simplify]: Simplify 0 into 0 0.459 * [backup-simplify]: Simplify 1 into 1 0.459 * [backup-simplify]: Simplify (/ 1 1) into 1 0.459 * [backup-simplify]: Simplify (sqrt 0) into 0 0.460 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.460 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.460 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.460 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.460 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.460 * [taylor]: Taking taylor expansion of 0.5 in k 0.460 * [backup-simplify]: Simplify 0.5 into 0.5 0.460 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.460 * [taylor]: Taking taylor expansion of 1.0 in k 0.460 * [backup-simplify]: Simplify 1.0 into 1.0 0.460 * [taylor]: Taking taylor expansion of k in k 0.460 * [backup-simplify]: Simplify 0 into 0 0.460 * [backup-simplify]: Simplify 1 into 1 0.460 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.460 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.460 * [taylor]: Taking taylor expansion of 2.0 in k 0.460 * [backup-simplify]: Simplify 2.0 into 2.0 0.460 * [taylor]: Taking taylor expansion of (* n PI) in k 0.460 * [taylor]: Taking taylor expansion of n in k 0.460 * [backup-simplify]: Simplify n into n 0.460 * [taylor]: Taking taylor expansion of PI in k 0.460 * [backup-simplify]: Simplify PI into PI 0.460 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.460 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.460 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.461 * [backup-simplify]: Simplify (- 0) into 0 0.461 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.461 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.461 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.461 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.462 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 0.462 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.462 * [taylor]: Taking taylor expansion of 0 in n 0.462 * [backup-simplify]: Simplify 0 into 0 0.462 * [backup-simplify]: Simplify 0 into 0 0.462 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 0.463 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 0.463 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 0.463 * [backup-simplify]: Simplify (- 1) into -1 0.463 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.464 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 0.465 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 0.465 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.466 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 0.467 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.467 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 0.467 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 0.467 * [taylor]: Taking taylor expansion of +nan.0 in n 0.467 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.467 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.467 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.467 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.467 * [taylor]: Taking taylor expansion of 0.5 in n 0.467 * [backup-simplify]: Simplify 0.5 into 0.5 0.467 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.468 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.468 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.468 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.468 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.468 * [taylor]: Taking taylor expansion of 1.0 in n 0.468 * [backup-simplify]: Simplify 1.0 into 1.0 0.468 * [taylor]: Taking taylor expansion of (log PI) in n 0.468 * [taylor]: Taking taylor expansion of PI in n 0.468 * [backup-simplify]: Simplify PI into PI 0.468 * [backup-simplify]: Simplify (log PI) into (log PI) 0.468 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.469 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.469 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.469 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.469 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.469 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.469 * [taylor]: Taking taylor expansion of 1.0 in n 0.469 * [backup-simplify]: Simplify 1.0 into 1.0 0.470 * [taylor]: Taking taylor expansion of (log n) in n 0.470 * [taylor]: Taking taylor expansion of n in n 0.470 * [backup-simplify]: Simplify 0 into 0 0.470 * [backup-simplify]: Simplify 1 into 1 0.470 * [backup-simplify]: Simplify (log 1) into 0 0.470 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.470 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.470 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.470 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.470 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.470 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.470 * [taylor]: Taking taylor expansion of 1.0 in n 0.470 * [backup-simplify]: Simplify 1.0 into 1.0 0.470 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.470 * [taylor]: Taking taylor expansion of 2.0 in n 0.470 * [backup-simplify]: Simplify 2.0 into 2.0 0.471 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.471 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.472 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.472 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 0.473 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 0.474 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 0.475 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 0.475 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.476 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 0.477 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 0.478 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.478 * [backup-simplify]: Simplify 0 into 0 0.478 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 0.479 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 0.480 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 0.480 * [backup-simplify]: Simplify (- 0) into 0 0.481 * [backup-simplify]: Simplify (+ 0 0) into 0 0.481 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.482 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 0.482 * [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))) 0.483 * [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 0.490 * [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 0.490 * [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 0.490 * [taylor]: Taking taylor expansion of +nan.0 in n 0.490 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.490 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.490 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.490 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.490 * [taylor]: Taking taylor expansion of 0.5 in n 0.490 * [backup-simplify]: Simplify 0.5 into 0.5 0.490 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.490 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.490 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.490 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.490 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.490 * [taylor]: Taking taylor expansion of 1.0 in n 0.490 * [backup-simplify]: Simplify 1.0 into 1.0 0.490 * [taylor]: Taking taylor expansion of (log PI) in n 0.490 * [taylor]: Taking taylor expansion of PI in n 0.490 * [backup-simplify]: Simplify PI into PI 0.490 * [backup-simplify]: Simplify (log PI) into (log PI) 0.491 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.492 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.492 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.492 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.492 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.492 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.492 * [taylor]: Taking taylor expansion of 1.0 in n 0.492 * [backup-simplify]: Simplify 1.0 into 1.0 0.492 * [taylor]: Taking taylor expansion of (log n) in n 0.492 * [taylor]: Taking taylor expansion of n in n 0.492 * [backup-simplify]: Simplify 0 into 0 0.492 * [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 0.493 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) 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 2.0) in n 0.493 * [taylor]: Taking taylor expansion of 2.0 in n 0.493 * [backup-simplify]: Simplify 2.0 into 2.0 0.493 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.494 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.495 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.495 * [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) 0.496 * [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) 0.497 * [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)) 0.498 * [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))) 0.498 * [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) 0.498 * [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 0.498 * [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 0.498 * [taylor]: Taking taylor expansion of +nan.0 in n 0.498 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.498 * [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 0.498 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.499 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.499 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.499 * [taylor]: Taking taylor expansion of 0.5 in n 0.499 * [backup-simplify]: Simplify 0.5 into 0.5 0.499 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.499 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.499 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.499 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.499 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.499 * [taylor]: Taking taylor expansion of 1.0 in n 0.499 * [backup-simplify]: Simplify 1.0 into 1.0 0.499 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.499 * [taylor]: Taking taylor expansion of 2.0 in n 0.499 * [backup-simplify]: Simplify 2.0 into 2.0 0.499 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.499 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.500 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.500 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.500 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.500 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.500 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) 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 PI) in n 0.500 * [taylor]: Taking taylor expansion of PI in n 0.501 * [backup-simplify]: Simplify PI into PI 0.501 * [backup-simplify]: Simplify (log PI) into (log PI) 0.501 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.502 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.502 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.502 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.502 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) 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 n) in n 0.502 * [taylor]: Taking taylor expansion of n in n 0.502 * [backup-simplify]: Simplify 0 into 0 0.502 * [backup-simplify]: Simplify 1 into 1 0.503 * [backup-simplify]: Simplify (log 1) into 0 0.503 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.503 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.503 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.503 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.504 * [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) 0.505 * [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)) 0.506 * [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))) 0.507 * [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) 0.507 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.507 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.507 * [taylor]: Taking taylor expansion of 2.0 in n 0.507 * [backup-simplify]: Simplify 2.0 into 2.0 0.507 * [taylor]: Taking taylor expansion of (* n PI) in n 0.507 * [taylor]: Taking taylor expansion of n in n 0.507 * [backup-simplify]: Simplify 0 into 0 0.507 * [backup-simplify]: Simplify 1 into 1 0.507 * [taylor]: Taking taylor expansion of PI in n 0.507 * [backup-simplify]: Simplify PI into PI 0.507 * [backup-simplify]: Simplify (* 0 PI) into 0 0.507 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.508 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.509 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.510 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.511 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 0.517 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.519 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.520 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.522 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))) 0.525 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.528 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.532 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.533 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 0.533 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 0.534 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 0.535 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 0.535 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.535 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.536 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 0.536 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 0.537 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 0.538 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 0.539 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 0.540 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 0.541 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 0.542 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 0.543 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 0.544 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 0.544 * [backup-simplify]: Simplify (- 0) into 0 0.544 * [backup-simplify]: Simplify 0 into 0 0.544 * [backup-simplify]: Simplify 0 into 0 0.545 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.546 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 0.547 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 0.548 * [backup-simplify]: Simplify (- 0) into 0 0.548 * [backup-simplify]: Simplify (+ 0 0) into 0 0.548 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 0.549 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 0.550 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.551 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.553 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.556 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 0.563 * [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)))))))) 0.563 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 0.563 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 0.563 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 0.563 * [taylor]: Taking taylor expansion of +nan.0 in n 0.563 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.563 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.563 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.563 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.563 * [taylor]: Taking taylor expansion of 0.5 in n 0.563 * [backup-simplify]: Simplify 0.5 into 0.5 0.563 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.563 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.563 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.563 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.563 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.563 * [taylor]: Taking taylor expansion of 1.0 in n 0.563 * [backup-simplify]: Simplify 1.0 into 1.0 0.563 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.563 * [taylor]: Taking taylor expansion of 2.0 in n 0.563 * [backup-simplify]: Simplify 2.0 into 2.0 0.563 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.564 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.565 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.565 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.565 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.565 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.565 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.565 * [taylor]: Taking taylor expansion of 1.0 in n 0.565 * [backup-simplify]: Simplify 1.0 into 1.0 0.565 * [taylor]: Taking taylor expansion of (log n) in n 0.565 * [taylor]: Taking taylor expansion of n in n 0.565 * [backup-simplify]: Simplify 0 into 0 0.565 * [backup-simplify]: Simplify 1 into 1 0.565 * [backup-simplify]: Simplify (log 1) into 0 0.565 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.566 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.566 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.566 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.566 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.566 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.566 * [taylor]: Taking taylor expansion of 1.0 in n 0.566 * [backup-simplify]: Simplify 1.0 into 1.0 0.566 * [taylor]: Taking taylor expansion of (log PI) in n 0.566 * [taylor]: Taking taylor expansion of PI in n 0.566 * [backup-simplify]: Simplify PI into PI 0.566 * [backup-simplify]: Simplify (log PI) into (log PI) 0.567 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.567 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.568 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.569 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.569 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.570 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.571 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.571 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 0.571 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 0.571 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 0.571 * [taylor]: Taking taylor expansion of +nan.0 in n 0.571 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.571 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 0.571 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.571 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.571 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.571 * [taylor]: Taking taylor expansion of 0.5 in n 0.571 * [backup-simplify]: Simplify 0.5 into 0.5 0.571 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.571 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.571 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.571 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.571 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.571 * [taylor]: Taking taylor expansion of 1.0 in n 0.571 * [backup-simplify]: Simplify 1.0 into 1.0 0.571 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.571 * [taylor]: Taking taylor expansion of 2.0 in n 0.571 * [backup-simplify]: Simplify 2.0 into 2.0 0.572 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.572 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.573 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.573 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.573 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.573 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.573 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.573 * [taylor]: Taking taylor expansion of 1.0 in n 0.573 * [backup-simplify]: Simplify 1.0 into 1.0 0.573 * [taylor]: Taking taylor expansion of (log PI) in n 0.573 * [taylor]: Taking taylor expansion of PI in n 0.573 * [backup-simplify]: Simplify PI into PI 0.574 * [backup-simplify]: Simplify (log PI) into (log PI) 0.574 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.575 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.575 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.575 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.575 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.575 * [taylor]: Taking taylor expansion of 1.0 in n 0.575 * [backup-simplify]: Simplify 1.0 into 1.0 0.575 * [taylor]: Taking taylor expansion of (log n) in n 0.575 * [taylor]: Taking taylor expansion of n in n 0.575 * [backup-simplify]: Simplify 0 into 0 0.575 * [backup-simplify]: Simplify 1 into 1 0.575 * [backup-simplify]: Simplify (log 1) into 0 0.576 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.576 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.576 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.576 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.577 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.578 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.578 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.579 * [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) 0.579 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.579 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.579 * [taylor]: Taking taylor expansion of 2.0 in n 0.579 * [backup-simplify]: Simplify 2.0 into 2.0 0.579 * [taylor]: Taking taylor expansion of (* n PI) in n 0.579 * [taylor]: Taking taylor expansion of n in n 0.579 * [backup-simplify]: Simplify 0 into 0 0.579 * [backup-simplify]: Simplify 1 into 1 0.579 * [taylor]: Taking taylor expansion of PI in n 0.579 * [backup-simplify]: Simplify PI into PI 0.580 * [backup-simplify]: Simplify (* 0 PI) into 0 0.580 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.581 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.582 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.582 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.582 * [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 0.582 * [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 0.582 * [taylor]: Taking taylor expansion of +nan.0 in n 0.582 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.582 * [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 0.583 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.583 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.583 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.583 * [taylor]: Taking taylor expansion of 0.5 in n 0.583 * [backup-simplify]: Simplify 0.5 into 0.5 0.583 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.583 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.583 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.583 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.583 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.583 * [taylor]: Taking taylor expansion of 1.0 in n 0.583 * [backup-simplify]: Simplify 1.0 into 1.0 0.583 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.583 * [taylor]: Taking taylor expansion of 2.0 in n 0.583 * [backup-simplify]: Simplify 2.0 into 2.0 0.583 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.584 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.584 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.584 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.584 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.584 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.584 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.584 * [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 PI) in n 0.585 * [taylor]: Taking taylor expansion of PI in n 0.585 * [backup-simplify]: Simplify PI into PI 0.585 * [backup-simplify]: Simplify (log PI) into (log PI) 0.585 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.586 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.586 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.586 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.586 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.586 * [taylor]: Taking taylor expansion of 1.0 in n 0.586 * [backup-simplify]: Simplify 1.0 into 1.0 0.586 * [taylor]: Taking taylor expansion of (log n) in n 0.586 * [taylor]: Taking taylor expansion of n in n 0.586 * [backup-simplify]: Simplify 0 into 0 0.586 * [backup-simplify]: Simplify 1 into 1 0.587 * [backup-simplify]: Simplify (log 1) into 0 0.587 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.587 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.587 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.588 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.588 * [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) 0.589 * [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)) 0.590 * [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))) 0.591 * [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) 0.591 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.591 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.591 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.591 * [taylor]: Taking taylor expansion of 2.0 in n 0.591 * [backup-simplify]: Simplify 2.0 into 2.0 0.591 * [taylor]: Taking taylor expansion of (* n PI) in n 0.591 * [taylor]: Taking taylor expansion of n in n 0.591 * [backup-simplify]: Simplify 0 into 0 0.591 * [backup-simplify]: Simplify 1 into 1 0.591 * [taylor]: Taking taylor expansion of PI in n 0.591 * [backup-simplify]: Simplify PI into PI 0.591 * [backup-simplify]: Simplify (* 0 PI) into 0 0.591 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.592 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.593 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.594 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.595 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.596 * [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)) 0.596 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.598 * [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)) 0.599 * [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))) 0.600 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.601 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.602 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 0.604 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (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)) 0.605 * [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))) 0.607 * [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)))))))) 0.619 * [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)))))))))))) 0.627 * [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)))))))))))) 0.636 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 0.646 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 0.655 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 0.669 * [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)))))))))))))))))))))) 0.670 * [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)))))) 0.670 * [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 0.670 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.670 * [taylor]: Taking taylor expansion of 1.0 in n 0.670 * [backup-simplify]: Simplify 1.0 into 1.0 0.670 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.670 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.670 * [taylor]: Taking taylor expansion of k in n 0.670 * [backup-simplify]: Simplify k into k 0.670 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 0.670 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 0.670 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.670 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.670 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.670 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.670 * [taylor]: Taking taylor expansion of 0.5 in n 0.670 * [backup-simplify]: Simplify 0.5 into 0.5 0.670 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.670 * [taylor]: Taking taylor expansion of 1.0 in n 0.670 * [backup-simplify]: Simplify 1.0 into 1.0 0.670 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.670 * [taylor]: Taking taylor expansion of k in n 0.670 * [backup-simplify]: Simplify k into k 0.670 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.670 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.670 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.670 * [taylor]: Taking taylor expansion of 2.0 in n 0.670 * [backup-simplify]: Simplify 2.0 into 2.0 0.670 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.670 * [taylor]: Taking taylor expansion of PI in n 0.670 * [backup-simplify]: Simplify PI into PI 0.670 * [taylor]: Taking taylor expansion of n in n 0.670 * [backup-simplify]: Simplify 0 into 0 0.670 * [backup-simplify]: Simplify 1 into 1 0.671 * [backup-simplify]: Simplify (/ PI 1) into PI 0.671 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.672 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.672 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.672 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.672 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.673 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.674 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 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))))) 0.675 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.675 * [taylor]: Taking taylor expansion of 1.0 in k 0.675 * [backup-simplify]: Simplify 1.0 into 1.0 0.675 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.675 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.675 * [taylor]: Taking taylor expansion of k in k 0.675 * [backup-simplify]: Simplify 0 into 0 0.675 * [backup-simplify]: Simplify 1 into 1 0.675 * [backup-simplify]: Simplify (sqrt 0) into 0 0.676 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.676 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.676 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.676 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.676 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.676 * [taylor]: Taking taylor expansion of 0.5 in k 0.676 * [backup-simplify]: Simplify 0.5 into 0.5 0.676 * [taylor]: Taking taylor expansion of (- 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 (/ 1 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 (/ 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)) 0.677 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.677 * [backup-simplify]: Simplify (- 1) into -1 0.677 * [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))))) 0.678 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.678 * [taylor]: Taking taylor expansion of 1.0 in k 0.678 * [backup-simplify]: Simplify 1.0 into 1.0 0.678 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.678 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.678 * [taylor]: Taking taylor expansion of k in k 0.678 * [backup-simplify]: Simplify 0 into 0 0.678 * [backup-simplify]: Simplify 1 into 1 0.678 * [backup-simplify]: Simplify (sqrt 0) into 0 0.679 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.679 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.679 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.679 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.679 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.679 * [taylor]: Taking taylor expansion of 0.5 in k 0.679 * [backup-simplify]: Simplify 0.5 into 0.5 0.679 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.679 * [taylor]: Taking taylor expansion of 1.0 in k 0.679 * [backup-simplify]: Simplify 1.0 into 1.0 0.679 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.679 * [taylor]: Taking taylor expansion of k in k 0.679 * [backup-simplify]: Simplify 0 into 0 0.679 * [backup-simplify]: Simplify 1 into 1 0.679 * [backup-simplify]: Simplify (/ 1 1) into 1 0.679 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.679 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.679 * [taylor]: Taking taylor expansion of 2.0 in k 0.679 * [backup-simplify]: Simplify 2.0 into 2.0 0.679 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.679 * [taylor]: Taking taylor expansion of PI in k 0.679 * [backup-simplify]: Simplify PI into PI 0.679 * [taylor]: Taking taylor expansion of n in k 0.679 * [backup-simplify]: Simplify n into n 0.680 * [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))) 0.680 * [backup-simplify]: Simplify (- 1) into -1 0.680 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.680 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.680 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.681 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 0.681 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 0.681 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.681 * [taylor]: Taking taylor expansion of 0 in n 0.681 * [backup-simplify]: Simplify 0 into 0 0.681 * [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))))))) 0.682 * [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))))))) 0.682 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.682 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.682 * [taylor]: Taking taylor expansion of +nan.0 in n 0.682 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.682 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.682 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.682 * [taylor]: Taking taylor expansion of 0.5 in n 0.682 * [backup-simplify]: Simplify 0.5 into 0.5 0.682 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.682 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.682 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.682 * [taylor]: Taking taylor expansion of 2.0 in n 0.682 * [backup-simplify]: Simplify 2.0 into 2.0 0.682 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.682 * [taylor]: Taking taylor expansion of PI in n 0.682 * [backup-simplify]: Simplify PI into PI 0.682 * [taylor]: Taking taylor expansion of n in n 0.682 * [backup-simplify]: Simplify 0 into 0 0.682 * [backup-simplify]: Simplify 1 into 1 0.683 * [backup-simplify]: Simplify (/ PI 1) into PI 0.683 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.683 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.683 * [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) 0.684 * [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)) 0.685 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.686 * [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)))) 0.687 * [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)))))) 0.688 * [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))))))) 0.689 * [backup-simplify]: Simplify 0 into 0 0.691 * [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))))))) 0.692 * [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))))))) 0.692 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.692 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.692 * [taylor]: Taking taylor expansion of +nan.0 in n 0.692 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.692 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.692 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.692 * [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 0.693 * [backup-simplify]: Simplify (/ PI 1) into PI 0.693 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.694 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.694 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.694 * [taylor]: Taking taylor expansion of 1.0 in n 0.694 * [backup-simplify]: Simplify 1.0 into 1.0 0.694 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.694 * [taylor]: Taking taylor expansion of k in n 0.694 * [backup-simplify]: Simplify k into k 0.694 * [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)) 0.695 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.695 * [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))) 0.696 * [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)))) 0.697 * [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))))))) 0.699 * [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 (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.700 * [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 0.701 * [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 0.703 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.704 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 0.710 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.711 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 0.712 * [backup-simplify]: Simplify (- 0) into 0 0.712 * [backup-simplify]: Simplify 0 into 0 0.712 * [backup-simplify]: Simplify 0 into 0 0.714 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.715 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 0.715 * [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))))))) 0.715 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.715 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.715 * [taylor]: Taking taylor expansion of +nan.0 in n 0.715 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.715 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.715 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.715 * [taylor]: Taking taylor expansion of 0.5 in n 0.715 * [backup-simplify]: Simplify 0.5 into 0.5 0.716 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.716 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.716 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.716 * [taylor]: Taking taylor expansion of 2.0 in n 0.716 * [backup-simplify]: Simplify 2.0 into 2.0 0.716 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.716 * [taylor]: Taking taylor expansion of PI in n 0.716 * [backup-simplify]: Simplify PI into PI 0.716 * [taylor]: Taking taylor expansion of n in n 0.716 * [backup-simplify]: Simplify 0 into 0 0.716 * [backup-simplify]: Simplify 1 into 1 0.716 * [backup-simplify]: Simplify (/ PI 1) into PI 0.716 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.717 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.717 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.717 * [taylor]: Taking taylor expansion of 1.0 in n 0.717 * [backup-simplify]: Simplify 1.0 into 1.0 0.717 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.717 * [taylor]: Taking taylor expansion of k in n 0.717 * [backup-simplify]: Simplify k into k 0.717 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.718 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.718 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.718 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.719 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.719 * [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)))) 0.720 * [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))))) 0.721 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 0.722 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.722 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.725 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 0.726 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 0.726 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 0.726 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.726 * [taylor]: Taking taylor expansion of 1.0 in n 0.726 * [backup-simplify]: Simplify 1.0 into 1.0 0.726 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.726 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.726 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.726 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.726 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.726 * [taylor]: Taking taylor expansion of 0.5 in n 0.726 * [backup-simplify]: Simplify 0.5 into 0.5 0.726 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.726 * [taylor]: Taking taylor expansion of (/ 1 k) in n 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 * [taylor]: Taking taylor expansion of 1.0 in n 0.726 * [backup-simplify]: Simplify 1.0 into 1.0 0.726 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.726 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.726 * [taylor]: Taking taylor expansion of -2.0 in n 0.726 * [backup-simplify]: Simplify -2.0 into -2.0 0.726 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.726 * [taylor]: Taking taylor expansion of PI in n 0.726 * [backup-simplify]: Simplify PI into PI 0.726 * [taylor]: Taking taylor expansion of n in n 0.726 * [backup-simplify]: Simplify 0 into 0 0.726 * [backup-simplify]: Simplify 1 into 1 0.726 * [backup-simplify]: Simplify (/ PI 1) into PI 0.727 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.727 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.727 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.727 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.728 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.729 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.730 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.730 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.730 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.730 * [taylor]: Taking taylor expansion of -1 in n 0.730 * [backup-simplify]: Simplify -1 into -1 0.730 * [taylor]: Taking taylor expansion of k in n 0.730 * [backup-simplify]: Simplify k into k 0.730 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 0.730 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 0.730 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 0.730 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 0.731 * [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))) 0.731 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 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 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.731 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.731 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.731 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.731 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.731 * [taylor]: Taking taylor expansion of 0.5 in k 0.731 * [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 0.732 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.732 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.732 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.732 * [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 0.733 * [backup-simplify]: Simplify (/ -1 1) into -1 0.733 * [backup-simplify]: Simplify (sqrt 0) into 0 0.734 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.734 * [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 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.734 * [taylor]: Taking taylor expansion of 1.0 in k 0.734 * [backup-simplify]: Simplify 1.0 into 1.0 0.734 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.734 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.734 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.734 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.734 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.734 * [taylor]: Taking taylor expansion of 0.5 in k 0.734 * [backup-simplify]: Simplify 0.5 into 0.5 0.734 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.734 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.734 * [taylor]: Taking taylor expansion of k in k 0.734 * [backup-simplify]: Simplify 0 into 0 0.734 * [backup-simplify]: Simplify 1 into 1 0.734 * [backup-simplify]: Simplify (/ 1 1) into 1 0.734 * [taylor]: Taking taylor expansion of 1.0 in k 0.734 * [backup-simplify]: Simplify 1.0 into 1.0 0.734 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.734 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.734 * [taylor]: Taking taylor expansion of -2.0 in k 0.734 * [backup-simplify]: Simplify -2.0 into -2.0 0.734 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.734 * [taylor]: Taking taylor expansion of PI in k 0.734 * [backup-simplify]: Simplify PI into PI 0.734 * [taylor]: Taking taylor expansion of n in k 0.734 * [backup-simplify]: Simplify n into n 0.735 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.735 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.735 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.735 * [backup-simplify]: Simplify (+ 1 0) into 1 0.735 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.735 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.735 * [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)))))) 0.735 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.735 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.735 * [taylor]: Taking taylor expansion of -1 in k 0.735 * [backup-simplify]: Simplify -1 into -1 0.735 * [taylor]: Taking taylor expansion of k in k 0.735 * [backup-simplify]: Simplify 0 into 0 0.735 * [backup-simplify]: Simplify 1 into 1 0.736 * [backup-simplify]: Simplify (/ -1 1) into -1 0.736 * [backup-simplify]: Simplify (sqrt 0) into 0 0.737 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.737 * [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))))))) 0.737 * [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))))))) 0.737 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.737 * [taylor]: Taking taylor expansion of +nan.0 in n 0.737 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.737 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.737 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.737 * [taylor]: Taking taylor expansion of 0.5 in n 0.737 * [backup-simplify]: Simplify 0.5 into 0.5 0.737 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.737 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.737 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.737 * [taylor]: Taking taylor expansion of k in n 0.737 * [backup-simplify]: Simplify k into k 0.737 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.737 * [taylor]: Taking taylor expansion of 1.0 in n 0.737 * [backup-simplify]: Simplify 1.0 into 1.0 0.737 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.737 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.737 * [taylor]: Taking taylor expansion of -2.0 in n 0.737 * [backup-simplify]: Simplify -2.0 into -2.0 0.737 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.737 * [taylor]: Taking taylor expansion of PI in n 0.738 * [backup-simplify]: Simplify PI into PI 0.738 * [taylor]: Taking taylor expansion of n in n 0.738 * [backup-simplify]: Simplify 0 into 0 0.738 * [backup-simplify]: Simplify 1 into 1 0.738 * [backup-simplify]: Simplify (/ PI 1) into PI 0.738 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.739 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.739 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.740 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.741 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.741 * [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)))) 0.742 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.743 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.743 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.746 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.746 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 0.747 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 0.747 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.747 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.747 * [taylor]: Taking taylor expansion of +nan.0 in n 0.747 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.747 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.747 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.747 * [taylor]: Taking taylor expansion of 0.5 in n 0.747 * [backup-simplify]: Simplify 0.5 into 0.5 0.747 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.747 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.747 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.747 * [taylor]: Taking taylor expansion of k in n 0.747 * [backup-simplify]: Simplify k into k 0.747 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.747 * [taylor]: Taking taylor expansion of 1.0 in n 0.747 * [backup-simplify]: Simplify 1.0 into 1.0 0.747 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.747 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.747 * [taylor]: Taking taylor expansion of -2.0 in n 0.747 * [backup-simplify]: Simplify -2.0 into -2.0 0.747 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.747 * [taylor]: Taking taylor expansion of PI in n 0.747 * [backup-simplify]: Simplify PI into PI 0.747 * [taylor]: Taking taylor expansion of n in n 0.747 * [backup-simplify]: Simplify 0 into 0 0.747 * [backup-simplify]: Simplify 1 into 1 0.747 * [backup-simplify]: Simplify (/ PI 1) into PI 0.748 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.748 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.748 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.749 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.750 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.751 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.751 * [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))))) 0.752 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.753 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 0.754 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 0.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.755 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.756 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.756 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.756 * [backup-simplify]: Simplify (+ 0 0) into 0 0.757 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.757 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.758 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 0.760 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.761 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 0.761 * [backup-simplify]: Simplify 0 into 0 0.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.763 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.764 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 0.765 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 0.765 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.765 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.765 * [taylor]: Taking taylor expansion of +nan.0 in n 0.765 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.765 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.765 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.765 * [taylor]: Taking taylor expansion of 0.5 in n 0.765 * [backup-simplify]: Simplify 0.5 into 0.5 0.765 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.765 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.765 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.765 * [taylor]: Taking taylor expansion of k in n 0.765 * [backup-simplify]: Simplify k into k 0.765 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.765 * [taylor]: Taking taylor expansion of 1.0 in n 0.765 * [backup-simplify]: Simplify 1.0 into 1.0 0.765 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.765 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.765 * [taylor]: Taking taylor expansion of -2.0 in n 0.765 * [backup-simplify]: Simplify -2.0 into -2.0 0.765 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.765 * [taylor]: Taking taylor expansion of PI in n 0.765 * [backup-simplify]: Simplify PI into PI 0.765 * [taylor]: Taking taylor expansion of n in n 0.765 * [backup-simplify]: Simplify 0 into 0 0.765 * [backup-simplify]: Simplify 1 into 1 0.766 * [backup-simplify]: Simplify (/ PI 1) into PI 0.766 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.767 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.767 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.767 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.768 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.769 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.770 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.770 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.771 * [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))))))) 0.772 * [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 (/ 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)))))))))))) 0.775 * * * [progress]: simplifying candidates 0.777 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) 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(/ (- 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)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* 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h2)) (/ (sqrt h1) h2) (expm1 (* (* h0 h4) h3)) (log1p (* (* h0 h4) h3)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (expm1 (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (log1p (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (+ (- (log h2) (log (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (+ (log (/ h2 (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (log (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (exp (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (* (* (/ h2 (sqrt h1)) (/ h2 (sqrt h1))) (/ h2 (sqrt h1))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (* (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (sqrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (sqrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* h2 (pow (* (* h0 h4) h3) (/ h2 h0))) (* (sqrt h1) (pow (* (* h0 h4) h3) (/ h1 h0))) (* (sqrt (/ h2 (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (sqrt (/ h2 (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ h2 (sqrt h1)) (pow (* h0 h4) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (* (/ h2 (sqrt h1)) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ h2 (sqrt h1)) 1) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ 1 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ h2 h0))) (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (- (+ (* h7 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h7 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (+ (* h6 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* 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)) (- (+ (* 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)))))))))))) 0.787 * * [simplify]: iteration 0 : 981 enodes (cost 1502 ) 0.803 * * [simplify]: iteration 1 : 4021 enodes (cost 1398 ) 0.868 * * [simplify]: iteration 2 : 5003 enodes (cost 1383 ) 0.874 * * * [progress]: adding candidates to table 1.330 * * [progress]: iteration 2 / 4 1.330 * * * [progress]: picking best candidate 1.361 * * * * [pick]: Picked # 1.361 * * * [progress]: localizing error 1.374 * * * [progress]: generating rewritten candidates 1.374 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 2) 1.396 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 2 1) 1.413 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 1.439 * * * [progress]: generating series expansions 1.439 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 2) 1.439 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.439 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.439 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.440 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.440 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.440 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.440 * [taylor]: Taking taylor expansion of 0.5 in k 1.440 * [backup-simplify]: Simplify 0.5 into 0.5 1.440 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.440 * [taylor]: Taking taylor expansion of 1.0 in k 1.440 * [backup-simplify]: Simplify 1.0 into 1.0 1.440 * [taylor]: Taking taylor expansion of k in k 1.440 * [backup-simplify]: Simplify 0 into 0 1.440 * [backup-simplify]: Simplify 1 into 1 1.440 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.440 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.440 * [taylor]: Taking taylor expansion of 2.0 in k 1.440 * [backup-simplify]: Simplify 2.0 into 2.0 1.440 * [taylor]: Taking taylor expansion of (* n PI) in k 1.440 * [taylor]: Taking taylor expansion of n in k 1.440 * [backup-simplify]: Simplify n into n 1.440 * [taylor]: Taking taylor expansion of PI in k 1.440 * [backup-simplify]: Simplify PI into PI 1.440 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.440 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.440 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.440 * [backup-simplify]: Simplify (- 0) into 0 1.440 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.441 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.441 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.441 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.441 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.441 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.441 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.441 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.441 * [taylor]: Taking taylor expansion of 0.5 in n 1.441 * [backup-simplify]: Simplify 0.5 into 0.5 1.441 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.441 * [taylor]: Taking taylor expansion of 1.0 in n 1.441 * [backup-simplify]: Simplify 1.0 into 1.0 1.441 * [taylor]: Taking taylor expansion of k in n 1.441 * [backup-simplify]: Simplify k into k 1.441 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.441 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.441 * [taylor]: Taking taylor expansion of 2.0 in n 1.441 * [backup-simplify]: Simplify 2.0 into 2.0 1.441 * [taylor]: Taking taylor expansion of (* n PI) in n 1.441 * [taylor]: Taking taylor expansion of n in n 1.441 * [backup-simplify]: Simplify 0 into 0 1.441 * [backup-simplify]: Simplify 1 into 1 1.441 * [taylor]: Taking taylor expansion of PI in n 1.441 * [backup-simplify]: Simplify PI into PI 1.442 * [backup-simplify]: Simplify (* 0 PI) into 0 1.442 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.443 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.444 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.444 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.444 * [backup-simplify]: Simplify (- k) into (- k) 1.444 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.444 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.445 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.446 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.447 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.447 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.447 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.447 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.447 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.447 * [taylor]: Taking taylor expansion of 0.5 in n 1.447 * [backup-simplify]: Simplify 0.5 into 0.5 1.447 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.447 * [taylor]: Taking taylor expansion of 1.0 in n 1.447 * [backup-simplify]: Simplify 1.0 into 1.0 1.447 * [taylor]: Taking taylor expansion of k in n 1.447 * [backup-simplify]: Simplify k into k 1.447 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.447 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.447 * [taylor]: Taking taylor expansion of 2.0 in n 1.447 * [backup-simplify]: Simplify 2.0 into 2.0 1.447 * [taylor]: Taking taylor expansion of (* n PI) in n 1.447 * [taylor]: Taking taylor expansion of n in n 1.447 * [backup-simplify]: Simplify 0 into 0 1.447 * [backup-simplify]: Simplify 1 into 1 1.447 * [taylor]: Taking taylor expansion of PI in n 1.447 * [backup-simplify]: Simplify PI into PI 1.447 * [backup-simplify]: Simplify (* 0 PI) into 0 1.448 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.449 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.449 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.450 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.450 * [backup-simplify]: Simplify (- k) into (- k) 1.450 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.450 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.451 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.452 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.452 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.452 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.452 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.452 * [taylor]: Taking taylor expansion of 0.5 in k 1.452 * [backup-simplify]: Simplify 0.5 into 0.5 1.453 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.453 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.453 * [taylor]: Taking taylor expansion of 1.0 in k 1.453 * [backup-simplify]: Simplify 1.0 into 1.0 1.453 * [taylor]: Taking taylor expansion of k in k 1.453 * [backup-simplify]: Simplify 0 into 0 1.453 * [backup-simplify]: Simplify 1 into 1 1.453 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.453 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.453 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.453 * [taylor]: Taking taylor expansion of 2.0 in k 1.453 * [backup-simplify]: Simplify 2.0 into 2.0 1.453 * [taylor]: Taking taylor expansion of PI in k 1.453 * [backup-simplify]: Simplify PI into PI 1.453 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.454 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.454 * [taylor]: Taking taylor expansion of (log n) in k 1.454 * [taylor]: Taking taylor expansion of n in k 1.454 * [backup-simplify]: Simplify n into n 1.454 * [backup-simplify]: Simplify (log n) into (log n) 1.454 * [backup-simplify]: Simplify (- 0) into 0 1.454 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.455 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.455 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.456 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.457 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.457 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.458 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.459 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.460 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.460 * [backup-simplify]: Simplify (- 0) into 0 1.460 * [backup-simplify]: Simplify (+ 0 0) into 0 1.460 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.461 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.462 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.463 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.463 * [taylor]: Taking taylor expansion of 0 in k 1.463 * [backup-simplify]: Simplify 0 into 0 1.463 * [backup-simplify]: Simplify 0 into 0 1.464 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.464 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.465 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.465 * [backup-simplify]: Simplify (+ 0 0) into 0 1.465 * [backup-simplify]: Simplify (- 1) into -1 1.466 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.467 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.468 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1.470 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.472 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.472 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.473 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.475 * [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 1.475 * [backup-simplify]: Simplify (- 0) into 0 1.475 * [backup-simplify]: Simplify (+ 0 0) into 0 1.476 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.476 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.477 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.479 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.479 * [taylor]: Taking taylor expansion of 0 in k 1.479 * [backup-simplify]: Simplify 0 into 0 1.479 * [backup-simplify]: Simplify 0 into 0 1.479 * [backup-simplify]: Simplify 0 into 0 1.479 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.481 * [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 1.482 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.483 * [backup-simplify]: Simplify (+ 0 0) into 0 1.483 * [backup-simplify]: Simplify (- 0) into 0 1.483 * [backup-simplify]: Simplify (+ 0 0) into 0 1.484 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.486 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.488 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 1.491 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 1.497 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 1.498 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 1.498 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.498 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.498 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.498 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.498 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.498 * [taylor]: Taking taylor expansion of 0.5 in k 1.498 * [backup-simplify]: Simplify 0.5 into 0.5 1.498 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.498 * [taylor]: Taking taylor expansion of 1.0 in k 1.498 * [backup-simplify]: Simplify 1.0 into 1.0 1.498 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.498 * [taylor]: Taking taylor expansion of k in k 1.498 * [backup-simplify]: Simplify 0 into 0 1.498 * [backup-simplify]: Simplify 1 into 1 1.503 * [backup-simplify]: Simplify (/ 1 1) into 1 1.503 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.503 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.503 * [taylor]: Taking taylor expansion of 2.0 in k 1.503 * [backup-simplify]: Simplify 2.0 into 2.0 1.503 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.503 * [taylor]: Taking taylor expansion of PI in k 1.503 * [backup-simplify]: Simplify PI into PI 1.503 * [taylor]: Taking taylor expansion of n in k 1.503 * [backup-simplify]: Simplify n into n 1.503 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.503 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.503 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.503 * [backup-simplify]: Simplify (- 1) into -1 1.504 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.504 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.504 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.504 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.504 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.504 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.504 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.504 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.504 * [taylor]: Taking taylor expansion of 0.5 in n 1.504 * [backup-simplify]: Simplify 0.5 into 0.5 1.504 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.504 * [taylor]: Taking taylor expansion of 1.0 in n 1.504 * [backup-simplify]: Simplify 1.0 into 1.0 1.504 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.504 * [taylor]: Taking taylor expansion of k in n 1.504 * [backup-simplify]: Simplify k into k 1.504 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.504 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.504 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.504 * [taylor]: Taking taylor expansion of 2.0 in n 1.504 * [backup-simplify]: Simplify 2.0 into 2.0 1.504 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.504 * [taylor]: Taking taylor expansion of PI in n 1.504 * [backup-simplify]: Simplify PI into PI 1.504 * [taylor]: Taking taylor expansion of n in n 1.504 * [backup-simplify]: Simplify 0 into 0 1.504 * [backup-simplify]: Simplify 1 into 1 1.505 * [backup-simplify]: Simplify (/ PI 1) into PI 1.505 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.506 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.506 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.506 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.506 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.507 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.507 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.508 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.508 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.508 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.508 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.508 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.508 * [taylor]: Taking taylor expansion of 0.5 in n 1.508 * [backup-simplify]: Simplify 0.5 into 0.5 1.508 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.508 * [taylor]: Taking taylor expansion of 1.0 in n 1.508 * [backup-simplify]: Simplify 1.0 into 1.0 1.508 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.508 * [taylor]: Taking taylor expansion of k in n 1.508 * [backup-simplify]: Simplify k into k 1.508 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.508 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.508 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.509 * [taylor]: Taking taylor expansion of 2.0 in n 1.509 * [backup-simplify]: Simplify 2.0 into 2.0 1.509 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.509 * [taylor]: Taking taylor expansion of PI in n 1.509 * [backup-simplify]: Simplify PI into PI 1.509 * [taylor]: Taking taylor expansion of n in n 1.509 * [backup-simplify]: Simplify 0 into 0 1.509 * [backup-simplify]: Simplify 1 into 1 1.509 * [backup-simplify]: Simplify (/ PI 1) into PI 1.509 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.510 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.510 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.510 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.510 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.511 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.512 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.512 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.512 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.512 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.512 * [taylor]: Taking taylor expansion of 0.5 in k 1.512 * [backup-simplify]: Simplify 0.5 into 0.5 1.512 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.512 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.512 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.512 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.512 * [taylor]: Taking taylor expansion of 2.0 in k 1.513 * [backup-simplify]: Simplify 2.0 into 2.0 1.513 * [taylor]: Taking taylor expansion of PI in k 1.513 * [backup-simplify]: Simplify PI into PI 1.513 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.513 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.513 * [taylor]: Taking taylor expansion of (log n) in k 1.513 * [taylor]: Taking taylor expansion of n in k 1.513 * [backup-simplify]: Simplify n into n 1.514 * [backup-simplify]: Simplify (log n) into (log n) 1.514 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.514 * [taylor]: Taking taylor expansion of 1.0 in k 1.514 * [backup-simplify]: Simplify 1.0 into 1.0 1.514 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.514 * [taylor]: Taking taylor expansion of k in k 1.514 * [backup-simplify]: Simplify 0 into 0 1.514 * [backup-simplify]: Simplify 1 into 1 1.514 * [backup-simplify]: Simplify (/ 1 1) into 1 1.514 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.515 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.515 * [backup-simplify]: Simplify (- 1) into -1 1.515 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.516 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.516 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.517 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.518 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.518 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.519 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.520 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.520 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.520 * [backup-simplify]: Simplify (- 0) into 0 1.520 * [backup-simplify]: Simplify (+ 0 0) into 0 1.521 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.521 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.522 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.523 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.523 * [taylor]: Taking taylor expansion of 0 in k 1.523 * [backup-simplify]: Simplify 0 into 0 1.523 * [backup-simplify]: Simplify 0 into 0 1.523 * [backup-simplify]: Simplify 0 into 0 1.524 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.524 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.526 * [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 1.526 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.527 * [backup-simplify]: Simplify (- 0) into 0 1.527 * [backup-simplify]: Simplify (+ 0 0) into 0 1.527 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.528 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.529 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.530 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.530 * [taylor]: Taking taylor expansion of 0 in k 1.530 * [backup-simplify]: Simplify 0 into 0 1.530 * [backup-simplify]: Simplify 0 into 0 1.531 * [backup-simplify]: Simplify 0 into 0 1.531 * [backup-simplify]: Simplify 0 into 0 1.531 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.532 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.535 * [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 1.535 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.535 * [backup-simplify]: Simplify (- 0) into 0 1.535 * [backup-simplify]: Simplify (+ 0 0) into 0 1.536 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.537 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.538 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.540 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.540 * [taylor]: Taking taylor expansion of 0 in k 1.540 * [backup-simplify]: Simplify 0 into 0 1.540 * [backup-simplify]: Simplify 0 into 0 1.541 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 1.541 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 1.541 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.541 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.541 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.541 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.541 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.541 * [taylor]: Taking taylor expansion of 0.5 in k 1.541 * [backup-simplify]: Simplify 0.5 into 0.5 1.541 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.541 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.541 * [taylor]: Taking taylor expansion of k in k 1.541 * [backup-simplify]: Simplify 0 into 0 1.541 * [backup-simplify]: Simplify 1 into 1 1.542 * [backup-simplify]: Simplify (/ 1 1) into 1 1.542 * [taylor]: Taking taylor expansion of 1.0 in k 1.542 * [backup-simplify]: Simplify 1.0 into 1.0 1.542 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.542 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.542 * [taylor]: Taking taylor expansion of -2.0 in k 1.542 * [backup-simplify]: Simplify -2.0 into -2.0 1.542 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.542 * [taylor]: Taking taylor expansion of PI in k 1.542 * [backup-simplify]: Simplify PI into PI 1.542 * [taylor]: Taking taylor expansion of n in k 1.542 * [backup-simplify]: Simplify n into n 1.542 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.542 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.542 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.542 * [backup-simplify]: Simplify (+ 1 0) into 1 1.543 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.543 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.543 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.543 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.543 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.543 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.543 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.543 * [taylor]: Taking taylor expansion of 0.5 in n 1.543 * [backup-simplify]: Simplify 0.5 into 0.5 1.543 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.543 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.543 * [taylor]: Taking taylor expansion of k in n 1.543 * [backup-simplify]: Simplify k into k 1.543 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.543 * [taylor]: Taking taylor expansion of 1.0 in n 1.543 * [backup-simplify]: Simplify 1.0 into 1.0 1.543 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.543 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.543 * [taylor]: Taking taylor expansion of -2.0 in n 1.543 * [backup-simplify]: Simplify -2.0 into -2.0 1.543 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.543 * [taylor]: Taking taylor expansion of PI in n 1.543 * [backup-simplify]: Simplify PI into PI 1.543 * [taylor]: Taking taylor expansion of n in n 1.543 * [backup-simplify]: Simplify 0 into 0 1.543 * [backup-simplify]: Simplify 1 into 1 1.543 * [backup-simplify]: Simplify (/ PI 1) into PI 1.544 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.544 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.544 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.544 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.545 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.546 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.547 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.547 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.547 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.547 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.547 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.547 * [taylor]: Taking taylor expansion of 0.5 in n 1.547 * [backup-simplify]: Simplify 0.5 into 0.5 1.547 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.547 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.547 * [taylor]: Taking taylor expansion of k in n 1.547 * [backup-simplify]: Simplify k into k 1.547 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.547 * [taylor]: Taking taylor expansion of 1.0 in n 1.547 * [backup-simplify]: Simplify 1.0 into 1.0 1.547 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.547 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.547 * [taylor]: Taking taylor expansion of -2.0 in n 1.547 * [backup-simplify]: Simplify -2.0 into -2.0 1.547 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.547 * [taylor]: Taking taylor expansion of PI in n 1.547 * [backup-simplify]: Simplify PI into PI 1.547 * [taylor]: Taking taylor expansion of n in n 1.547 * [backup-simplify]: Simplify 0 into 0 1.547 * [backup-simplify]: Simplify 1 into 1 1.547 * [backup-simplify]: Simplify (/ PI 1) into PI 1.548 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.548 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.548 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.548 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.549 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.550 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.551 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.551 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.551 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.551 * [taylor]: Taking taylor expansion of 0.5 in k 1.551 * [backup-simplify]: Simplify 0.5 into 0.5 1.551 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.551 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.551 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.551 * [taylor]: Taking taylor expansion of k in k 1.551 * [backup-simplify]: Simplify 0 into 0 1.551 * [backup-simplify]: Simplify 1 into 1 1.551 * [backup-simplify]: Simplify (/ 1 1) into 1 1.551 * [taylor]: Taking taylor expansion of 1.0 in k 1.551 * [backup-simplify]: Simplify 1.0 into 1.0 1.551 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.551 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.551 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.551 * [taylor]: Taking taylor expansion of -2.0 in k 1.551 * [backup-simplify]: Simplify -2.0 into -2.0 1.551 * [taylor]: Taking taylor expansion of PI in k 1.551 * [backup-simplify]: Simplify PI into PI 1.552 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.552 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.552 * [taylor]: Taking taylor expansion of (log n) in k 1.552 * [taylor]: Taking taylor expansion of n in k 1.552 * [backup-simplify]: Simplify n into n 1.552 * [backup-simplify]: Simplify (log n) into (log n) 1.553 * [backup-simplify]: Simplify (+ 1 0) into 1 1.553 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.553 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.554 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.555 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.555 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.556 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.557 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.557 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.558 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.558 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.558 * [backup-simplify]: Simplify (+ 0 0) into 0 1.559 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.560 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.561 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.561 * [taylor]: Taking taylor expansion of 0 in k 1.561 * [backup-simplify]: Simplify 0 into 0 1.561 * [backup-simplify]: Simplify 0 into 0 1.561 * [backup-simplify]: Simplify 0 into 0 1.562 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.563 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.564 * [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 1.564 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.565 * [backup-simplify]: Simplify (+ 0 0) into 0 1.565 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.566 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.567 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.568 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.568 * [taylor]: Taking taylor expansion of 0 in k 1.568 * [backup-simplify]: Simplify 0 into 0 1.568 * [backup-simplify]: Simplify 0 into 0 1.568 * [backup-simplify]: Simplify 0 into 0 1.568 * [backup-simplify]: Simplify 0 into 0 1.569 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.570 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.573 * [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 1.573 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.573 * [backup-simplify]: Simplify (+ 0 0) into 0 1.574 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.575 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.576 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.577 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.577 * [taylor]: Taking taylor expansion of 0 in k 1.577 * [backup-simplify]: Simplify 0 into 0 1.577 * [backup-simplify]: Simplify 0 into 0 1.578 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 1.578 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 2 1) 1.579 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.579 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.579 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.579 * [taylor]: Taking taylor expansion of 2.0 in n 1.579 * [backup-simplify]: Simplify 2.0 into 2.0 1.579 * [taylor]: Taking taylor expansion of (* n PI) in n 1.579 * [taylor]: Taking taylor expansion of n in n 1.579 * [backup-simplify]: Simplify 0 into 0 1.579 * [backup-simplify]: Simplify 1 into 1 1.579 * [taylor]: Taking taylor expansion of PI in n 1.579 * [backup-simplify]: Simplify PI into PI 1.579 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.579 * [taylor]: Taking taylor expansion of 2.0 in n 1.579 * [backup-simplify]: Simplify 2.0 into 2.0 1.579 * [taylor]: Taking taylor expansion of (* n PI) in n 1.579 * [taylor]: Taking taylor expansion of n in n 1.579 * [backup-simplify]: Simplify 0 into 0 1.579 * [backup-simplify]: Simplify 1 into 1 1.579 * [taylor]: Taking taylor expansion of PI in n 1.579 * [backup-simplify]: Simplify PI into PI 1.579 * [backup-simplify]: Simplify (* 0 PI) into 0 1.579 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.579 * [backup-simplify]: Simplify 0 into 0 1.580 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.581 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.581 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.582 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.583 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.583 * [backup-simplify]: Simplify 0 into 0 1.583 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.584 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.584 * [backup-simplify]: Simplify 0 into 0 1.585 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.586 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.586 * [backup-simplify]: Simplify 0 into 0 1.586 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.587 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.587 * [backup-simplify]: Simplify 0 into 0 1.588 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.589 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.589 * [backup-simplify]: Simplify 0 into 0 1.590 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.591 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.591 * [backup-simplify]: Simplify 0 into 0 1.591 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.592 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.592 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.592 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.592 * [taylor]: Taking taylor expansion of 2.0 in n 1.592 * [backup-simplify]: Simplify 2.0 into 2.0 1.592 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.592 * [taylor]: Taking taylor expansion of PI in n 1.592 * [backup-simplify]: Simplify PI into PI 1.592 * [taylor]: Taking taylor expansion of n in n 1.592 * [backup-simplify]: Simplify 0 into 0 1.592 * [backup-simplify]: Simplify 1 into 1 1.592 * [backup-simplify]: Simplify (/ PI 1) into PI 1.592 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.592 * [taylor]: Taking taylor expansion of 2.0 in n 1.592 * [backup-simplify]: Simplify 2.0 into 2.0 1.592 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.592 * [taylor]: Taking taylor expansion of PI in n 1.592 * [backup-simplify]: Simplify PI into PI 1.592 * [taylor]: Taking taylor expansion of n in n 1.592 * [backup-simplify]: Simplify 0 into 0 1.592 * [backup-simplify]: Simplify 1 into 1 1.598 * [backup-simplify]: Simplify (/ PI 1) into PI 1.599 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.599 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.600 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.600 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.600 * [backup-simplify]: Simplify 0 into 0 1.601 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.601 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.601 * [backup-simplify]: Simplify 0 into 0 1.602 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.603 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.603 * [backup-simplify]: Simplify 0 into 0 1.603 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.604 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.604 * [backup-simplify]: Simplify 0 into 0 1.605 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.605 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.605 * [backup-simplify]: Simplify 0 into 0 1.606 * [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 1.607 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.607 * [backup-simplify]: Simplify 0 into 0 1.607 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.608 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.608 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.608 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.608 * [taylor]: Taking taylor expansion of -2.0 in n 1.608 * [backup-simplify]: Simplify -2.0 into -2.0 1.608 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.608 * [taylor]: Taking taylor expansion of PI in n 1.608 * [backup-simplify]: Simplify PI into PI 1.608 * [taylor]: Taking taylor expansion of n in n 1.608 * [backup-simplify]: Simplify 0 into 0 1.608 * [backup-simplify]: Simplify 1 into 1 1.608 * [backup-simplify]: Simplify (/ PI 1) into PI 1.608 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.608 * [taylor]: Taking taylor expansion of -2.0 in n 1.608 * [backup-simplify]: Simplify -2.0 into -2.0 1.608 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.608 * [taylor]: Taking taylor expansion of PI in n 1.608 * [backup-simplify]: Simplify PI into PI 1.608 * [taylor]: Taking taylor expansion of n in n 1.608 * [backup-simplify]: Simplify 0 into 0 1.608 * [backup-simplify]: Simplify 1 into 1 1.609 * [backup-simplify]: Simplify (/ PI 1) into PI 1.609 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.609 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.610 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.610 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.610 * [backup-simplify]: Simplify 0 into 0 1.611 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.611 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.612 * [backup-simplify]: Simplify 0 into 0 1.612 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.613 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.613 * [backup-simplify]: Simplify 0 into 0 1.613 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.614 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.614 * [backup-simplify]: Simplify 0 into 0 1.615 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.616 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.616 * [backup-simplify]: Simplify 0 into 0 1.616 * [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 1.617 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.617 * [backup-simplify]: Simplify 0 into 0 1.617 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.617 * * * * [progress]: [ 3 / 3 ] generating series at (2) 1.618 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 1.618 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (n k) around 0 1.618 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 1.618 * [taylor]: Taking taylor expansion of 1.0 in k 1.618 * [backup-simplify]: Simplify 1.0 into 1.0 1.618 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 1.618 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.618 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.618 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.618 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.618 * [taylor]: Taking taylor expansion of 0.5 in k 1.618 * [backup-simplify]: Simplify 0.5 into 0.5 1.618 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.618 * [taylor]: Taking taylor expansion of 1.0 in k 1.618 * [backup-simplify]: Simplify 1.0 into 1.0 1.618 * [taylor]: Taking taylor expansion of k in k 1.618 * [backup-simplify]: Simplify 0 into 0 1.618 * [backup-simplify]: Simplify 1 into 1 1.618 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.618 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.618 * [taylor]: Taking taylor expansion of 2.0 in k 1.618 * [backup-simplify]: Simplify 2.0 into 2.0 1.618 * [taylor]: Taking taylor expansion of (* n PI) in k 1.618 * [taylor]: Taking taylor expansion of n in k 1.618 * [backup-simplify]: Simplify n into n 1.618 * [taylor]: Taking taylor expansion of PI in k 1.618 * [backup-simplify]: Simplify PI into PI 1.618 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.618 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.619 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.619 * [backup-simplify]: Simplify (- 0) into 0 1.619 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.619 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.619 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.619 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.619 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.619 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.619 * [taylor]: Taking taylor expansion of k in k 1.619 * [backup-simplify]: Simplify 0 into 0 1.620 * [backup-simplify]: Simplify 1 into 1 1.620 * [backup-simplify]: Simplify (/ 1 1) into 1 1.620 * [backup-simplify]: Simplify (sqrt 0) into 0 1.621 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.621 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 1.621 * [taylor]: Taking taylor expansion of 1.0 in n 1.621 * [backup-simplify]: Simplify 1.0 into 1.0 1.621 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 1.621 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.621 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.621 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.621 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.621 * [taylor]: Taking taylor expansion of 0.5 in n 1.621 * [backup-simplify]: Simplify 0.5 into 0.5 1.621 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.621 * [taylor]: Taking taylor expansion of 1.0 in n 1.621 * [backup-simplify]: Simplify 1.0 into 1.0 1.621 * [taylor]: Taking taylor expansion of k in n 1.621 * [backup-simplify]: Simplify k into k 1.621 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.621 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.621 * [taylor]: Taking taylor expansion of 2.0 in n 1.621 * [backup-simplify]: Simplify 2.0 into 2.0 1.621 * [taylor]: Taking taylor expansion of (* n PI) in n 1.621 * [taylor]: Taking taylor expansion of n in n 1.621 * [backup-simplify]: Simplify 0 into 0 1.621 * [backup-simplify]: Simplify 1 into 1 1.621 * [taylor]: Taking taylor expansion of PI in n 1.621 * [backup-simplify]: Simplify PI into PI 1.621 * [backup-simplify]: Simplify (* 0 PI) into 0 1.622 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.623 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.624 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.624 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.624 * [backup-simplify]: Simplify (- k) into (- k) 1.624 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.624 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.625 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.626 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.627 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.627 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 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 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1.627 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.627 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1.627 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 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 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 1.627 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.627 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.627 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.627 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.627 * [taylor]: Taking taylor expansion of 0.5 in n 1.627 * [backup-simplify]: Simplify 0.5 into 0.5 1.627 * [taylor]: Taking taylor expansion of (- 1.0 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 k in n 1.627 * [backup-simplify]: Simplify k into k 1.627 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.627 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) 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 (* n PI) in n 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 1.627 * [taylor]: Taking taylor expansion of PI in n 1.627 * [backup-simplify]: Simplify PI into PI 1.627 * [backup-simplify]: Simplify (* 0 PI) into 0 1.628 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.629 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.630 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.630 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.630 * [backup-simplify]: Simplify (- k) into (- k) 1.630 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.630 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.631 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.632 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.633 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.633 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 1.633 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.633 * [taylor]: Taking taylor expansion of k in n 1.633 * [backup-simplify]: Simplify k into k 1.633 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.633 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1.633 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.633 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1.634 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 1.635 * [backup-simplify]: Simplify (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) into (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) 1.635 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) in k 1.635 * [taylor]: Taking taylor expansion of 1.0 in k 1.635 * [backup-simplify]: Simplify 1.0 into 1.0 1.635 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k 1.635 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.635 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.635 * [taylor]: Taking taylor expansion of k in k 1.635 * [backup-simplify]: Simplify 0 into 0 1.635 * [backup-simplify]: Simplify 1 into 1 1.635 * [backup-simplify]: Simplify (/ 1 1) into 1 1.635 * [backup-simplify]: Simplify (sqrt 0) into 0 1.636 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.636 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.636 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.636 * [taylor]: Taking taylor expansion of 0.5 in k 1.636 * [backup-simplify]: Simplify 0.5 into 0.5 1.636 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.636 * [taylor]: Taking taylor expansion of (- 1.0 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 k in k 1.636 * [backup-simplify]: Simplify 0 into 0 1.636 * [backup-simplify]: Simplify 1 into 1 1.636 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.636 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.636 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.636 * [taylor]: Taking taylor expansion of 2.0 in k 1.636 * [backup-simplify]: Simplify 2.0 into 2.0 1.636 * [taylor]: Taking taylor expansion of PI in k 1.636 * [backup-simplify]: Simplify PI into PI 1.637 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.637 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.637 * [taylor]: Taking taylor expansion of (log n) in k 1.637 * [taylor]: Taking taylor expansion of n in k 1.637 * [backup-simplify]: Simplify n into n 1.637 * [backup-simplify]: Simplify (log n) into (log n) 1.637 * [backup-simplify]: Simplify (- 0) into 0 1.638 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.638 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.639 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.640 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.640 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.641 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) into 0 1.641 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.641 * [backup-simplify]: Simplify 0 into 0 1.642 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.642 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.643 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.644 * [backup-simplify]: Simplify (- 0) into 0 1.644 * [backup-simplify]: Simplify (+ 0 0) into 0 1.644 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.645 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.646 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.647 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.648 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 1.649 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))) into 0 1.649 * [taylor]: Taking taylor expansion of 0 in k 1.649 * [backup-simplify]: Simplify 0 into 0 1.649 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.650 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.650 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.651 * [backup-simplify]: Simplify (+ 0 0) into 0 1.651 * [backup-simplify]: Simplify (- 1) into -1 1.651 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.652 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.653 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1.655 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.658 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.659 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.659 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.659 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.660 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1.660 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.661 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.663 * [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 1.663 * [backup-simplify]: Simplify (- 0) into 0 1.663 * [backup-simplify]: Simplify (+ 0 0) into 0 1.664 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.665 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.665 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.667 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.668 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 1.669 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))))) into 0 1.669 * [taylor]: Taking taylor expansion of 0 in k 1.669 * [backup-simplify]: Simplify 0 into 0 1.669 * [backup-simplify]: Simplify 0 into 0 1.670 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.671 * [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 1.672 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.673 * [backup-simplify]: Simplify (+ 0 0) into 0 1.673 * [backup-simplify]: Simplify (- 0) into 0 1.673 * [backup-simplify]: Simplify (+ 0 0) into 0 1.674 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.676 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.678 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 1.679 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.681 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.687 * [backup-simplify]: Simplify (+ (* 0 (* (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))))))) (+ (* +nan.0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) 1.697 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) 1.700 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) 1.700 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.701 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1.701 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.705 * [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 1.705 * [backup-simplify]: Simplify (- 0) into 0 1.705 * [backup-simplify]: Simplify (+ 0 0) into 0 1.706 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0 1.707 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.708 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.710 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.711 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 1.712 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))))) into 0 1.712 * [taylor]: Taking taylor expansion of 0 in k 1.712 * [backup-simplify]: Simplify 0 into 0 1.712 * [backup-simplify]: Simplify 0 into 0 1.712 * [backup-simplify]: Simplify 0 into 0 1.713 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.716 * [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 1.718 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 1.718 * [backup-simplify]: Simplify (+ 0 0) into 0 1.718 * [backup-simplify]: Simplify (- 0) into 0 1.718 * [backup-simplify]: Simplify (+ 0 0) into 0 1.720 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.721 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0 1.725 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n))) (* 0.020833333333333332 (pow (log n) 3))))))) 1.726 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.728 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.738 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n))) (* 0.020833333333333332 (pow (log n) 3)))))))) (+ (* +nan.0 (* (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))))))) (+ (* +nan.0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))) 1.749 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) 1.757 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) 1.768 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (pow k 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))))))))) 1.769 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 1.769 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (n k) around 0 1.769 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 1.769 * [taylor]: Taking taylor expansion of 1.0 in k 1.769 * [backup-simplify]: Simplify 1.0 into 1.0 1.769 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 1.769 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.769 * [taylor]: Taking taylor expansion of k in k 1.769 * [backup-simplify]: Simplify 0 into 0 1.769 * [backup-simplify]: Simplify 1 into 1 1.769 * [backup-simplify]: Simplify (sqrt 0) into 0 1.770 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.770 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.770 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.770 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.770 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.770 * [taylor]: Taking taylor expansion of 0.5 in k 1.770 * [backup-simplify]: Simplify 0.5 into 0.5 1.770 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.770 * [taylor]: Taking taylor expansion of 1.0 in k 1.770 * [backup-simplify]: Simplify 1.0 into 1.0 1.770 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.770 * [taylor]: Taking taylor expansion of k in k 1.770 * [backup-simplify]: Simplify 0 into 0 1.770 * [backup-simplify]: Simplify 1 into 1 1.770 * [backup-simplify]: Simplify (/ 1 1) into 1 1.770 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.770 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.770 * [taylor]: Taking taylor expansion of 2.0 in k 1.771 * [backup-simplify]: Simplify 2.0 into 2.0 1.771 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.771 * [taylor]: Taking taylor expansion of PI in k 1.771 * [backup-simplify]: Simplify PI into PI 1.771 * [taylor]: Taking taylor expansion of n in k 1.771 * [backup-simplify]: Simplify n into n 1.771 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.771 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.771 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.771 * [backup-simplify]: Simplify (- 1) into -1 1.771 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.771 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.772 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.772 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.772 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 1.772 * [taylor]: Taking taylor expansion of 1.0 in n 1.772 * [backup-simplify]: Simplify 1.0 into 1.0 1.772 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 1.772 * [taylor]: Taking taylor expansion of (sqrt k) in n 1.772 * [taylor]: Taking taylor expansion of k in n 1.772 * [backup-simplify]: Simplify k into k 1.772 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 1.772 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 1.772 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.772 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.772 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.772 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.772 * [taylor]: Taking taylor expansion of 0.5 in n 1.772 * [backup-simplify]: Simplify 0.5 into 0.5 1.772 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.772 * [taylor]: Taking taylor expansion of 1.0 in n 1.772 * [backup-simplify]: Simplify 1.0 into 1.0 1.772 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.772 * [taylor]: Taking taylor expansion of k in n 1.772 * [backup-simplify]: Simplify k into k 1.772 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.772 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 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 1.773 * [backup-simplify]: Simplify (/ PI 1) into PI 1.773 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.773 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.774 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.774 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.774 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.774 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.775 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.776 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.776 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 1.776 * [taylor]: Taking taylor expansion of 1.0 in n 1.776 * [backup-simplify]: Simplify 1.0 into 1.0 1.776 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 1.776 * [taylor]: Taking taylor expansion of (sqrt k) in n 1.776 * [taylor]: Taking taylor expansion of k in n 1.776 * [backup-simplify]: Simplify k into k 1.776 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 1.776 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 1.776 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.776 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.776 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.776 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.776 * [taylor]: Taking taylor expansion of 0.5 in n 1.776 * [backup-simplify]: Simplify 0.5 into 0.5 1.776 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.776 * [taylor]: Taking taylor expansion of 1.0 in n 1.776 * [backup-simplify]: Simplify 1.0 into 1.0 1.776 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.776 * [taylor]: Taking taylor expansion of k in n 1.776 * [backup-simplify]: Simplify k into k 1.776 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.776 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.776 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.776 * [taylor]: Taking taylor expansion of 2.0 in n 1.776 * [backup-simplify]: Simplify 2.0 into 2.0 1.776 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.776 * [taylor]: Taking taylor expansion of PI in n 1.776 * [backup-simplify]: Simplify PI into PI 1.776 * [taylor]: Taking taylor expansion of n in n 1.776 * [backup-simplify]: Simplify 0 into 0 1.776 * [backup-simplify]: Simplify 1 into 1 1.777 * [backup-simplify]: Simplify (/ PI 1) into PI 1.777 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.778 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.778 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.778 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.778 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.779 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.779 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.780 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.781 * [backup-simplify]: Simplify (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 1.782 * [backup-simplify]: Simplify (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 1.782 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) in k 1.782 * [taylor]: Taking taylor expansion of 1.0 in k 1.782 * [backup-simplify]: Simplify 1.0 into 1.0 1.782 * [taylor]: Taking taylor expansion of (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) in k 1.782 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.782 * [taylor]: Taking taylor expansion of k in k 1.782 * [backup-simplify]: Simplify 0 into 0 1.782 * [backup-simplify]: Simplify 1 into 1 1.782 * [backup-simplify]: Simplify (sqrt 0) into 0 1.788 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.788 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.788 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.789 * [taylor]: Taking taylor expansion of 0.5 in k 1.789 * [backup-simplify]: Simplify 0.5 into 0.5 1.789 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.789 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.789 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.789 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.789 * [taylor]: Taking taylor expansion of 2.0 in k 1.789 * [backup-simplify]: Simplify 2.0 into 2.0 1.789 * [taylor]: Taking taylor expansion of PI in k 1.789 * [backup-simplify]: Simplify PI into PI 1.789 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.790 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.790 * [taylor]: Taking taylor expansion of (log n) in k 1.790 * [taylor]: Taking taylor expansion of n in k 1.790 * [backup-simplify]: Simplify n into n 1.790 * [backup-simplify]: Simplify (log n) into (log n) 1.790 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.790 * [taylor]: Taking taylor expansion of 1.0 in k 1.790 * [backup-simplify]: Simplify 1.0 into 1.0 1.790 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.790 * [taylor]: Taking taylor expansion of k in k 1.790 * [backup-simplify]: Simplify 0 into 0 1.790 * [backup-simplify]: Simplify 1 into 1 1.790 * [backup-simplify]: Simplify (/ 1 1) into 1 1.790 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.791 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.791 * [backup-simplify]: Simplify (- 1) into -1 1.791 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.792 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.792 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.793 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.794 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into 0 1.794 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.794 * [backup-simplify]: Simplify 0 into 0 1.795 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.795 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.796 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.796 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.797 * [backup-simplify]: Simplify (- 0) into 0 1.797 * [backup-simplify]: Simplify (+ 0 0) into 0 1.797 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.798 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.799 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.800 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.801 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 1.802 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 1.802 * [taylor]: Taking taylor expansion of 0 in k 1.802 * [backup-simplify]: Simplify 0 into 0 1.802 * [backup-simplify]: Simplify 0 into 0 1.803 * [backup-simplify]: Simplify (+ (* 0 0) (* +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))))))) 1.804 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 1.805 * [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))))))) 1.805 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.806 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.808 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.808 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.808 * [backup-simplify]: Simplify (- 0) into 0 1.808 * [backup-simplify]: Simplify (+ 0 0) into 0 1.809 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.810 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.811 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.812 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.812 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1.813 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 1.815 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0 1.815 * [taylor]: Taking taylor expansion of 0 in k 1.815 * [backup-simplify]: Simplify 0 into 0 1.815 * [backup-simplify]: Simplify 0 into 0 1.815 * [backup-simplify]: Simplify 0 into 0 1.816 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.818 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +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))))))) 1.819 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 1.820 * [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))))))) 1.821 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.822 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.824 * [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 1.825 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.825 * [backup-simplify]: Simplify (- 0) into 0 1.825 * [backup-simplify]: Simplify (+ 0 0) into 0 1.826 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.827 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.828 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.829 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.830 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1.831 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0 1.832 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))))) into 0 1.832 * [taylor]: Taking taylor expansion of 0 in k 1.832 * [backup-simplify]: Simplify 0 into 0 1.832 * [backup-simplify]: Simplify 0 into 0 1.832 * [backup-simplify]: Simplify 0 into 0 1.832 * [backup-simplify]: Simplify 0 into 0 1.835 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.836 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +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))))))) 1.838 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 1.839 * [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))))))) 1.842 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) 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)))))))) 1.842 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 1.842 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (n k) around 0 1.843 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 1.843 * [taylor]: Taking taylor expansion of 1.0 in k 1.843 * [backup-simplify]: Simplify 1.0 into 1.0 1.843 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 1.843 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.843 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.843 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.843 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.843 * [taylor]: Taking taylor expansion of 0.5 in k 1.843 * [backup-simplify]: Simplify 0.5 into 0.5 1.843 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.843 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.843 * [taylor]: Taking taylor expansion of k in k 1.843 * [backup-simplify]: Simplify 0 into 0 1.843 * [backup-simplify]: Simplify 1 into 1 1.843 * [backup-simplify]: Simplify (/ 1 1) into 1 1.843 * [taylor]: Taking taylor expansion of 1.0 in k 1.843 * [backup-simplify]: Simplify 1.0 into 1.0 1.843 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.843 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.843 * [taylor]: Taking taylor expansion of -2.0 in k 1.843 * [backup-simplify]: Simplify -2.0 into -2.0 1.843 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.843 * [taylor]: Taking taylor expansion of PI in k 1.843 * [backup-simplify]: Simplify PI into PI 1.843 * [taylor]: Taking taylor expansion of n in k 1.843 * [backup-simplify]: Simplify n into n 1.843 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.843 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.843 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.844 * [backup-simplify]: Simplify (+ 1 0) into 1 1.844 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.844 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.844 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.844 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.844 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.844 * [taylor]: Taking taylor expansion of -1 in k 1.844 * [backup-simplify]: Simplify -1 into -1 1.844 * [taylor]: Taking taylor expansion of k in k 1.844 * [backup-simplify]: Simplify 0 into 0 1.844 * [backup-simplify]: Simplify 1 into 1 1.845 * [backup-simplify]: Simplify (/ -1 1) into -1 1.845 * [backup-simplify]: Simplify (sqrt 0) into 0 1.846 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.846 * [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))))))) 1.846 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 1.846 * [taylor]: Taking taylor expansion of 1.0 in n 1.846 * [backup-simplify]: Simplify 1.0 into 1.0 1.846 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 1.846 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.846 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.846 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.846 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.846 * [taylor]: Taking taylor expansion of 0.5 in n 1.846 * [backup-simplify]: Simplify 0.5 into 0.5 1.846 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.846 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.846 * [taylor]: Taking taylor expansion of k in n 1.846 * [backup-simplify]: Simplify k into k 1.846 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.846 * [taylor]: Taking taylor expansion of 1.0 in n 1.846 * [backup-simplify]: Simplify 1.0 into 1.0 1.846 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.846 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.846 * [taylor]: Taking taylor expansion of -2.0 in n 1.846 * [backup-simplify]: Simplify -2.0 into -2.0 1.846 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.846 * [taylor]: Taking taylor expansion of PI in n 1.846 * [backup-simplify]: Simplify PI into PI 1.846 * [taylor]: Taking taylor expansion of n in n 1.846 * [backup-simplify]: Simplify 0 into 0 1.846 * [backup-simplify]: Simplify 1 into 1 1.847 * [backup-simplify]: Simplify (/ PI 1) into PI 1.847 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.847 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.848 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.848 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.848 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.849 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.850 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.850 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 1.850 * [taylor]: Taking taylor expansion of (/ -1 k) in n 1.850 * [taylor]: Taking taylor expansion of -1 in n 1.850 * [backup-simplify]: Simplify -1 into -1 1.850 * [taylor]: Taking taylor expansion of k in n 1.850 * [backup-simplify]: Simplify k into k 1.850 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 1.850 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1.850 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1.850 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1.851 * [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))) 1.851 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 1.851 * [taylor]: Taking taylor expansion of 1.0 in n 1.851 * [backup-simplify]: Simplify 1.0 into 1.0 1.851 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 1.851 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.851 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.851 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.851 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.851 * [taylor]: Taking taylor expansion of 0.5 in n 1.851 * [backup-simplify]: Simplify 0.5 into 0.5 1.851 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.851 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.851 * [taylor]: Taking taylor expansion of k in n 1.851 * [backup-simplify]: Simplify k into k 1.851 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.851 * [taylor]: Taking taylor expansion of 1.0 in n 1.851 * [backup-simplify]: Simplify 1.0 into 1.0 1.851 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.851 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.851 * [taylor]: Taking taylor expansion of -2.0 in n 1.851 * [backup-simplify]: Simplify -2.0 into -2.0 1.851 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.851 * [taylor]: Taking taylor expansion of PI in n 1.851 * [backup-simplify]: Simplify PI into PI 1.851 * [taylor]: Taking taylor expansion of n in n 1.851 * [backup-simplify]: Simplify 0 into 0 1.851 * [backup-simplify]: Simplify 1 into 1 1.852 * [backup-simplify]: Simplify (/ PI 1) into PI 1.852 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.853 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.853 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.853 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.854 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.854 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.855 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.855 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 1.855 * [taylor]: Taking taylor expansion of (/ -1 k) in n 1.855 * [taylor]: Taking taylor expansion of -1 in n 1.855 * [backup-simplify]: Simplify -1 into -1 1.855 * [taylor]: Taking taylor expansion of k in n 1.855 * [backup-simplify]: Simplify k into k 1.855 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 1.855 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1.855 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1.855 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1.856 * [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))) 1.857 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))) 1.857 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))) in k 1.857 * [taylor]: Taking taylor expansion of 1.0 in k 1.857 * [backup-simplify]: Simplify 1.0 into 1.0 1.857 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) in k 1.857 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.857 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.857 * [taylor]: Taking taylor expansion of 0.5 in k 1.857 * [backup-simplify]: Simplify 0.5 into 0.5 1.857 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.857 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.857 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.857 * [taylor]: Taking taylor expansion of k in k 1.857 * [backup-simplify]: Simplify 0 into 0 1.857 * [backup-simplify]: Simplify 1 into 1 1.857 * [backup-simplify]: Simplify (/ 1 1) into 1 1.857 * [taylor]: Taking taylor expansion of 1.0 in k 1.857 * [backup-simplify]: Simplify 1.0 into 1.0 1.857 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.857 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.857 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.858 * [taylor]: Taking taylor expansion of -2.0 in k 1.858 * [backup-simplify]: Simplify -2.0 into -2.0 1.858 * [taylor]: Taking taylor expansion of PI in k 1.858 * [backup-simplify]: Simplify PI into PI 1.858 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.858 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.859 * [taylor]: Taking taylor expansion of (log n) in k 1.859 * [taylor]: Taking taylor expansion of n in k 1.859 * [backup-simplify]: Simplify n into n 1.859 * [backup-simplify]: Simplify (log n) into (log n) 1.859 * [backup-simplify]: Simplify (+ 1 0) into 1 1.859 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.860 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.860 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.861 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.861 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.862 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.862 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.862 * [taylor]: Taking taylor expansion of -1 in k 1.862 * [backup-simplify]: Simplify -1 into -1 1.862 * [taylor]: Taking taylor expansion of k in k 1.862 * [backup-simplify]: Simplify 0 into 0 1.862 * [backup-simplify]: Simplify 1 into 1 1.862 * [backup-simplify]: Simplify (/ -1 1) into -1 1.862 * [backup-simplify]: Simplify (sqrt 0) into 0 1.863 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.864 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 1.864 * [backup-simplify]: Simplify (* 1.0 (* +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)))))) 1.865 * [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)))))) 1.866 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.866 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.867 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.867 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.867 * [backup-simplify]: Simplify (+ 0 0) into 0 1.868 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.869 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.869 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.870 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.871 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1.872 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))))) into 0 1.872 * [taylor]: Taking taylor expansion of 0 in k 1.872 * [backup-simplify]: Simplify 0 into 0 1.872 * [backup-simplify]: Simplify 0 into 0 1.873 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.875 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.876 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 1.877 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (* 0 (* +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))))))) 1.878 * [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))))))) 1.879 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.885 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.887 * [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 1.887 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.887 * [backup-simplify]: Simplify (+ 0 0) into 0 1.888 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.888 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.889 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.891 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.891 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.891 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1.892 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1.894 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0 1.894 * [taylor]: Taking taylor expansion of 0 in k 1.894 * [backup-simplify]: Simplify 0 into 0 1.894 * [backup-simplify]: Simplify 0 into 0 1.894 * [backup-simplify]: Simplify 0 into 0 1.894 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.897 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.899 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 1.901 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (* 0 (* +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))))))) 1.902 * [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))))))) 1.905 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +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)))))))))))) 1.905 * * * [progress]: simplifying candidates 1.907 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (log1p (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (- (+ (log 1.0) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k))) (- (+ (log 1.0) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k))) (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k))) (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k))) (- (+ (log 1.0) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k))) (- (log (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k))) (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (exp (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* (* (* 1.0 1.0) 1.0) (* (* (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 k) (sqrt k)) (sqrt k))) (/ (* (* (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (* (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (- (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (- (sqrt k)) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))) (/ 1.0 (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ 1.0 (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ 1.0 1) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt k) (cbrt k)))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ 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 (* (pow k 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 1.907 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (log1p (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0)) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0)) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0)) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0)) (* 1 (/ (- h2 h1) h0)) (* 1 (/ (- h2 h1) h0)) (* 1 (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ h2 h0)) (pow (* (* h0 h4) h3) (/ h1 h0)) (pow (* (* h0 h4) h3) (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0)))) (pow (* (* h0 h4) h3) (sqrt (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 h4) h3) (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0))) (pow (* (* h0 h4) h3) (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1)) (pow (* (* h0 h4) h3) (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 h4) h3) (/ (sqrt (- h2 h1)) (sqrt h0))) (pow (* (* h0 h4) h3) (/ (sqrt (- h2 h1)) 1)) (pow (* (* h0 h4) h3) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 h4) h3) (/ 1 (sqrt h0))) (pow (* (* h0 h4) h3) (/ 1 1)) (pow (* (* h0 h4) h3) (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 h4) h3) (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0))) (pow (* (* h0 h4) h3) (/ (+ (sqrt h2) (sqrt h1)) 1)) (pow (* (* h0 h4) h3) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 h4) h3) (/ 1 (sqrt h0))) (pow (* (* h0 h4) h3) (/ 1 1)) (pow (* (* h0 h4) h3) 1) (pow (* (* h0 h4) h3) (- h2 h1)) (pow (* h0 h4) (/ (- h2 h1) h0)) (pow h3 (/ (- h2 h1) h0)) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (exp (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (expm1 (* (* h0 h4) h3)) (log1p (* (* h0 h4) h3)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (expm1 (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1))) (log1p (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1))) (- (+ (log h2) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (log (sqrt h1))) (- (+ (log h2) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (log (sqrt h1))) (- (+ (log h2) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (log (sqrt h1))) (- (+ (log h2) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (log (sqrt h1))) (- (+ (log h2) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (log (sqrt h1))) (- (log (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (log (sqrt h1))) (log (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1))) (exp (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1))) (/ (* (* (* h2 h2) h2) (* (* (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (/ (* (* (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (cbrt (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1))) (cbrt (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1)))) (cbrt (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1))) (* (* (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1)) (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1))) (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1))) (sqrt (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1))) (sqrt (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt h1))) (- (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (- (sqrt h1)) (/ h2 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (cbrt (sqrt h1))) (/ h2 (sqrt (* (cbrt h1) (cbrt h1)))) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (sqrt (cbrt h1))) (/ h2 (sqrt (sqrt h1))) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (sqrt (sqrt h1))) (/ h2 (sqrt 1)) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (sqrt h1)) (/ h2 (sqrt (sqrt h1))) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (sqrt (sqrt h1))) (/ h2 1) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (sqrt h1)) (/ 1 (sqrt h1)) (/ (sqrt h1) (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt (sqrt h1))) (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt 1)) (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (sqrt (sqrt h1))) (/ (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) 1) (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (sqrt h1) (pow (* (* h0 h4) h3) (/ 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 (* (pow h1 2) (exp (* h5 (+ (log (* h0 h4)) (log h3)))))) (- (+ (* h9 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))) (- (+ (* h9 (* (pow h1 2) (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (- (+ (* h9 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))) (- (+ (* h9 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (- (+ (* h9 (* h1 (exp (* h5 (+ (log (* h0 h4)) (log h3)))))) (- (+ (* h9 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (- (+ (* h9 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (- (+ (* h9 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (- (* h9 (exp (* h5 (+ (log (* h0 h4)) (log h3)))))))))))))))))))))))) (- (+ (* 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)))))))))))) 1.914 * * [simplify]: iteration 0 : 732 enodes (cost 973 ) 1.926 * * [simplify]: iteration 1 : 3046 enodes (cost 872 ) 1.978 * * [simplify]: iteration 2 : 5001 enodes (cost 836 ) 1.982 * * * [progress]: adding candidates to table 2.235 * * [progress]: iteration 3 / 4 2.235 * * * [progress]: picking best candidate 2.264 * * * * [pick]: Picked # 2.264 * * * [progress]: localizing error 2.277 * * * [progress]: generating rewritten candidates 2.277 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 2.298 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 2.315 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 2.339 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 2.364 * * * [progress]: generating series expansions 2.364 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 2.365 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 2.365 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.365 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.365 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.365 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.365 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.365 * [taylor]: Taking taylor expansion of 0.5 in k 2.365 * [backup-simplify]: Simplify 0.5 into 0.5 2.365 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.365 * [taylor]: Taking taylor expansion of 1.0 in k 2.365 * [backup-simplify]: Simplify 1.0 into 1.0 2.365 * [taylor]: Taking taylor expansion of k in k 2.365 * [backup-simplify]: Simplify 0 into 0 2.365 * [backup-simplify]: Simplify 1 into 1 2.365 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.365 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.365 * [taylor]: Taking taylor expansion of 2.0 in k 2.365 * [backup-simplify]: Simplify 2.0 into 2.0 2.365 * [taylor]: Taking taylor expansion of (* n PI) in k 2.365 * [taylor]: Taking taylor expansion of n in k 2.365 * [backup-simplify]: Simplify n into n 2.365 * [taylor]: Taking taylor expansion of PI in k 2.365 * [backup-simplify]: Simplify PI into PI 2.365 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.365 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.365 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.366 * [backup-simplify]: Simplify (- 0) into 0 2.366 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.366 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.366 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.366 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.366 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.366 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.366 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.366 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.366 * [taylor]: Taking taylor expansion of 0.5 in n 2.366 * [backup-simplify]: Simplify 0.5 into 0.5 2.366 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.366 * [taylor]: Taking taylor expansion of 1.0 in n 2.366 * [backup-simplify]: Simplify 1.0 into 1.0 2.366 * [taylor]: Taking taylor expansion of k in n 2.367 * [backup-simplify]: Simplify k into k 2.367 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.367 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.367 * [taylor]: Taking taylor expansion of 2.0 in n 2.367 * [backup-simplify]: Simplify 2.0 into 2.0 2.367 * [taylor]: Taking taylor expansion of (* n PI) in n 2.367 * [taylor]: Taking taylor expansion of n in n 2.367 * [backup-simplify]: Simplify 0 into 0 2.367 * [backup-simplify]: Simplify 1 into 1 2.367 * [taylor]: Taking taylor expansion of PI in n 2.367 * [backup-simplify]: Simplify PI into PI 2.367 * [backup-simplify]: Simplify (* 0 PI) into 0 2.367 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.368 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.369 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.370 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.370 * [backup-simplify]: Simplify (- k) into (- k) 2.370 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.370 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.371 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.371 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.372 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.372 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.372 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.372 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.372 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.372 * [taylor]: Taking taylor expansion of 0.5 in n 2.372 * [backup-simplify]: Simplify 0.5 into 0.5 2.372 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.372 * [taylor]: Taking taylor expansion of 1.0 in n 2.372 * [backup-simplify]: Simplify 1.0 into 1.0 2.372 * [taylor]: Taking taylor expansion of k in n 2.372 * [backup-simplify]: Simplify k into k 2.372 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.372 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.372 * [taylor]: Taking taylor expansion of 2.0 in n 2.372 * [backup-simplify]: Simplify 2.0 into 2.0 2.372 * [taylor]: Taking taylor expansion of (* n PI) in n 2.372 * [taylor]: Taking taylor expansion of n in n 2.372 * [backup-simplify]: Simplify 0 into 0 2.372 * [backup-simplify]: Simplify 1 into 1 2.372 * [taylor]: Taking taylor expansion of PI in n 2.372 * [backup-simplify]: Simplify PI into PI 2.373 * [backup-simplify]: Simplify (* 0 PI) into 0 2.373 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.374 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.375 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.375 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.375 * [backup-simplify]: Simplify (- k) into (- k) 2.376 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.376 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.376 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.377 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.378 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.378 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.378 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.378 * [taylor]: Taking taylor expansion of 0.5 in k 2.378 * [backup-simplify]: Simplify 0.5 into 0.5 2.378 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.378 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.378 * [taylor]: Taking taylor expansion of 1.0 in k 2.378 * [backup-simplify]: Simplify 1.0 into 1.0 2.378 * [taylor]: Taking taylor expansion of k in k 2.378 * [backup-simplify]: Simplify 0 into 0 2.378 * [backup-simplify]: Simplify 1 into 1 2.378 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.378 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.378 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.378 * [taylor]: Taking taylor expansion of 2.0 in k 2.378 * [backup-simplify]: Simplify 2.0 into 2.0 2.378 * [taylor]: Taking taylor expansion of PI in k 2.378 * [backup-simplify]: Simplify PI into PI 2.379 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.379 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.379 * [taylor]: Taking taylor expansion of (log n) in k 2.379 * [taylor]: Taking taylor expansion of n in k 2.379 * [backup-simplify]: Simplify n into n 2.379 * [backup-simplify]: Simplify (log n) into (log n) 2.379 * [backup-simplify]: Simplify (- 0) into 0 2.380 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.381 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.381 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.382 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 2.383 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.383 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.384 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.384 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.385 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.386 * [backup-simplify]: Simplify (- 0) into 0 2.386 * [backup-simplify]: Simplify (+ 0 0) into 0 2.386 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 2.387 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.388 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.389 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.389 * [taylor]: Taking taylor expansion of 0 in k 2.389 * [backup-simplify]: Simplify 0 into 0 2.389 * [backup-simplify]: Simplify 0 into 0 2.389 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.390 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.391 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.391 * [backup-simplify]: Simplify (+ 0 0) into 0 2.391 * [backup-simplify]: Simplify (- 1) into -1 2.392 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.393 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.394 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2.396 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 2.403 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 2.404 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.404 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.406 * [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 2.406 * [backup-simplify]: Simplify (- 0) into 0 2.406 * [backup-simplify]: Simplify (+ 0 0) into 0 2.407 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.408 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.409 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.410 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.410 * [taylor]: Taking taylor expansion of 0 in k 2.410 * [backup-simplify]: Simplify 0 into 0 2.410 * [backup-simplify]: Simplify 0 into 0 2.410 * [backup-simplify]: Simplify 0 into 0 2.411 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.412 * [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 2.413 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.414 * [backup-simplify]: Simplify (+ 0 0) into 0 2.414 * [backup-simplify]: Simplify (- 0) into 0 2.414 * [backup-simplify]: Simplify (+ 0 0) into 0 2.415 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.417 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.419 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.422 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.428 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.429 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 2.429 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.429 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.429 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.429 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.429 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.429 * [taylor]: Taking taylor expansion of 0.5 in k 2.429 * [backup-simplify]: Simplify 0.5 into 0.5 2.429 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.429 * [taylor]: Taking taylor expansion of 1.0 in k 2.429 * [backup-simplify]: Simplify 1.0 into 1.0 2.429 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.429 * [taylor]: Taking taylor expansion of k in k 2.429 * [backup-simplify]: Simplify 0 into 0 2.429 * [backup-simplify]: Simplify 1 into 1 2.429 * [backup-simplify]: Simplify (/ 1 1) into 1 2.429 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.429 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.429 * [taylor]: Taking taylor expansion of 2.0 in k 2.429 * [backup-simplify]: Simplify 2.0 into 2.0 2.429 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.429 * [taylor]: Taking taylor expansion of PI in k 2.429 * [backup-simplify]: Simplify PI into PI 2.429 * [taylor]: Taking taylor expansion of n in k 2.429 * [backup-simplify]: Simplify n into n 2.429 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.429 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.429 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.430 * [backup-simplify]: Simplify (- 1) into -1 2.430 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.430 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.430 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.430 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.430 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.430 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.430 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.430 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.431 * [taylor]: Taking taylor expansion of 0.5 in n 2.431 * [backup-simplify]: Simplify 0.5 into 0.5 2.431 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.431 * [taylor]: Taking taylor expansion of 1.0 in n 2.431 * [backup-simplify]: Simplify 1.0 into 1.0 2.431 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.431 * [taylor]: Taking taylor expansion of k in n 2.431 * [backup-simplify]: Simplify k into k 2.431 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.431 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.431 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.431 * [taylor]: Taking taylor expansion of 2.0 in n 2.431 * [backup-simplify]: Simplify 2.0 into 2.0 2.431 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.431 * [taylor]: Taking taylor expansion of PI in n 2.431 * [backup-simplify]: Simplify PI into PI 2.431 * [taylor]: Taking taylor expansion of n in n 2.431 * [backup-simplify]: Simplify 0 into 0 2.431 * [backup-simplify]: Simplify 1 into 1 2.431 * [backup-simplify]: Simplify (/ PI 1) into PI 2.431 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.432 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.432 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.432 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.432 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.433 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.434 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.435 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.435 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.435 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.435 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.435 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.435 * [taylor]: Taking taylor expansion of 0.5 in n 2.435 * [backup-simplify]: Simplify 0.5 into 0.5 2.435 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.435 * [taylor]: Taking taylor expansion of 1.0 in n 2.435 * [backup-simplify]: Simplify 1.0 into 1.0 2.435 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.435 * [taylor]: Taking taylor expansion of k in n 2.435 * [backup-simplify]: Simplify k into k 2.435 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.435 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.435 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.435 * [taylor]: Taking taylor expansion of 2.0 in n 2.435 * [backup-simplify]: Simplify 2.0 into 2.0 2.435 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.435 * [taylor]: Taking taylor expansion of PI in n 2.435 * [backup-simplify]: Simplify PI into PI 2.435 * [taylor]: Taking taylor expansion of n in n 2.435 * [backup-simplify]: Simplify 0 into 0 2.435 * [backup-simplify]: Simplify 1 into 1 2.435 * [backup-simplify]: Simplify (/ PI 1) into PI 2.435 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.436 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.436 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.436 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.436 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.437 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.438 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.439 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.439 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.439 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.439 * [taylor]: Taking taylor expansion of 0.5 in k 2.439 * [backup-simplify]: Simplify 0.5 into 0.5 2.439 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.439 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.439 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.439 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.439 * [taylor]: Taking taylor expansion of 2.0 in k 2.439 * [backup-simplify]: Simplify 2.0 into 2.0 2.439 * [taylor]: Taking taylor expansion of PI in k 2.439 * [backup-simplify]: Simplify PI into PI 2.439 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.440 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.440 * [taylor]: Taking taylor expansion of (log n) in k 2.440 * [taylor]: Taking taylor expansion of n in k 2.440 * [backup-simplify]: Simplify n into n 2.440 * [backup-simplify]: Simplify (log n) into (log n) 2.440 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.440 * [taylor]: Taking taylor expansion of 1.0 in k 2.440 * [backup-simplify]: Simplify 1.0 into 1.0 2.440 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.440 * [taylor]: Taking taylor expansion of k in k 2.440 * [backup-simplify]: Simplify 0 into 0 2.440 * [backup-simplify]: Simplify 1 into 1 2.440 * [backup-simplify]: Simplify (/ 1 1) into 1 2.440 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.441 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.441 * [backup-simplify]: Simplify (- 1) into -1 2.441 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.442 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.443 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.443 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.444 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.445 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.445 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.446 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.446 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.446 * [backup-simplify]: Simplify (- 0) into 0 2.447 * [backup-simplify]: Simplify (+ 0 0) into 0 2.447 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.448 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.449 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.450 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.450 * [taylor]: Taking taylor expansion of 0 in k 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.451 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.453 * [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 2.453 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.453 * [backup-simplify]: Simplify (- 0) into 0 2.453 * [backup-simplify]: Simplify (+ 0 0) into 0 2.454 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.455 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.456 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.457 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.457 * [taylor]: Taking taylor expansion of 0 in k 2.457 * [backup-simplify]: Simplify 0 into 0 2.457 * [backup-simplify]: Simplify 0 into 0 2.457 * [backup-simplify]: Simplify 0 into 0 2.457 * [backup-simplify]: Simplify 0 into 0 2.458 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.458 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.461 * [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 2.461 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.462 * [backup-simplify]: Simplify (- 0) into 0 2.462 * [backup-simplify]: Simplify (+ 0 0) into 0 2.463 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.463 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.465 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.466 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.466 * [taylor]: Taking taylor expansion of 0 in k 2.466 * [backup-simplify]: Simplify 0 into 0 2.466 * [backup-simplify]: Simplify 0 into 0 2.467 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.467 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 2.467 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.467 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.467 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.467 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.467 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.467 * [taylor]: Taking taylor expansion of 0.5 in k 2.468 * [backup-simplify]: Simplify 0.5 into 0.5 2.468 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.468 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.468 * [taylor]: Taking taylor expansion of k in k 2.468 * [backup-simplify]: Simplify 0 into 0 2.468 * [backup-simplify]: Simplify 1 into 1 2.468 * [backup-simplify]: Simplify (/ 1 1) into 1 2.468 * [taylor]: Taking taylor expansion of 1.0 in k 2.468 * [backup-simplify]: Simplify 1.0 into 1.0 2.468 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.468 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.468 * [taylor]: Taking taylor expansion of -2.0 in k 2.468 * [backup-simplify]: Simplify -2.0 into -2.0 2.468 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.468 * [taylor]: Taking taylor expansion of PI in k 2.468 * [backup-simplify]: Simplify PI into PI 2.468 * [taylor]: Taking taylor expansion of n in k 2.468 * [backup-simplify]: Simplify n into n 2.468 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.468 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.468 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.468 * [backup-simplify]: Simplify (+ 1 0) into 1 2.469 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.469 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.469 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.469 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.469 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.469 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.469 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.469 * [taylor]: Taking taylor expansion of 0.5 in n 2.469 * [backup-simplify]: Simplify 0.5 into 0.5 2.469 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.469 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.469 * [taylor]: Taking taylor expansion of k in n 2.469 * [backup-simplify]: Simplify k into k 2.469 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.469 * [taylor]: Taking taylor expansion of 1.0 in n 2.469 * [backup-simplify]: Simplify 1.0 into 1.0 2.469 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.469 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.469 * [taylor]: Taking taylor expansion of -2.0 in n 2.469 * [backup-simplify]: Simplify -2.0 into -2.0 2.469 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.469 * [taylor]: Taking taylor expansion of PI in n 2.469 * [backup-simplify]: Simplify PI into PI 2.469 * [taylor]: Taking taylor expansion of n in n 2.469 * [backup-simplify]: Simplify 0 into 0 2.469 * [backup-simplify]: Simplify 1 into 1 2.470 * [backup-simplify]: Simplify (/ PI 1) into PI 2.470 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.470 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.471 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.471 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.471 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.472 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.473 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.473 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.473 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.473 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.473 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.473 * [taylor]: Taking taylor expansion of 0.5 in n 2.473 * [backup-simplify]: Simplify 0.5 into 0.5 2.473 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.473 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.473 * [taylor]: Taking taylor expansion of k in n 2.473 * [backup-simplify]: Simplify k into k 2.473 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.473 * [taylor]: Taking taylor expansion of 1.0 in n 2.473 * [backup-simplify]: Simplify 1.0 into 1.0 2.473 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.473 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.473 * [taylor]: Taking taylor expansion of -2.0 in n 2.473 * [backup-simplify]: Simplify -2.0 into -2.0 2.473 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.473 * [taylor]: Taking taylor expansion of PI in n 2.473 * [backup-simplify]: Simplify PI into PI 2.473 * [taylor]: Taking taylor expansion of n in n 2.473 * [backup-simplify]: Simplify 0 into 0 2.473 * [backup-simplify]: Simplify 1 into 1 2.474 * [backup-simplify]: Simplify (/ PI 1) into PI 2.474 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.475 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.475 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.475 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.475 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.476 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.477 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.477 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.477 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.477 * [taylor]: Taking taylor expansion of 0.5 in k 2.477 * [backup-simplify]: Simplify 0.5 into 0.5 2.477 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.477 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.477 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.477 * [taylor]: Taking taylor expansion of k in k 2.477 * [backup-simplify]: Simplify 0 into 0 2.477 * [backup-simplify]: Simplify 1 into 1 2.477 * [backup-simplify]: Simplify (/ 1 1) into 1 2.477 * [taylor]: Taking taylor expansion of 1.0 in k 2.477 * [backup-simplify]: Simplify 1.0 into 1.0 2.477 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.477 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.477 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.477 * [taylor]: Taking taylor expansion of -2.0 in k 2.477 * [backup-simplify]: Simplify -2.0 into -2.0 2.478 * [taylor]: Taking taylor expansion of PI in k 2.478 * [backup-simplify]: Simplify PI into PI 2.478 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.478 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.478 * [taylor]: Taking taylor expansion of (log n) in k 2.478 * [taylor]: Taking taylor expansion of n in k 2.478 * [backup-simplify]: Simplify n into n 2.479 * [backup-simplify]: Simplify (log n) into (log n) 2.479 * [backup-simplify]: Simplify (+ 1 0) into 1 2.479 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.479 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.480 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.481 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.482 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.482 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.483 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.483 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.484 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.484 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.485 * [backup-simplify]: Simplify (+ 0 0) into 0 2.485 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.486 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.487 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.488 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.488 * [taylor]: Taking taylor expansion of 0 in k 2.488 * [backup-simplify]: Simplify 0 into 0 2.488 * [backup-simplify]: Simplify 0 into 0 2.488 * [backup-simplify]: Simplify 0 into 0 2.489 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.489 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.491 * [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 2.491 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.491 * [backup-simplify]: Simplify (+ 0 0) into 0 2.492 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.498 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.499 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.500 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.500 * [taylor]: Taking taylor expansion of 0 in k 2.500 * [backup-simplify]: Simplify 0 into 0 2.500 * [backup-simplify]: Simplify 0 into 0 2.501 * [backup-simplify]: Simplify 0 into 0 2.501 * [backup-simplify]: Simplify 0 into 0 2.501 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.502 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.505 * [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 2.505 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.505 * [backup-simplify]: Simplify (+ 0 0) into 0 2.506 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.507 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.508 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.509 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.509 * [taylor]: Taking taylor expansion of 0 in k 2.509 * [backup-simplify]: Simplify 0 into 0 2.509 * [backup-simplify]: Simplify 0 into 0 2.510 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.510 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 2.511 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.511 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.511 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.511 * [taylor]: Taking taylor expansion of 2.0 in n 2.511 * [backup-simplify]: Simplify 2.0 into 2.0 2.511 * [taylor]: Taking taylor expansion of (* n PI) in n 2.511 * [taylor]: Taking taylor expansion of n in n 2.511 * [backup-simplify]: Simplify 0 into 0 2.511 * [backup-simplify]: Simplify 1 into 1 2.511 * [taylor]: Taking taylor expansion of PI in n 2.511 * [backup-simplify]: Simplify PI into PI 2.511 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.511 * [taylor]: Taking taylor expansion of 2.0 in n 2.511 * [backup-simplify]: Simplify 2.0 into 2.0 2.511 * [taylor]: Taking taylor expansion of (* n PI) in n 2.511 * [taylor]: Taking taylor expansion of n in n 2.511 * [backup-simplify]: Simplify 0 into 0 2.511 * [backup-simplify]: Simplify 1 into 1 2.511 * [taylor]: Taking taylor expansion of PI in n 2.511 * [backup-simplify]: Simplify PI into PI 2.511 * [backup-simplify]: Simplify (* 0 PI) into 0 2.511 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.511 * [backup-simplify]: Simplify 0 into 0 2.512 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.513 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.513 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.514 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.515 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.515 * [backup-simplify]: Simplify 0 into 0 2.515 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.516 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.516 * [backup-simplify]: Simplify 0 into 0 2.517 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.517 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.518 * [backup-simplify]: Simplify 0 into 0 2.518 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.519 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.519 * [backup-simplify]: Simplify 0 into 0 2.520 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.521 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.521 * [backup-simplify]: Simplify 0 into 0 2.522 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.523 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.523 * [backup-simplify]: Simplify 0 into 0 2.523 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.524 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.524 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.524 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.524 * [taylor]: Taking taylor expansion of 2.0 in n 2.524 * [backup-simplify]: Simplify 2.0 into 2.0 2.524 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.524 * [taylor]: Taking taylor expansion of PI in n 2.524 * [backup-simplify]: Simplify PI into PI 2.524 * [taylor]: Taking taylor expansion of n in n 2.524 * [backup-simplify]: Simplify 0 into 0 2.524 * [backup-simplify]: Simplify 1 into 1 2.524 * [backup-simplify]: Simplify (/ PI 1) into PI 2.524 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.524 * [taylor]: Taking taylor expansion of 2.0 in n 2.524 * [backup-simplify]: Simplify 2.0 into 2.0 2.524 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.524 * [taylor]: Taking taylor expansion of PI in n 2.524 * [backup-simplify]: Simplify PI into PI 2.524 * [taylor]: Taking taylor expansion of n in n 2.524 * [backup-simplify]: Simplify 0 into 0 2.524 * [backup-simplify]: Simplify 1 into 1 2.524 * [backup-simplify]: Simplify (/ PI 1) into PI 2.525 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.525 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.526 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.526 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.526 * [backup-simplify]: Simplify 0 into 0 2.527 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.527 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.527 * [backup-simplify]: Simplify 0 into 0 2.528 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.528 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.528 * [backup-simplify]: Simplify 0 into 0 2.529 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.530 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.530 * [backup-simplify]: Simplify 0 into 0 2.530 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.531 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.531 * [backup-simplify]: Simplify 0 into 0 2.532 * [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 2.533 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.533 * [backup-simplify]: Simplify 0 into 0 2.533 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.534 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.534 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.534 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.534 * [taylor]: Taking taylor expansion of -2.0 in n 2.534 * [backup-simplify]: Simplify -2.0 into -2.0 2.534 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.534 * [taylor]: Taking taylor expansion of PI in n 2.534 * [backup-simplify]: Simplify PI into PI 2.534 * [taylor]: Taking taylor expansion of n in n 2.534 * [backup-simplify]: Simplify 0 into 0 2.534 * [backup-simplify]: Simplify 1 into 1 2.534 * [backup-simplify]: Simplify (/ PI 1) into PI 2.534 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.534 * [taylor]: Taking taylor expansion of -2.0 in n 2.534 * [backup-simplify]: Simplify -2.0 into -2.0 2.534 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.534 * [taylor]: Taking taylor expansion of PI in n 2.534 * [backup-simplify]: Simplify PI into PI 2.534 * [taylor]: Taking taylor expansion of n in n 2.534 * [backup-simplify]: Simplify 0 into 0 2.534 * [backup-simplify]: Simplify 1 into 1 2.534 * [backup-simplify]: Simplify (/ PI 1) into PI 2.535 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.535 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.536 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.536 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.536 * [backup-simplify]: Simplify 0 into 0 2.537 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.537 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.537 * [backup-simplify]: Simplify 0 into 0 2.538 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.538 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.538 * [backup-simplify]: Simplify 0 into 0 2.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.540 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.540 * [backup-simplify]: Simplify 0 into 0 2.540 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.541 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.541 * [backup-simplify]: Simplify 0 into 0 2.542 * [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 2.543 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.543 * [backup-simplify]: Simplify 0 into 0 2.543 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.543 * * * * [progress]: [ 3 / 4 ] generating series at (2) 2.544 * [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))))) 2.544 * [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 2.544 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 2.544 * [taylor]: Taking taylor expansion of 1.0 in n 2.544 * [backup-simplify]: Simplify 1.0 into 1.0 2.544 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 2.544 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.544 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.544 * [taylor]: Taking taylor expansion of k in n 2.544 * [backup-simplify]: Simplify k into k 2.544 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.544 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.544 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.544 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.544 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.544 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.544 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.544 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.544 * [taylor]: Taking taylor expansion of 0.5 in n 2.544 * [backup-simplify]: Simplify 0.5 into 0.5 2.544 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.544 * [taylor]: Taking taylor expansion of 1.0 in n 2.544 * [backup-simplify]: Simplify 1.0 into 1.0 2.544 * [taylor]: Taking taylor expansion of k in n 2.544 * [backup-simplify]: Simplify k into k 2.544 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.544 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.544 * [taylor]: Taking taylor expansion of 2.0 in n 2.544 * [backup-simplify]: Simplify 2.0 into 2.0 2.544 * [taylor]: Taking taylor expansion of (* n PI) in n 2.544 * [taylor]: Taking taylor expansion of n in n 2.544 * [backup-simplify]: Simplify 0 into 0 2.544 * [backup-simplify]: Simplify 1 into 1 2.544 * [taylor]: Taking taylor expansion of PI in n 2.544 * [backup-simplify]: Simplify PI into PI 2.545 * [backup-simplify]: Simplify (* 0 PI) into 0 2.545 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.546 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.547 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.547 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.547 * [backup-simplify]: Simplify (- k) into (- k) 2.547 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.547 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.548 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.549 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.550 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.550 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.550 * [taylor]: Taking taylor expansion of 1.0 in k 2.550 * [backup-simplify]: Simplify 1.0 into 1.0 2.550 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.550 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.550 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.550 * [taylor]: Taking taylor expansion of k in k 2.550 * [backup-simplify]: Simplify 0 into 0 2.550 * [backup-simplify]: Simplify 1 into 1 2.550 * [backup-simplify]: Simplify (/ 1 1) into 1 2.550 * [backup-simplify]: Simplify (sqrt 0) into 0 2.551 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.551 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.551 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.551 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.551 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.551 * [taylor]: Taking taylor expansion of 0.5 in k 2.551 * [backup-simplify]: Simplify 0.5 into 0.5 2.551 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.551 * [taylor]: Taking taylor expansion of 1.0 in k 2.551 * [backup-simplify]: Simplify 1.0 into 1.0 2.551 * [taylor]: Taking taylor expansion of k in k 2.551 * [backup-simplify]: Simplify 0 into 0 2.551 * [backup-simplify]: Simplify 1 into 1 2.551 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.551 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.551 * [taylor]: Taking taylor expansion of 2.0 in k 2.551 * [backup-simplify]: Simplify 2.0 into 2.0 2.551 * [taylor]: Taking taylor expansion of (* n PI) in k 2.551 * [taylor]: Taking taylor expansion of n in k 2.551 * [backup-simplify]: Simplify n into n 2.551 * [taylor]: Taking taylor expansion of PI in k 2.551 * [backup-simplify]: Simplify PI into PI 2.551 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.551 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.551 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.552 * [backup-simplify]: Simplify (- 0) into 0 2.552 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.552 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.552 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.552 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.552 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.552 * [taylor]: Taking taylor expansion of 1.0 in k 2.552 * [backup-simplify]: Simplify 1.0 into 1.0 2.552 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.552 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.552 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.553 * [taylor]: Taking taylor expansion of k in k 2.553 * [backup-simplify]: Simplify 0 into 0 2.553 * [backup-simplify]: Simplify 1 into 1 2.553 * [backup-simplify]: Simplify (/ 1 1) into 1 2.553 * [backup-simplify]: Simplify (sqrt 0) into 0 2.554 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.554 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.554 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.554 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.554 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.554 * [taylor]: Taking taylor expansion of 0.5 in k 2.554 * [backup-simplify]: Simplify 0.5 into 0.5 2.554 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.554 * [taylor]: Taking taylor expansion of 1.0 in k 2.554 * [backup-simplify]: Simplify 1.0 into 1.0 2.554 * [taylor]: Taking taylor expansion of k in k 2.554 * [backup-simplify]: Simplify 0 into 0 2.554 * [backup-simplify]: Simplify 1 into 1 2.554 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.554 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.554 * [taylor]: Taking taylor expansion of 2.0 in k 2.554 * [backup-simplify]: Simplify 2.0 into 2.0 2.554 * [taylor]: Taking taylor expansion of (* n PI) in k 2.554 * [taylor]: Taking taylor expansion of n in k 2.554 * [backup-simplify]: Simplify n into n 2.554 * [taylor]: Taking taylor expansion of PI in k 2.554 * [backup-simplify]: Simplify PI into PI 2.554 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.554 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.554 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.554 * [backup-simplify]: Simplify (- 0) into 0 2.555 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.555 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.555 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.555 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.555 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 2.556 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.556 * [taylor]: Taking taylor expansion of 0 in n 2.556 * [backup-simplify]: Simplify 0 into 0 2.556 * [backup-simplify]: Simplify 0 into 0 2.556 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 2.556 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 2.557 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 2.557 * [backup-simplify]: Simplify (- 1) into -1 2.557 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.558 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 2.559 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 2.559 * [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))) 2.560 * [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))) 2.561 * [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))) 2.561 * [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 2.561 * [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 2.561 * [taylor]: Taking taylor expansion of +nan.0 in n 2.561 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.561 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.561 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.561 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.561 * [taylor]: Taking taylor expansion of 0.5 in n 2.561 * [backup-simplify]: Simplify 0.5 into 0.5 2.561 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.561 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.561 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.561 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.561 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.561 * [taylor]: Taking taylor expansion of 1.0 in n 2.561 * [backup-simplify]: Simplify 1.0 into 1.0 2.561 * [taylor]: Taking taylor expansion of (log PI) in n 2.561 * [taylor]: Taking taylor expansion of PI in n 2.561 * [backup-simplify]: Simplify PI into PI 2.562 * [backup-simplify]: Simplify (log PI) into (log PI) 2.562 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.563 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.563 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.563 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.563 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.563 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.563 * [taylor]: Taking taylor expansion of 1.0 in n 2.563 * [backup-simplify]: Simplify 1.0 into 1.0 2.563 * [taylor]: Taking taylor expansion of (log n) in n 2.563 * [taylor]: Taking taylor expansion of n in n 2.563 * [backup-simplify]: Simplify 0 into 0 2.563 * [backup-simplify]: Simplify 1 into 1 2.563 * [backup-simplify]: Simplify (log 1) into 0 2.564 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.564 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.564 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.564 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.564 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.564 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.564 * [taylor]: Taking taylor expansion of 1.0 in n 2.564 * [backup-simplify]: Simplify 1.0 into 1.0 2.564 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.564 * [taylor]: Taking taylor expansion of 2.0 in n 2.564 * [backup-simplify]: Simplify 2.0 into 2.0 2.564 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.565 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.566 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.566 * [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) 2.567 * [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) 2.568 * [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)) 2.568 * [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))) 2.569 * [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) 2.570 * [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)) 2.571 * [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))) 2.572 * [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))) 2.572 * [backup-simplify]: Simplify 0 into 0 2.572 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 2.573 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 2.574 * [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 2.574 * [backup-simplify]: Simplify (- 0) into 0 2.574 * [backup-simplify]: Simplify (+ 0 0) into 0 2.575 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 2.575 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 2.576 * [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))) 2.576 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.578 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.580 * [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)))))))) 2.583 * [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)))))))) 2.583 * [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 2.583 * [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 2.583 * [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 2.583 * [taylor]: Taking taylor expansion of +nan.0 in n 2.584 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.584 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.584 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.584 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.584 * [taylor]: Taking taylor expansion of 0.5 in n 2.584 * [backup-simplify]: Simplify 0.5 into 0.5 2.584 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.584 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.584 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.584 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.584 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.584 * [taylor]: Taking taylor expansion of 1.0 in n 2.584 * [backup-simplify]: Simplify 1.0 into 1.0 2.584 * [taylor]: Taking taylor expansion of (log PI) in n 2.584 * [taylor]: Taking taylor expansion of PI in n 2.584 * [backup-simplify]: Simplify PI into PI 2.584 * [backup-simplify]: Simplify (log PI) into (log PI) 2.585 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.586 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.586 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.586 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.586 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.586 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.586 * [taylor]: Taking taylor expansion of 1.0 in n 2.586 * [backup-simplify]: Simplify 1.0 into 1.0 2.586 * [taylor]: Taking taylor expansion of (log n) in n 2.586 * [taylor]: Taking taylor expansion of n in n 2.586 * [backup-simplify]: Simplify 0 into 0 2.586 * [backup-simplify]: Simplify 1 into 1 2.586 * [backup-simplify]: Simplify (log 1) into 0 2.587 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.587 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.587 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.587 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.587 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.587 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.587 * [taylor]: Taking taylor expansion of 1.0 in n 2.587 * [backup-simplify]: Simplify 1.0 into 1.0 2.587 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.587 * [taylor]: Taking taylor expansion of 2.0 in n 2.587 * [backup-simplify]: Simplify 2.0 into 2.0 2.587 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.588 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.588 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.589 * [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) 2.595 * [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) 2.596 * [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)) 2.597 * [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))) 2.598 * [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) 2.598 * [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 2.598 * [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 2.598 * [taylor]: Taking taylor expansion of +nan.0 in n 2.598 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.598 * [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 2.598 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.598 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.598 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.598 * [taylor]: Taking taylor expansion of 0.5 in n 2.598 * [backup-simplify]: Simplify 0.5 into 0.5 2.598 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.598 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.598 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.598 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.598 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.598 * [taylor]: Taking taylor expansion of 1.0 in n 2.598 * [backup-simplify]: Simplify 1.0 into 1.0 2.598 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.598 * [taylor]: Taking taylor expansion of 2.0 in n 2.598 * [backup-simplify]: Simplify 2.0 into 2.0 2.598 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.599 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.600 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.600 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.600 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.600 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.600 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.600 * [taylor]: Taking taylor expansion of 1.0 in n 2.600 * [backup-simplify]: Simplify 1.0 into 1.0 2.600 * [taylor]: Taking taylor expansion of (log PI) in n 2.600 * [taylor]: Taking taylor expansion of PI in n 2.600 * [backup-simplify]: Simplify PI into PI 2.600 * [backup-simplify]: Simplify (log PI) into (log PI) 2.601 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.602 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.602 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.602 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.602 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.602 * [taylor]: Taking taylor expansion of 1.0 in n 2.602 * [backup-simplify]: Simplify 1.0 into 1.0 2.602 * [taylor]: Taking taylor expansion of (log n) in n 2.602 * [taylor]: Taking taylor expansion of n in n 2.602 * [backup-simplify]: Simplify 0 into 0 2.602 * [backup-simplify]: Simplify 1 into 1 2.602 * [backup-simplify]: Simplify (log 1) into 0 2.602 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.602 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.603 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.603 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.604 * [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) 2.604 * [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)) 2.605 * [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))) 2.606 * [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) 2.606 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.606 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.606 * [taylor]: Taking taylor expansion of 2.0 in n 2.606 * [backup-simplify]: Simplify 2.0 into 2.0 2.606 * [taylor]: Taking taylor expansion of (* n PI) in n 2.606 * [taylor]: Taking taylor expansion of n in n 2.606 * [backup-simplify]: Simplify 0 into 0 2.606 * [backup-simplify]: Simplify 1 into 1 2.606 * [taylor]: Taking taylor expansion of PI in n 2.606 * [backup-simplify]: Simplify PI into PI 2.607 * [backup-simplify]: Simplify (* 0 PI) into 0 2.607 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.608 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.609 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.609 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.610 * [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)) 2.611 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.612 * [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)) 2.614 * [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))) 2.615 * [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)))))) 2.619 * [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)))))))) 2.622 * [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)))))))) 2.626 * [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)))))))) 2.626 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 2.627 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 2.628 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 2.629 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.629 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.629 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 2.630 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.630 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 2.631 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 2.631 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 2.632 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 2.633 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 2.635 * [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 2.636 * [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 2.637 * [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 2.638 * [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 2.638 * [backup-simplify]: Simplify (- 0) into 0 2.638 * [backup-simplify]: Simplify 0 into 0 2.638 * [backup-simplify]: Simplify 0 into 0 2.639 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.640 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 2.641 * [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 2.642 * [backup-simplify]: Simplify (- 0) into 0 2.642 * [backup-simplify]: Simplify (+ 0 0) into 0 2.643 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 2.643 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 2.645 * [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))) 2.645 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.648 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.651 * [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)))))))) 2.657 * [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)))))))) 2.657 * [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 2.657 * [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 2.657 * [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 2.657 * [taylor]: Taking taylor expansion of +nan.0 in n 2.657 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.657 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 2.657 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 2.657 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 2.657 * [taylor]: Taking taylor expansion of 0.5 in n 2.657 * [backup-simplify]: Simplify 0.5 into 0.5 2.657 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 2.657 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 2.657 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.657 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.657 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.657 * [taylor]: Taking taylor expansion of 1.0 in n 2.657 * [backup-simplify]: Simplify 1.0 into 1.0 2.657 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.658 * [taylor]: Taking taylor expansion of 2.0 in n 2.658 * [backup-simplify]: Simplify 2.0 into 2.0 2.658 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.658 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.659 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.659 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 2.659 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.659 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.659 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.659 * [taylor]: Taking taylor expansion of 1.0 in n 2.659 * [backup-simplify]: Simplify 1.0 into 1.0 2.659 * [taylor]: Taking taylor expansion of (log n) in n 2.659 * [taylor]: Taking taylor expansion of n in n 2.659 * [backup-simplify]: Simplify 0 into 0 2.659 * [backup-simplify]: Simplify 1 into 1 2.660 * [backup-simplify]: Simplify (log 1) into 0 2.660 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.660 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.660 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.660 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.660 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.660 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.660 * [taylor]: Taking taylor expansion of 1.0 in n 2.660 * [backup-simplify]: Simplify 1.0 into 1.0 2.660 * [taylor]: Taking taylor expansion of (log PI) in n 2.660 * [taylor]: Taking taylor expansion of PI in n 2.660 * [backup-simplify]: Simplify PI into PI 2.660 * [backup-simplify]: Simplify (log PI) into (log PI) 2.661 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.662 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.662 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.663 * [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) 2.664 * [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)) 2.665 * [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))) 2.665 * [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) 2.665 * [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 2.665 * [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 2.666 * [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 2.666 * [taylor]: Taking taylor expansion of +nan.0 in n 2.666 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.666 * [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 2.666 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.666 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.666 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.666 * [taylor]: Taking taylor expansion of 0.5 in n 2.666 * [backup-simplify]: Simplify 0.5 into 0.5 2.666 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.666 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.666 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.666 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.666 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.666 * [taylor]: Taking taylor expansion of 1.0 in n 2.666 * [backup-simplify]: Simplify 1.0 into 1.0 2.666 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.666 * [taylor]: Taking taylor expansion of 2.0 in n 2.666 * [backup-simplify]: Simplify 2.0 into 2.0 2.666 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.667 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.667 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.667 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.668 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.668 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.668 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.668 * [taylor]: Taking taylor expansion of 1.0 in n 2.668 * [backup-simplify]: Simplify 1.0 into 1.0 2.668 * [taylor]: Taking taylor expansion of (log PI) in n 2.668 * [taylor]: Taking taylor expansion of PI in n 2.668 * [backup-simplify]: Simplify PI into PI 2.668 * [backup-simplify]: Simplify (log PI) into (log PI) 2.668 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.669 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.669 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.669 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.669 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.670 * [taylor]: Taking taylor expansion of 1.0 in n 2.670 * [backup-simplify]: Simplify 1.0 into 1.0 2.670 * [taylor]: Taking taylor expansion of (log n) in n 2.670 * [taylor]: Taking taylor expansion of n in n 2.670 * [backup-simplify]: Simplify 0 into 0 2.670 * [backup-simplify]: Simplify 1 into 1 2.670 * [backup-simplify]: Simplify (log 1) into 0 2.670 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.670 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.670 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.671 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.671 * [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) 2.672 * [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)) 2.673 * [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))) 2.674 * [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) 2.674 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.674 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.674 * [taylor]: Taking taylor expansion of 2.0 in n 2.674 * [backup-simplify]: Simplify 2.0 into 2.0 2.674 * [taylor]: Taking taylor expansion of (* n PI) in n 2.674 * [taylor]: Taking taylor expansion of n in n 2.674 * [backup-simplify]: Simplify 0 into 0 2.674 * [backup-simplify]: Simplify 1 into 1 2.674 * [taylor]: Taking taylor expansion of PI in n 2.674 * [backup-simplify]: Simplify PI into PI 2.674 * [backup-simplify]: Simplify (* 0 PI) into 0 2.675 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.675 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.676 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.677 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.677 * [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 2.677 * [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 2.677 * [taylor]: Taking taylor expansion of +nan.0 in n 2.677 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.677 * [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 2.677 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.677 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.677 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.677 * [taylor]: Taking taylor expansion of 0.5 in n 2.677 * [backup-simplify]: Simplify 0.5 into 0.5 2.677 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.677 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.677 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.677 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.677 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.677 * [taylor]: Taking taylor expansion of 1.0 in n 2.677 * [backup-simplify]: Simplify 1.0 into 1.0 2.677 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.677 * [taylor]: Taking taylor expansion of 2.0 in n 2.677 * [backup-simplify]: Simplify 2.0 into 2.0 2.678 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.678 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.679 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.679 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.679 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.679 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.679 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.679 * [taylor]: Taking taylor expansion of 1.0 in n 2.679 * [backup-simplify]: Simplify 1.0 into 1.0 2.679 * [taylor]: Taking taylor expansion of (log PI) in n 2.679 * [taylor]: Taking taylor expansion of PI in n 2.679 * [backup-simplify]: Simplify PI into PI 2.679 * [backup-simplify]: Simplify (log PI) into (log PI) 2.680 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.681 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.681 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.681 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.681 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.681 * [taylor]: Taking taylor expansion of 1.0 in n 2.681 * [backup-simplify]: Simplify 1.0 into 1.0 2.681 * [taylor]: Taking taylor expansion of (log n) in n 2.681 * [taylor]: Taking taylor expansion of n in n 2.681 * [backup-simplify]: Simplify 0 into 0 2.681 * [backup-simplify]: Simplify 1 into 1 2.681 * [backup-simplify]: Simplify (log 1) into 0 2.682 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.682 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.682 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.682 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.683 * [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) 2.684 * [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)) 2.685 * [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))) 2.685 * [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) 2.686 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 2.686 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.686 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.686 * [taylor]: Taking taylor expansion of 2.0 in n 2.686 * [backup-simplify]: Simplify 2.0 into 2.0 2.686 * [taylor]: Taking taylor expansion of (* n PI) in n 2.686 * [taylor]: Taking taylor expansion of n in n 2.686 * [backup-simplify]: Simplify 0 into 0 2.686 * [backup-simplify]: Simplify 1 into 1 2.686 * [taylor]: Taking taylor expansion of PI in n 2.686 * [backup-simplify]: Simplify PI into PI 2.686 * [backup-simplify]: Simplify (* 0 PI) into 0 2.687 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.688 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.689 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.690 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.690 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.691 * [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)) 2.698 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.699 * [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)) 2.701 * [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))) 2.701 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.702 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.704 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 2.705 * [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)) 2.707 * [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))) 2.709 * [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)))))))) 2.715 * [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)))))))))))) 2.723 * [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)))))))))))) 2.733 * [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)))))))))))))) 2.742 * [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)))))))))))))) 2.751 * [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)))))))))))))) 2.765 * [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)))))))))))))))))))))) 2.766 * [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)))))) 2.766 * [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 2.766 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 2.766 * [taylor]: Taking taylor expansion of 1.0 in n 2.766 * [backup-simplify]: Simplify 1.0 into 1.0 2.766 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 2.766 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.766 * [taylor]: Taking taylor expansion of k in n 2.766 * [backup-simplify]: Simplify k into k 2.766 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.766 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.766 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.766 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.766 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.766 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.766 * [taylor]: Taking taylor expansion of 0.5 in n 2.766 * [backup-simplify]: Simplify 0.5 into 0.5 2.766 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.766 * [taylor]: Taking taylor expansion of 1.0 in n 2.766 * [backup-simplify]: Simplify 1.0 into 1.0 2.766 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.767 * [taylor]: Taking taylor expansion of k in n 2.767 * [backup-simplify]: Simplify k into k 2.767 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.767 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.767 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.767 * [taylor]: Taking taylor expansion of 2.0 in n 2.767 * [backup-simplify]: Simplify 2.0 into 2.0 2.767 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.767 * [taylor]: Taking taylor expansion of PI in n 2.767 * [backup-simplify]: Simplify PI into PI 2.767 * [taylor]: Taking taylor expansion of n in n 2.767 * [backup-simplify]: Simplify 0 into 0 2.767 * [backup-simplify]: Simplify 1 into 1 2.767 * [backup-simplify]: Simplify (/ PI 1) into PI 2.767 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.768 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.768 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.768 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.768 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.769 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.770 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.770 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.770 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.770 * [taylor]: Taking taylor expansion of 1.0 in k 2.770 * [backup-simplify]: Simplify 1.0 into 1.0 2.770 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.770 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.770 * [taylor]: Taking taylor expansion of k in k 2.770 * [backup-simplify]: Simplify 0 into 0 2.771 * [backup-simplify]: Simplify 1 into 1 2.771 * [backup-simplify]: Simplify (sqrt 0) into 0 2.772 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.772 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.772 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.772 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.772 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.772 * [taylor]: Taking taylor expansion of 0.5 in k 2.772 * [backup-simplify]: Simplify 0.5 into 0.5 2.772 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.772 * [taylor]: Taking taylor expansion of 1.0 in k 2.772 * [backup-simplify]: Simplify 1.0 into 1.0 2.772 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.772 * [taylor]: Taking taylor expansion of k in k 2.772 * [backup-simplify]: Simplify 0 into 0 2.772 * [backup-simplify]: Simplify 1 into 1 2.772 * [backup-simplify]: Simplify (/ 1 1) into 1 2.772 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.772 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.772 * [taylor]: Taking taylor expansion of 2.0 in k 2.772 * [backup-simplify]: Simplify 2.0 into 2.0 2.772 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.772 * [taylor]: Taking taylor expansion of PI in k 2.772 * [backup-simplify]: Simplify PI into PI 2.772 * [taylor]: Taking taylor expansion of n in k 2.772 * [backup-simplify]: Simplify n into n 2.772 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.772 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.772 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.773 * [backup-simplify]: Simplify (- 1) into -1 2.773 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.773 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.773 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.773 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.773 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.773 * [taylor]: Taking taylor expansion of 1.0 in k 2.773 * [backup-simplify]: Simplify 1.0 into 1.0 2.773 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.773 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.773 * [taylor]: Taking taylor expansion of k in k 2.773 * [backup-simplify]: Simplify 0 into 0 2.773 * [backup-simplify]: Simplify 1 into 1 2.774 * [backup-simplify]: Simplify (sqrt 0) into 0 2.774 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.774 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.774 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.774 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.774 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.774 * [taylor]: Taking taylor expansion of 0.5 in k 2.775 * [backup-simplify]: Simplify 0.5 into 0.5 2.775 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.775 * [taylor]: Taking taylor expansion of 1.0 in k 2.775 * [backup-simplify]: Simplify 1.0 into 1.0 2.775 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.775 * [taylor]: Taking taylor expansion of k in k 2.775 * [backup-simplify]: Simplify 0 into 0 2.775 * [backup-simplify]: Simplify 1 into 1 2.775 * [backup-simplify]: Simplify (/ 1 1) into 1 2.775 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.775 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.775 * [taylor]: Taking taylor expansion of 2.0 in k 2.775 * [backup-simplify]: Simplify 2.0 into 2.0 2.775 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.775 * [taylor]: Taking taylor expansion of PI in k 2.775 * [backup-simplify]: Simplify PI into PI 2.775 * [taylor]: Taking taylor expansion of n in k 2.775 * [backup-simplify]: Simplify n into n 2.775 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.775 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.775 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.775 * [backup-simplify]: Simplify (- 1) into -1 2.776 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.776 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.776 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.776 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.776 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 2.777 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.777 * [taylor]: Taking taylor expansion of 0 in n 2.777 * [backup-simplify]: Simplify 0 into 0 2.777 * [backup-simplify]: Simplify 0 into 0 2.777 * [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))))))) 2.777 * [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))))))) 2.777 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.777 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.777 * [taylor]: Taking taylor expansion of +nan.0 in n 2.777 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.778 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.778 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.778 * [taylor]: Taking taylor expansion of 0.5 in n 2.778 * [backup-simplify]: Simplify 0.5 into 0.5 2.778 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.778 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.778 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.778 * [taylor]: Taking taylor expansion of 2.0 in n 2.778 * [backup-simplify]: Simplify 2.0 into 2.0 2.778 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.778 * [taylor]: Taking taylor expansion of PI in n 2.778 * [backup-simplify]: Simplify PI into PI 2.778 * [taylor]: Taking taylor expansion of n in n 2.778 * [backup-simplify]: Simplify 0 into 0 2.778 * [backup-simplify]: Simplify 1 into 1 2.778 * [backup-simplify]: Simplify (/ PI 1) into PI 2.778 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.779 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.779 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.779 * [taylor]: Taking taylor expansion of 1.0 in n 2.779 * [backup-simplify]: Simplify 1.0 into 1.0 2.779 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.779 * [taylor]: Taking taylor expansion of k in n 2.779 * [backup-simplify]: Simplify k into k 2.779 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.780 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.780 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.780 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.781 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.781 * [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)))) 2.782 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.783 * [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)))))) 2.784 * [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))))))) 2.785 * [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))))))) 2.785 * [backup-simplify]: Simplify 0 into 0 2.792 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.792 * [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))))))) 2.793 * [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))))))) 2.793 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.793 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.793 * [taylor]: Taking taylor expansion of +nan.0 in n 2.793 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.793 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.793 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.793 * [taylor]: Taking taylor expansion of 0.5 in n 2.793 * [backup-simplify]: Simplify 0.5 into 0.5 2.793 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.793 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.793 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.793 * [taylor]: Taking taylor expansion of 2.0 in n 2.793 * [backup-simplify]: Simplify 2.0 into 2.0 2.793 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.793 * [taylor]: Taking taylor expansion of PI in n 2.793 * [backup-simplify]: Simplify PI into PI 2.793 * [taylor]: Taking taylor expansion of n in n 2.793 * [backup-simplify]: Simplify 0 into 0 2.793 * [backup-simplify]: Simplify 1 into 1 2.794 * [backup-simplify]: Simplify (/ PI 1) into PI 2.794 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.795 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.795 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.795 * [taylor]: Taking taylor expansion of 1.0 in n 2.795 * [backup-simplify]: Simplify 1.0 into 1.0 2.795 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.795 * [taylor]: Taking taylor expansion of k in n 2.795 * [backup-simplify]: Simplify k into k 2.795 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 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 (- (/ 1 k)) into (- (/ 1 k)) 2.796 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.796 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.797 * [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)))) 2.798 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.799 * [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)))))) 2.799 * [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))))))) 2.800 * [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))))))) 2.801 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.801 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.801 * [backup-simplify]: Simplify (- 0) into 0 2.802 * [backup-simplify]: Simplify (+ 0 0) into 0 2.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.803 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) 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 (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.805 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 2.806 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.807 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 2.808 * [backup-simplify]: Simplify (- 0) into 0 2.808 * [backup-simplify]: Simplify 0 into 0 2.808 * [backup-simplify]: Simplify 0 into 0 2.810 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.811 * [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))))))) 2.811 * [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))))))) 2.811 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.811 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.811 * [taylor]: Taking taylor expansion of +nan.0 in n 2.811 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.811 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.811 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.811 * [taylor]: Taking taylor expansion of 0.5 in n 2.811 * [backup-simplify]: Simplify 0.5 into 0.5 2.811 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.812 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.812 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.812 * [taylor]: Taking taylor expansion of 2.0 in n 2.812 * [backup-simplify]: Simplify 2.0 into 2.0 2.812 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.812 * [taylor]: Taking taylor expansion of PI in n 2.812 * [backup-simplify]: Simplify PI into PI 2.812 * [taylor]: Taking taylor expansion of n in n 2.812 * [backup-simplify]: Simplify 0 into 0 2.812 * [backup-simplify]: Simplify 1 into 1 2.812 * [backup-simplify]: Simplify (/ PI 1) into PI 2.812 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.813 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.813 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.813 * [taylor]: Taking taylor expansion of 1.0 in n 2.813 * [backup-simplify]: Simplify 1.0 into 1.0 2.813 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.813 * [taylor]: Taking taylor expansion of k in n 2.813 * [backup-simplify]: Simplify k into k 2.813 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.814 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.814 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.814 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.815 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.815 * [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)))) 2.816 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.817 * [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)))))) 2.818 * [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))))))) 2.818 * [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))))))) 2.821 * [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)))))))) 2.822 * [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)))) 2.822 * [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 2.822 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 2.822 * [taylor]: Taking taylor expansion of 1.0 in n 2.822 * [backup-simplify]: Simplify 1.0 into 1.0 2.822 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 2.822 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.822 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.822 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.822 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.822 * [taylor]: Taking taylor expansion of 0.5 in n 2.822 * [backup-simplify]: Simplify 0.5 into 0.5 2.822 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.822 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.822 * [taylor]: Taking taylor expansion of k in n 2.822 * [backup-simplify]: Simplify k into k 2.822 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.822 * [taylor]: Taking taylor expansion of 1.0 in n 2.822 * [backup-simplify]: Simplify 1.0 into 1.0 2.822 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.822 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.822 * [taylor]: Taking taylor expansion of -2.0 in n 2.822 * [backup-simplify]: Simplify -2.0 into -2.0 2.822 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.822 * [taylor]: Taking taylor expansion of PI in n 2.822 * [backup-simplify]: Simplify PI into PI 2.822 * [taylor]: Taking taylor expansion of n in n 2.822 * [backup-simplify]: Simplify 0 into 0 2.822 * [backup-simplify]: Simplify 1 into 1 2.822 * [backup-simplify]: Simplify (/ PI 1) into PI 2.823 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.823 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.823 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.823 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.824 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.825 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.826 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.826 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.826 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.826 * [taylor]: Taking taylor expansion of -1 in n 2.826 * [backup-simplify]: Simplify -1 into -1 2.826 * [taylor]: Taking taylor expansion of k in n 2.826 * [backup-simplify]: Simplify k into k 2.826 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.826 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.826 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.826 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.827 * [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))) 2.827 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.827 * [taylor]: Taking taylor expansion of 1.0 in k 2.827 * [backup-simplify]: Simplify 1.0 into 1.0 2.827 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.827 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.827 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.827 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.827 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.827 * [taylor]: Taking taylor expansion of 0.5 in k 2.827 * [backup-simplify]: Simplify 0.5 into 0.5 2.827 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.827 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.827 * [taylor]: Taking taylor expansion of k in k 2.827 * [backup-simplify]: Simplify 0 into 0 2.827 * [backup-simplify]: Simplify 1 into 1 2.827 * [backup-simplify]: Simplify (/ 1 1) into 1 2.827 * [taylor]: Taking taylor expansion of 1.0 in k 2.827 * [backup-simplify]: Simplify 1.0 into 1.0 2.827 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.827 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.827 * [taylor]: Taking taylor expansion of -2.0 in k 2.827 * [backup-simplify]: Simplify -2.0 into -2.0 2.827 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.827 * [taylor]: Taking taylor expansion of PI in k 2.827 * [backup-simplify]: Simplify PI into PI 2.827 * [taylor]: Taking taylor expansion of n in k 2.827 * [backup-simplify]: Simplify n into n 2.827 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.828 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.828 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.828 * [backup-simplify]: Simplify (+ 1 0) into 1 2.828 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.828 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.828 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.828 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.828 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.828 * [taylor]: Taking taylor expansion of -1 in k 2.828 * [backup-simplify]: Simplify -1 into -1 2.828 * [taylor]: Taking taylor expansion of k in k 2.828 * [backup-simplify]: Simplify 0 into 0 2.828 * [backup-simplify]: Simplify 1 into 1 2.829 * [backup-simplify]: Simplify (/ -1 1) into -1 2.829 * [backup-simplify]: Simplify (sqrt 0) into 0 2.830 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.830 * [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))))))) 2.830 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.830 * [taylor]: Taking taylor expansion of 1.0 in k 2.830 * [backup-simplify]: Simplify 1.0 into 1.0 2.830 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.830 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.830 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.830 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.830 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.830 * [taylor]: Taking taylor expansion of 0.5 in k 2.830 * [backup-simplify]: Simplify 0.5 into 0.5 2.830 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.830 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.830 * [taylor]: Taking taylor expansion of k in k 2.830 * [backup-simplify]: Simplify 0 into 0 2.830 * [backup-simplify]: Simplify 1 into 1 2.830 * [backup-simplify]: Simplify (/ 1 1) into 1 2.830 * [taylor]: Taking taylor expansion of 1.0 in k 2.830 * [backup-simplify]: Simplify 1.0 into 1.0 2.830 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.830 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.830 * [taylor]: Taking taylor expansion of -2.0 in k 2.830 * [backup-simplify]: Simplify -2.0 into -2.0 2.830 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.830 * [taylor]: Taking taylor expansion of PI in k 2.830 * [backup-simplify]: Simplify PI into PI 2.830 * [taylor]: Taking taylor expansion of n in k 2.830 * [backup-simplify]: Simplify n into n 2.831 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.831 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.831 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.831 * [backup-simplify]: Simplify (+ 1 0) into 1 2.831 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.831 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.831 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.831 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.831 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.831 * [taylor]: Taking taylor expansion of -1 in k 2.831 * [backup-simplify]: Simplify -1 into -1 2.831 * [taylor]: Taking taylor expansion of k in k 2.831 * [backup-simplify]: Simplify 0 into 0 2.831 * [backup-simplify]: Simplify 1 into 1 2.832 * [backup-simplify]: Simplify (/ -1 1) into -1 2.832 * [backup-simplify]: Simplify (sqrt 0) into 0 2.833 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.833 * [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))))))) 2.833 * [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))))))) 2.833 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.833 * [taylor]: Taking taylor expansion of +nan.0 in n 2.833 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.833 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.833 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.833 * [taylor]: Taking taylor expansion of 0.5 in n 2.833 * [backup-simplify]: Simplify 0.5 into 0.5 2.833 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.833 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.833 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.833 * [taylor]: Taking taylor expansion of k in n 2.833 * [backup-simplify]: Simplify k into k 2.834 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.834 * [taylor]: Taking taylor expansion of 1.0 in n 2.834 * [backup-simplify]: Simplify 1.0 into 1.0 2.834 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.834 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.834 * [taylor]: Taking taylor expansion of -2.0 in n 2.834 * [backup-simplify]: Simplify -2.0 into -2.0 2.834 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.834 * [taylor]: Taking taylor expansion of PI in n 2.834 * [backup-simplify]: Simplify PI into PI 2.834 * [taylor]: Taking taylor expansion of n in n 2.834 * [backup-simplify]: Simplify 0 into 0 2.834 * [backup-simplify]: Simplify 1 into 1 2.834 * [backup-simplify]: Simplify (/ PI 1) into PI 2.834 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.835 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.835 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.836 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.836 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.837 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.838 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.839 * [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)))))) 2.839 * [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)))))) 2.840 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.842 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.842 * [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)))))))) 2.843 * [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)))))))) 2.843 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.843 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.843 * [taylor]: Taking taylor expansion of +nan.0 in n 2.843 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.843 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.843 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.843 * [taylor]: Taking taylor expansion of 0.5 in n 2.843 * [backup-simplify]: Simplify 0.5 into 0.5 2.843 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.843 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.843 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.843 * [taylor]: Taking taylor expansion of k in n 2.843 * [backup-simplify]: Simplify k into k 2.843 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.843 * [taylor]: Taking taylor expansion of 1.0 in n 2.843 * [backup-simplify]: Simplify 1.0 into 1.0 2.843 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.843 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.843 * [taylor]: Taking taylor expansion of -2.0 in n 2.843 * [backup-simplify]: Simplify -2.0 into -2.0 2.843 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.843 * [taylor]: Taking taylor expansion of PI in n 2.843 * [backup-simplify]: Simplify PI into PI 2.843 * [taylor]: Taking taylor expansion of n in n 2.843 * [backup-simplify]: Simplify 0 into 0 2.843 * [backup-simplify]: Simplify 1 into 1 2.843 * [backup-simplify]: Simplify (/ PI 1) into PI 2.844 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.844 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.844 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.845 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.846 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.847 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.847 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.848 * [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)))))) 2.849 * [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))))))) 2.850 * [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))))))) 2.850 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.851 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.851 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.852 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.852 * [backup-simplify]: Simplify (+ 0 0) into 0 2.853 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.853 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.854 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 2.855 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.856 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 2.856 * [backup-simplify]: Simplify 0 into 0 2.857 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.859 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.860 * [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)))))))) 2.861 * [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)))))))) 2.861 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.861 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.861 * [taylor]: Taking taylor expansion of +nan.0 in n 2.861 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.861 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.861 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.861 * [taylor]: Taking taylor expansion of 0.5 in n 2.861 * [backup-simplify]: Simplify 0.5 into 0.5 2.861 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.861 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.861 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.861 * [taylor]: Taking taylor expansion of k in n 2.861 * [backup-simplify]: Simplify k into k 2.861 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.861 * [taylor]: Taking taylor expansion of 1.0 in n 2.861 * [backup-simplify]: Simplify 1.0 into 1.0 2.861 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.861 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.861 * [taylor]: Taking taylor expansion of -2.0 in n 2.861 * [backup-simplify]: Simplify -2.0 into -2.0 2.861 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.861 * [taylor]: Taking taylor expansion of PI in n 2.861 * [backup-simplify]: Simplify PI into PI 2.861 * [taylor]: Taking taylor expansion of n in n 2.861 * [backup-simplify]: Simplify 0 into 0 2.861 * [backup-simplify]: Simplify 1 into 1 2.861 * [backup-simplify]: Simplify (/ PI 1) into PI 2.862 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.862 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.862 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.863 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.864 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.865 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.865 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.866 * [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)))))) 2.867 * [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))))))) 2.868 * [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))))))) 2.870 * [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)))))))))))) 2.871 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 2.871 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 2.871 * [approximate]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 2.871 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 2.871 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.871 * [taylor]: Taking taylor expansion of k in n 2.871 * [backup-simplify]: Simplify k into k 2.871 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.871 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.871 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 2.871 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.871 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.871 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.871 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.871 * [taylor]: Taking taylor expansion of 0.5 in n 2.871 * [backup-simplify]: Simplify 0.5 into 0.5 2.871 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.871 * [taylor]: Taking taylor expansion of 1.0 in n 2.871 * [backup-simplify]: Simplify 1.0 into 1.0 2.871 * [taylor]: Taking taylor expansion of k in n 2.872 * [backup-simplify]: Simplify k into k 2.872 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.872 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.872 * [taylor]: Taking taylor expansion of 2.0 in n 2.872 * [backup-simplify]: Simplify 2.0 into 2.0 2.872 * [taylor]: Taking taylor expansion of (* n PI) in n 2.872 * [taylor]: Taking taylor expansion of n in n 2.872 * [backup-simplify]: Simplify 0 into 0 2.872 * [backup-simplify]: Simplify 1 into 1 2.872 * [taylor]: Taking taylor expansion of PI in n 2.872 * [backup-simplify]: Simplify PI into PI 2.872 * [backup-simplify]: Simplify (* 0 PI) into 0 2.872 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.873 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.874 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.875 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.875 * [backup-simplify]: Simplify (- k) into (- k) 2.875 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.875 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.876 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.876 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.877 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.878 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 2.878 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.878 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.878 * [taylor]: Taking taylor expansion of k in k 2.878 * [backup-simplify]: Simplify 0 into 0 2.878 * [backup-simplify]: Simplify 1 into 1 2.878 * [backup-simplify]: Simplify (sqrt 0) into 0 2.879 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.879 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.879 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.879 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.879 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.879 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.879 * [taylor]: Taking taylor expansion of 0.5 in k 2.879 * [backup-simplify]: Simplify 0.5 into 0.5 2.879 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.879 * [taylor]: Taking taylor expansion of 1.0 in k 2.879 * [backup-simplify]: Simplify 1.0 into 1.0 2.879 * [taylor]: Taking taylor expansion of k in k 2.879 * [backup-simplify]: Simplify 0 into 0 2.879 * [backup-simplify]: Simplify 1 into 1 2.879 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.879 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.879 * [taylor]: Taking taylor expansion of 2.0 in k 2.879 * [backup-simplify]: Simplify 2.0 into 2.0 2.879 * [taylor]: Taking taylor expansion of (* n PI) in k 2.879 * [taylor]: Taking taylor expansion of n in k 2.879 * [backup-simplify]: Simplify n into n 2.879 * [taylor]: Taking taylor expansion of PI in k 2.879 * [backup-simplify]: Simplify PI into PI 2.879 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.879 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.879 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.880 * [backup-simplify]: Simplify (- 0) into 0 2.880 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.880 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.880 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.880 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.881 * [backup-simplify]: Simplify (/ 1 (pow (* 2.0 (* n PI)) 0.5)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) 2.881 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.881 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.881 * [taylor]: Taking taylor expansion of k in k 2.881 * [backup-simplify]: Simplify 0 into 0 2.881 * [backup-simplify]: Simplify 1 into 1 2.881 * [backup-simplify]: Simplify (sqrt 0) into 0 2.882 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.882 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.882 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.882 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.882 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.882 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.882 * [taylor]: Taking taylor expansion of 0.5 in k 2.882 * [backup-simplify]: Simplify 0.5 into 0.5 2.882 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.882 * [taylor]: Taking taylor expansion of 1.0 in k 2.882 * [backup-simplify]: Simplify 1.0 into 1.0 2.882 * [taylor]: Taking taylor expansion of k in k 2.882 * [backup-simplify]: Simplify 0 into 0 2.882 * [backup-simplify]: Simplify 1 into 1 2.882 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.882 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.882 * [taylor]: Taking taylor expansion of 2.0 in k 2.882 * [backup-simplify]: Simplify 2.0 into 2.0 2.882 * [taylor]: Taking taylor expansion of (* n PI) in k 2.882 * [taylor]: Taking taylor expansion of n in k 2.882 * [backup-simplify]: Simplify n into n 2.882 * [taylor]: Taking taylor expansion of PI in k 2.882 * [backup-simplify]: Simplify PI into PI 2.882 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.882 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.882 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.882 * [backup-simplify]: Simplify (- 0) into 0 2.883 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.883 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.883 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.883 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.883 * [backup-simplify]: Simplify (/ 1 (pow (* 2.0 (* n PI)) 0.5)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) 2.884 * [backup-simplify]: Simplify (* 0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) into 0 2.884 * [taylor]: Taking taylor expansion of 0 in n 2.884 * [backup-simplify]: Simplify 0 into 0 2.884 * [backup-simplify]: Simplify 0 into 0 2.885 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 2.885 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 2.886 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 2.892 * [backup-simplify]: Simplify (- 1) into -1 2.892 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.893 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 2.894 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 2.894 * [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))) 2.896 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI))))) 2.898 * [backup-simplify]: Simplify (+ (* 0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) 2.898 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n 2.898 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n 2.898 * [taylor]: Taking taylor expansion of +nan.0 in n 2.898 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.898 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n 2.898 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n 2.898 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.898 * [taylor]: Taking taylor expansion of 0.5 in n 2.898 * [backup-simplify]: Simplify 0.5 into 0.5 2.898 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.898 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.898 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.898 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.898 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.898 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.898 * [taylor]: Taking taylor expansion of 1.0 in n 2.898 * [backup-simplify]: Simplify 1.0 into 1.0 2.898 * [taylor]: Taking taylor expansion of (log PI) in n 2.898 * [taylor]: Taking taylor expansion of PI in n 2.898 * [backup-simplify]: Simplify PI into PI 2.898 * [backup-simplify]: Simplify (log PI) into (log PI) 2.899 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.900 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.900 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.900 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.900 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.900 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.900 * [taylor]: Taking taylor expansion of 1.0 in n 2.900 * [backup-simplify]: Simplify 1.0 into 1.0 2.900 * [taylor]: Taking taylor expansion of (log n) in n 2.900 * [taylor]: Taking taylor expansion of n in n 2.900 * [backup-simplify]: Simplify 0 into 0 2.900 * [backup-simplify]: Simplify 1 into 1 2.900 * [backup-simplify]: Simplify (log 1) into 0 2.900 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.900 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.901 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.901 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.901 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.901 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.901 * [taylor]: Taking taylor expansion of 1.0 in n 2.901 * [backup-simplify]: Simplify 1.0 into 1.0 2.901 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.901 * [taylor]: Taking taylor expansion of 2.0 in n 2.901 * [backup-simplify]: Simplify 2.0 into 2.0 2.901 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.902 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.902 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.903 * [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) 2.904 * [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) 2.904 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 2.905 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0)) 2.906 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0))) 2.907 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.908 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) 2.909 * [backup-simplify]: Simplify (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) 2.910 * [backup-simplify]: Simplify (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) 2.910 * [backup-simplify]: Simplify 0 into 0 2.910 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 2.911 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 2.912 * [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 2.912 * [backup-simplify]: Simplify (- 0) into 0 2.912 * [backup-simplify]: Simplify (+ 0 0) into 0 2.913 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 2.913 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 2.914 * [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))) 2.918 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* 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))) (pow (* 2.0 (* n PI)) 0.5))) (* (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI))))) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) 2.920 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.923 * [backup-simplify]: Simplify (+ (* 0 (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) (+ (* +nan.0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) into (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))) 2.924 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))) in n 2.924 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) in n 2.924 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) in n 2.924 * [taylor]: Taking taylor expansion of +nan.0 in n 2.924 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.924 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5) in n 2.924 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))))) in n 2.924 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 2.924 * [taylor]: Taking taylor expansion of 0.5 in n 2.924 * [backup-simplify]: Simplify 0.5 into 0.5 2.924 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 2.924 * [taylor]: Taking taylor expansion of (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 2.924 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 2.924 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.924 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.924 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.924 * [taylor]: Taking taylor expansion of 1.0 in n 2.924 * [backup-simplify]: Simplify 1.0 into 1.0 2.924 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.924 * [taylor]: Taking taylor expansion of 2.0 in n 2.924 * [backup-simplify]: Simplify 2.0 into 2.0 2.924 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.925 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.926 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.926 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 2.926 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.926 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.926 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.926 * [taylor]: Taking taylor expansion of 1.0 in n 2.926 * [backup-simplify]: Simplify 1.0 into 1.0 2.926 * [taylor]: Taking taylor expansion of (log n) in n 2.926 * [taylor]: Taking taylor expansion of n in n 2.926 * [backup-simplify]: Simplify 0 into 0 2.926 * [backup-simplify]: Simplify 1 into 1 2.926 * [backup-simplify]: Simplify (log 1) into 0 2.926 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.926 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.926 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.926 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.926 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.926 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.926 * [taylor]: Taking taylor expansion of 1.0 in n 2.926 * [backup-simplify]: Simplify 1.0 into 1.0 2.926 * [taylor]: Taking taylor expansion of (log PI) in n 2.926 * [taylor]: Taking taylor expansion of PI in n 2.926 * [backup-simplify]: Simplify PI into PI 2.927 * [backup-simplify]: Simplify (log PI) into (log PI) 2.927 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.928 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.929 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.929 * [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) 2.930 * [backup-simplify]: Simplify (/ 1 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 2.931 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0)) 2.932 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0))) 2.933 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.933 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) in n 2.933 * [taylor]: Taking taylor expansion of (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n 2.933 * [taylor]: Taking taylor expansion of +nan.0 in n 2.933 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.933 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n 2.933 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.933 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.933 * [taylor]: Taking taylor expansion of 2.0 in n 2.933 * [backup-simplify]: Simplify 2.0 into 2.0 2.933 * [taylor]: Taking taylor expansion of (* n PI) in n 2.933 * [taylor]: Taking taylor expansion of n in n 2.933 * [backup-simplify]: Simplify 0 into 0 2.933 * [backup-simplify]: Simplify 1 into 1 2.933 * [taylor]: Taking taylor expansion of PI in n 2.933 * [backup-simplify]: Simplify PI into PI 2.933 * [backup-simplify]: Simplify (* 0 PI) into 0 2.934 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.935 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.935 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.936 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.936 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n 2.936 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n 2.936 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.936 * [taylor]: Taking taylor expansion of 0.5 in n 2.936 * [backup-simplify]: Simplify 0.5 into 0.5 2.936 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.936 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.936 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.936 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.936 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.936 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.936 * [taylor]: Taking taylor expansion of 1.0 in n 2.936 * [backup-simplify]: Simplify 1.0 into 1.0 2.936 * [taylor]: Taking taylor expansion of (log PI) in n 2.936 * [taylor]: Taking taylor expansion of PI in n 2.936 * [backup-simplify]: Simplify PI into PI 2.937 * [backup-simplify]: Simplify (log PI) into (log PI) 2.937 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.938 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.938 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.938 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.938 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.938 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.938 * [taylor]: Taking taylor expansion of 1.0 in n 2.938 * [backup-simplify]: Simplify 1.0 into 1.0 2.938 * [taylor]: Taking taylor expansion of (log n) in n 2.938 * [taylor]: Taking taylor expansion of n in n 2.938 * [backup-simplify]: Simplify 0 into 0 2.938 * [backup-simplify]: Simplify 1 into 1 2.939 * [backup-simplify]: Simplify (log 1) into 0 2.939 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.939 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.939 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.939 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.939 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.939 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.939 * [taylor]: Taking taylor expansion of 1.0 in n 2.939 * [backup-simplify]: Simplify 1.0 into 1.0 2.939 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.939 * [taylor]: Taking taylor expansion of 2.0 in n 2.939 * [backup-simplify]: Simplify 2.0 into 2.0 2.939 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.940 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.941 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.941 * [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) 2.942 * [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) 2.943 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 2.943 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0)) 2.944 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0))) 2.945 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.946 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) 2.947 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.949 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) 2.950 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) 2.952 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))) 2.955 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) 2.959 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) 2.962 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) 2.963 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 2.964 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 2.965 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 2.965 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.966 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.966 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 2.966 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.967 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 2.968 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 2.968 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 2.969 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 2.970 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 2.971 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) (/ 0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0))))) into 0 2.973 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1)))) 1) into 0 2.974 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0)))) into 0 2.975 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 2.976 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 2.976 * [backup-simplify]: Simplify (- 0) into 0 2.976 * [backup-simplify]: Simplify 0 into 0 2.977 * [backup-simplify]: Simplify 0 into 0 2.977 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.978 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 2.979 * [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 2.980 * [backup-simplify]: Simplify (- 0) into 0 2.980 * [backup-simplify]: Simplify (+ 0 0) into 0 2.981 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 2.981 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 2.983 * [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))) 2.996 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* -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))) (pow (* 2.0 (* n PI)) 0.5))) (* (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI))))) (/ (* 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))) (pow (* 2.0 (* n PI)) 0.5))) (* (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (* 0.020833333333333332 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 2.998 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.003 * [backup-simplify]: Simplify (+ (* 0 (* 0.020833333333333332 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 3)))) (+ (* +nan.0 (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) (+ (* +nan.0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) into (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))) 3.003 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))) in n 3.003 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) in n 3.003 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n 3.003 * [taylor]: Taking taylor expansion of +nan.0 in n 3.003 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.003 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n 3.003 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n 3.003 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.003 * [taylor]: Taking taylor expansion of 0.5 in n 3.003 * [backup-simplify]: Simplify 0.5 into 0.5 3.003 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.003 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.003 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.004 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.004 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.004 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.004 * [taylor]: Taking taylor expansion of 1.0 in n 3.004 * [backup-simplify]: Simplify 1.0 into 1.0 3.004 * [taylor]: Taking taylor expansion of (log PI) in n 3.004 * [taylor]: Taking taylor expansion of PI in n 3.004 * [backup-simplify]: Simplify PI into PI 3.004 * [backup-simplify]: Simplify (log PI) into (log PI) 3.004 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.005 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.005 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.005 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.005 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.005 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.006 * [taylor]: Taking taylor expansion of 1.0 in n 3.006 * [backup-simplify]: Simplify 1.0 into 1.0 3.006 * [taylor]: Taking taylor expansion of (log n) in n 3.006 * [taylor]: Taking taylor expansion of n in n 3.006 * [backup-simplify]: Simplify 0 into 0 3.006 * [backup-simplify]: Simplify 1 into 1 3.006 * [backup-simplify]: Simplify (log 1) into 0 3.006 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.006 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.006 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.006 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.006 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.006 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.006 * [taylor]: Taking taylor expansion of 1.0 in n 3.006 * [backup-simplify]: Simplify 1.0 into 1.0 3.006 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.006 * [taylor]: Taking taylor expansion of 2.0 in n 3.006 * [backup-simplify]: Simplify 2.0 into 2.0 3.007 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.007 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.008 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.008 * [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) 3.009 * [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) 3.010 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 3.011 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0)) 3.012 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0))) 3.013 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.013 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) in n 3.013 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))) in n 3.013 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 3.013 * [taylor]: Taking taylor expansion of +nan.0 in n 3.013 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.013 * [taylor]: Taking taylor expansion of (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 3.013 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) in n 3.013 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))))) in n 3.013 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 3.013 * [taylor]: Taking taylor expansion of 0.5 in n 3.013 * [backup-simplify]: Simplify 0.5 into 0.5 3.013 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 3.013 * [taylor]: Taking taylor expansion of (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 3.013 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 3.013 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.013 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.013 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.013 * [taylor]: Taking taylor expansion of 1.0 in n 3.013 * [backup-simplify]: Simplify 1.0 into 1.0 3.013 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.013 * [taylor]: Taking taylor expansion of 2.0 in n 3.013 * [backup-simplify]: Simplify 2.0 into 2.0 3.013 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.014 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.015 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.015 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 3.015 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.015 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.015 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.015 * [taylor]: Taking taylor expansion of 1.0 in n 3.015 * [backup-simplify]: Simplify 1.0 into 1.0 3.015 * [taylor]: Taking taylor expansion of (log PI) in n 3.015 * [taylor]: Taking taylor expansion of PI in n 3.015 * [backup-simplify]: Simplify PI into PI 3.015 * [backup-simplify]: Simplify (log PI) into (log PI) 3.016 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.017 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.017 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.017 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.017 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.017 * [taylor]: Taking taylor expansion of 1.0 in n 3.017 * [backup-simplify]: Simplify 1.0 into 1.0 3.017 * [taylor]: Taking taylor expansion of (log n) in n 3.017 * [taylor]: Taking taylor expansion of n in n 3.017 * [backup-simplify]: Simplify 0 into 0 3.017 * [backup-simplify]: Simplify 1 into 1 3.017 * [backup-simplify]: Simplify (log 1) into 0 3.017 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.017 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.017 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.018 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.019 * [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) 3.019 * [backup-simplify]: Simplify (/ 1 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 3.020 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0)) 3.021 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0))) 3.022 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.022 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 3.022 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.022 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.022 * [taylor]: Taking taylor expansion of 2.0 in n 3.022 * [backup-simplify]: Simplify 2.0 into 2.0 3.022 * [taylor]: Taking taylor expansion of (* n PI) in n 3.022 * [taylor]: Taking taylor expansion of n in n 3.022 * [backup-simplify]: Simplify 0 into 0 3.022 * [backup-simplify]: Simplify 1 into 1 3.022 * [taylor]: Taking taylor expansion of PI in n 3.022 * [backup-simplify]: Simplify PI into PI 3.022 * [backup-simplify]: Simplify (* 0 PI) into 0 3.023 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.023 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.024 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.025 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.026 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.026 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))) in n 3.026 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) in n 3.026 * [taylor]: Taking taylor expansion of (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n 3.026 * [taylor]: Taking taylor expansion of +nan.0 in n 3.026 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.026 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n 3.026 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.026 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.026 * [taylor]: Taking taylor expansion of 2.0 in n 3.026 * [backup-simplify]: Simplify 2.0 into 2.0 3.026 * [taylor]: Taking taylor expansion of (* n PI) in n 3.026 * [taylor]: Taking taylor expansion of n in n 3.026 * [backup-simplify]: Simplify 0 into 0 3.026 * [backup-simplify]: Simplify 1 into 1 3.026 * [taylor]: Taking taylor expansion of PI in n 3.026 * [backup-simplify]: Simplify PI into PI 3.026 * [backup-simplify]: Simplify (* 0 PI) into 0 3.027 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.028 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.029 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.029 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.029 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n 3.029 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n 3.029 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.029 * [taylor]: Taking taylor expansion of 0.5 in n 3.029 * [backup-simplify]: Simplify 0.5 into 0.5 3.029 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.029 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.029 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.029 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.029 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.029 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.029 * [taylor]: Taking taylor expansion of 1.0 in n 3.029 * [backup-simplify]: Simplify 1.0 into 1.0 3.029 * [taylor]: Taking taylor expansion of (log PI) in n 3.029 * [taylor]: Taking taylor expansion of PI in n 3.029 * [backup-simplify]: Simplify PI into PI 3.030 * [backup-simplify]: Simplify (log PI) into (log PI) 3.030 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.031 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.031 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.031 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.031 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.031 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.031 * [taylor]: Taking taylor expansion of 1.0 in n 3.031 * [backup-simplify]: Simplify 1.0 into 1.0 3.031 * [taylor]: Taking taylor expansion of (log n) in n 3.031 * [taylor]: Taking taylor expansion of n in n 3.031 * [backup-simplify]: Simplify 0 into 0 3.031 * [backup-simplify]: Simplify 1 into 1 3.032 * [backup-simplify]: Simplify (log 1) into 0 3.032 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.032 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.032 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.032 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.032 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.032 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.032 * [taylor]: Taking taylor expansion of 1.0 in n 3.032 * [backup-simplify]: Simplify 1.0 into 1.0 3.032 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.032 * [taylor]: Taking taylor expansion of 2.0 in n 3.032 * [backup-simplify]: Simplify 2.0 into 2.0 3.032 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.033 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.034 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.034 * [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) 3.035 * [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) 3.036 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 3.037 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0)) 3.038 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0))) 3.038 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.039 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) in n 3.039 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n 3.039 * [taylor]: Taking taylor expansion of +nan.0 in n 3.039 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.039 * [taylor]: Taking taylor expansion of (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n 3.039 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 3.039 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.039 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.039 * [taylor]: Taking taylor expansion of 2.0 in n 3.039 * [backup-simplify]: Simplify 2.0 into 2.0 3.039 * [taylor]: Taking taylor expansion of (* n PI) in n 3.039 * [taylor]: Taking taylor expansion of n in n 3.039 * [backup-simplify]: Simplify 0 into 0 3.039 * [backup-simplify]: Simplify 1 into 1 3.039 * [taylor]: Taking taylor expansion of PI in n 3.039 * [backup-simplify]: Simplify PI into PI 3.039 * [backup-simplify]: Simplify (* 0 PI) into 0 3.039 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.040 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.041 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.042 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.043 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.043 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n 3.043 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n 3.043 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.043 * [taylor]: Taking taylor expansion of 0.5 in n 3.043 * [backup-simplify]: Simplify 0.5 into 0.5 3.043 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.043 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.043 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.043 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.043 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.043 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.043 * [taylor]: Taking taylor expansion of 1.0 in n 3.043 * [backup-simplify]: Simplify 1.0 into 1.0 3.043 * [taylor]: Taking taylor expansion of (log PI) in n 3.043 * [taylor]: Taking taylor expansion of PI in n 3.043 * [backup-simplify]: Simplify PI into PI 3.043 * [backup-simplify]: Simplify (log PI) into (log PI) 3.044 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.045 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.045 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.045 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.045 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.045 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.045 * [taylor]: Taking taylor expansion of 1.0 in n 3.045 * [backup-simplify]: Simplify 1.0 into 1.0 3.045 * [taylor]: Taking taylor expansion of (log n) in n 3.045 * [taylor]: Taking taylor expansion of n in n 3.045 * [backup-simplify]: Simplify 0 into 0 3.045 * [backup-simplify]: Simplify 1 into 1 3.045 * [backup-simplify]: Simplify (log 1) into 0 3.045 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.045 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.045 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.045 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.045 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.045 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.045 * [taylor]: Taking taylor expansion of 1.0 in n 3.045 * [backup-simplify]: Simplify 1.0 into 1.0 3.045 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.045 * [taylor]: Taking taylor expansion of 2.0 in n 3.045 * [backup-simplify]: Simplify 2.0 into 2.0 3.046 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.046 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.047 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.048 * [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) 3.048 * [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) 3.049 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 3.050 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0)) 3.051 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0))) 3.052 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.053 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) 3.053 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.054 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.055 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 3.057 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) 3.059 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) 3.059 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.061 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) 3.062 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) 3.063 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.064 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.065 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 3.067 * [backup-simplify]: Simplify (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) 3.069 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) 3.070 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) 3.077 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))) 3.091 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))) 3.102 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))) 3.114 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))) 3.126 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))))) 3.140 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))))) 3.153 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))))) 3.172 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))))) (pow (* 1 k) 3)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 1 k)))) into (- (+ (* +nan.0 (* (pow k 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow k 3) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log (* 2.0 PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* k (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log n) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (* (pow k 3) (* (log (* 2.0 PI)) (log n))) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5)))))))))))))))))))))))) 3.173 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 3.173 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 3.173 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 3.173 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.173 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.173 * [taylor]: Taking taylor expansion of k in n 3.173 * [backup-simplify]: Simplify k into k 3.173 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.173 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 3.173 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.173 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 3.173 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 3.173 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.173 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.173 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.173 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.173 * [taylor]: Taking taylor expansion of 0.5 in n 3.173 * [backup-simplify]: Simplify 0.5 into 0.5 3.173 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.173 * [taylor]: Taking taylor expansion of 1.0 in n 3.173 * [backup-simplify]: Simplify 1.0 into 1.0 3.173 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.173 * [taylor]: Taking taylor expansion of k in n 3.173 * [backup-simplify]: Simplify k into k 3.178 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.178 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.178 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.178 * [taylor]: Taking taylor expansion of 2.0 in n 3.178 * [backup-simplify]: Simplify 2.0 into 2.0 3.178 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.178 * [taylor]: Taking taylor expansion of PI in n 3.178 * [backup-simplify]: Simplify PI into PI 3.178 * [taylor]: Taking taylor expansion of n in n 3.178 * [backup-simplify]: Simplify 0 into 0 3.178 * [backup-simplify]: Simplify 1 into 1 3.178 * [backup-simplify]: Simplify (/ PI 1) into PI 3.179 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.179 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.179 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.179 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.180 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.180 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.181 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 3.182 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 3.183 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 3.183 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 3.183 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.183 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.183 * [taylor]: Taking taylor expansion of k in k 3.183 * [backup-simplify]: Simplify 0 into 0 3.183 * [backup-simplify]: Simplify 1 into 1 3.183 * [backup-simplify]: Simplify (/ 1 1) into 1 3.183 * [backup-simplify]: Simplify (sqrt 0) into 0 3.184 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.184 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 3.184 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.184 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.184 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.184 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.184 * [taylor]: Taking taylor expansion of 0.5 in k 3.184 * [backup-simplify]: Simplify 0.5 into 0.5 3.184 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.184 * [taylor]: Taking taylor expansion of 1.0 in k 3.184 * [backup-simplify]: Simplify 1.0 into 1.0 3.184 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.184 * [taylor]: Taking taylor expansion of k in k 3.184 * [backup-simplify]: Simplify 0 into 0 3.184 * [backup-simplify]: Simplify 1 into 1 3.185 * [backup-simplify]: Simplify (/ 1 1) into 1 3.185 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.185 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.185 * [taylor]: Taking taylor expansion of 2.0 in k 3.185 * [backup-simplify]: Simplify 2.0 into 2.0 3.185 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.185 * [taylor]: Taking taylor expansion of PI in k 3.185 * [backup-simplify]: Simplify PI into PI 3.185 * [taylor]: Taking taylor expansion of n in k 3.185 * [backup-simplify]: Simplify n into n 3.185 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.185 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.185 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.185 * [backup-simplify]: Simplify (- 1) into -1 3.186 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.186 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.186 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.186 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 3.186 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) 3.186 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 3.186 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.186 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.186 * [taylor]: Taking taylor expansion of k in k 3.186 * [backup-simplify]: Simplify 0 into 0 3.186 * [backup-simplify]: Simplify 1 into 1 3.187 * [backup-simplify]: Simplify (/ 1 1) into 1 3.187 * [backup-simplify]: Simplify (sqrt 0) into 0 3.188 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.188 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 3.188 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.188 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.188 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.188 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.188 * [taylor]: Taking taylor expansion of 0.5 in k 3.188 * [backup-simplify]: Simplify 0.5 into 0.5 3.188 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.188 * [taylor]: Taking taylor expansion of 1.0 in k 3.188 * [backup-simplify]: Simplify 1.0 into 1.0 3.188 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.188 * [taylor]: Taking taylor expansion of k in k 3.188 * [backup-simplify]: Simplify 0 into 0 3.188 * [backup-simplify]: Simplify 1 into 1 3.188 * [backup-simplify]: Simplify (/ 1 1) into 1 3.188 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.188 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.188 * [taylor]: Taking taylor expansion of 2.0 in k 3.188 * [backup-simplify]: Simplify 2.0 into 2.0 3.188 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.188 * [taylor]: Taking taylor expansion of PI in k 3.188 * [backup-simplify]: Simplify PI into PI 3.188 * [taylor]: Taking taylor expansion of n in k 3.188 * [backup-simplify]: Simplify n into n 3.188 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.188 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.189 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.189 * [backup-simplify]: Simplify (- 1) into -1 3.189 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.189 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.189 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.189 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 3.190 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) 3.190 * [backup-simplify]: Simplify (* 0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into 0 3.190 * [taylor]: Taking taylor expansion of 0 in n 3.190 * [backup-simplify]: Simplify 0 into 0 3.190 * [backup-simplify]: Simplify 0 into 0 3.190 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0 3.191 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) 3.191 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n 3.191 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 3.191 * [taylor]: Taking taylor expansion of +nan.0 in n 3.191 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.191 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 3.191 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 3.191 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 3.191 * [taylor]: Taking taylor expansion of 0.5 in n 3.191 * [backup-simplify]: Simplify 0.5 into 0.5 3.191 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 3.191 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.191 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.191 * [taylor]: Taking taylor expansion of 2.0 in n 3.191 * [backup-simplify]: Simplify 2.0 into 2.0 3.191 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.191 * [taylor]: Taking taylor expansion of PI in n 3.191 * [backup-simplify]: Simplify PI into PI 3.191 * [taylor]: Taking taylor expansion of n in n 3.191 * [backup-simplify]: Simplify 0 into 0 3.191 * [backup-simplify]: Simplify 1 into 1 3.191 * [backup-simplify]: Simplify (/ PI 1) into PI 3.192 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.192 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.192 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.192 * [taylor]: Taking taylor expansion of 1.0 in n 3.192 * [backup-simplify]: Simplify 1.0 into 1.0 3.192 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.192 * [taylor]: Taking taylor expansion of k in n 3.192 * [backup-simplify]: Simplify k into k 3.192 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.193 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.193 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.193 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.194 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 3.195 * [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)))) 3.195 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 3.196 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 3.197 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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)))))) 3.198 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 3.199 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 3.199 * [backup-simplify]: Simplify 0 into 0 3.199 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0 3.200 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.201 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.202 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) 3.202 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n 3.202 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 3.202 * [taylor]: Taking taylor expansion of +nan.0 in n 3.202 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.202 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 3.202 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 3.202 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 3.202 * [taylor]: Taking taylor expansion of 0.5 in n 3.202 * [backup-simplify]: Simplify 0.5 into 0.5 3.202 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 3.202 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.202 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.202 * [taylor]: Taking taylor expansion of 2.0 in n 3.202 * [backup-simplify]: Simplify 2.0 into 2.0 3.202 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.202 * [taylor]: Taking taylor expansion of PI in n 3.202 * [backup-simplify]: Simplify PI into PI 3.202 * [taylor]: Taking taylor expansion of n in n 3.202 * [backup-simplify]: Simplify 0 into 0 3.202 * [backup-simplify]: Simplify 1 into 1 3.203 * [backup-simplify]: Simplify (/ PI 1) into PI 3.203 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.203 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.203 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.203 * [taylor]: Taking taylor expansion of 1.0 in n 3.204 * [backup-simplify]: Simplify 1.0 into 1.0 3.204 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.204 * [taylor]: Taking taylor expansion of k in n 3.204 * [backup-simplify]: Simplify k into k 3.204 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.204 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.205 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.205 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.205 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 3.206 * [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)))) 3.207 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 3.207 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 3.208 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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)))))) 3.209 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 3.210 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 3.211 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.211 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.211 * [backup-simplify]: Simplify (- 0) into 0 3.211 * [backup-simplify]: Simplify (+ 0 0) into 0 3.212 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.212 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.213 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.214 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.215 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 3.216 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.218 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0 3.219 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 3.219 * [backup-simplify]: Simplify (- 0) into 0 3.219 * [backup-simplify]: Simplify 0 into 0 3.219 * [backup-simplify]: Simplify 0 into 0 3.219 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0 3.220 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.222 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.223 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) 3.223 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n 3.223 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 3.223 * [taylor]: Taking taylor expansion of +nan.0 in n 3.223 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.223 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 3.223 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 3.223 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 3.223 * [taylor]: Taking taylor expansion of 0.5 in n 3.223 * [backup-simplify]: Simplify 0.5 into 0.5 3.223 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 3.223 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.223 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.223 * [taylor]: Taking taylor expansion of 2.0 in n 3.223 * [backup-simplify]: Simplify 2.0 into 2.0 3.223 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.223 * [taylor]: Taking taylor expansion of PI in n 3.223 * [backup-simplify]: Simplify PI into PI 3.223 * [taylor]: Taking taylor expansion of n in n 3.223 * [backup-simplify]: Simplify 0 into 0 3.223 * [backup-simplify]: Simplify 1 into 1 3.224 * [backup-simplify]: Simplify (/ PI 1) into PI 3.224 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.225 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.225 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.225 * [taylor]: Taking taylor expansion of 1.0 in n 3.225 * [backup-simplify]: Simplify 1.0 into 1.0 3.225 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.225 * [taylor]: Taking taylor expansion of k in n 3.225 * [backup-simplify]: Simplify k into k 3.225 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.226 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.226 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.226 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.226 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 3.227 * [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)))) 3.228 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 3.229 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 3.229 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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)))))) 3.230 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 3.231 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 3.233 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))))) into (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (+ (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))))))) 3.234 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) 3.234 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in (k n) around 0 3.234 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n 3.234 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.234 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.234 * [taylor]: Taking taylor expansion of -1 in n 3.234 * [backup-simplify]: Simplify -1 into -1 3.234 * [taylor]: Taking taylor expansion of k in n 3.234 * [backup-simplify]: Simplify k into k 3.234 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 3.234 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 3.234 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 3.234 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 3.234 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.234 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.234 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.234 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.235 * [taylor]: Taking taylor expansion of 0.5 in n 3.235 * [backup-simplify]: Simplify 0.5 into 0.5 3.235 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.235 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.235 * [taylor]: Taking taylor expansion of k in n 3.235 * [backup-simplify]: Simplify k into k 3.235 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.235 * [taylor]: Taking taylor expansion of 1.0 in n 3.235 * [backup-simplify]: Simplify 1.0 into 1.0 3.235 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.235 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.235 * [taylor]: Taking taylor expansion of -2.0 in n 3.235 * [backup-simplify]: Simplify -2.0 into -2.0 3.235 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.235 * [taylor]: Taking taylor expansion of PI in n 3.235 * [backup-simplify]: Simplify PI into PI 3.235 * [taylor]: Taking taylor expansion of n in n 3.235 * [backup-simplify]: Simplify 0 into 0 3.235 * [backup-simplify]: Simplify 1 into 1 3.235 * [backup-simplify]: Simplify (/ PI 1) into PI 3.236 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.236 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.236 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.236 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.237 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.238 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 3.239 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 3.239 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 3.239 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k 3.239 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.239 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.239 * [taylor]: Taking taylor expansion of -1 in k 3.240 * [backup-simplify]: Simplify -1 into -1 3.240 * [taylor]: Taking taylor expansion of k in k 3.240 * [backup-simplify]: Simplify 0 into 0 3.240 * [backup-simplify]: Simplify 1 into 1 3.240 * [backup-simplify]: Simplify (/ -1 1) into -1 3.240 * [backup-simplify]: Simplify (sqrt 0) into 0 3.241 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.241 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.241 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.241 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.241 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.241 * [taylor]: Taking taylor expansion of 0.5 in k 3.241 * [backup-simplify]: Simplify 0.5 into 0.5 3.241 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.241 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.241 * [taylor]: Taking taylor expansion of k in k 3.241 * [backup-simplify]: Simplify 0 into 0 3.241 * [backup-simplify]: Simplify 1 into 1 3.241 * [backup-simplify]: Simplify (/ 1 1) into 1 3.241 * [taylor]: Taking taylor expansion of 1.0 in k 3.241 * [backup-simplify]: Simplify 1.0 into 1.0 3.241 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.241 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.241 * [taylor]: Taking taylor expansion of -2.0 in k 3.241 * [backup-simplify]: Simplify -2.0 into -2.0 3.241 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.241 * [taylor]: Taking taylor expansion of PI in k 3.241 * [backup-simplify]: Simplify PI into PI 3.241 * [taylor]: Taking taylor expansion of n in k 3.242 * [backup-simplify]: Simplify n into n 3.242 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.242 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.242 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.242 * [backup-simplify]: Simplify (+ 1 0) into 1 3.242 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.242 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.242 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 3.243 * [backup-simplify]: Simplify (/ +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))))))) 3.243 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k 3.243 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.243 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.243 * [taylor]: Taking taylor expansion of -1 in k 3.243 * [backup-simplify]: Simplify -1 into -1 3.243 * [taylor]: Taking taylor expansion of k in k 3.243 * [backup-simplify]: Simplify 0 into 0 3.243 * [backup-simplify]: Simplify 1 into 1 3.243 * [backup-simplify]: Simplify (/ -1 1) into -1 3.243 * [backup-simplify]: Simplify (sqrt 0) into 0 3.244 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.244 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.244 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.244 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.244 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.244 * [taylor]: Taking taylor expansion of 0.5 in k 3.244 * [backup-simplify]: Simplify 0.5 into 0.5 3.244 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.244 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.244 * [taylor]: Taking taylor expansion of k in k 3.244 * [backup-simplify]: Simplify 0 into 0 3.244 * [backup-simplify]: Simplify 1 into 1 3.244 * [backup-simplify]: Simplify (/ 1 1) into 1 3.244 * [taylor]: Taking taylor expansion of 1.0 in k 3.244 * [backup-simplify]: Simplify 1.0 into 1.0 3.244 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.244 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.244 * [taylor]: Taking taylor expansion of -2.0 in k 3.244 * [backup-simplify]: Simplify -2.0 into -2.0 3.244 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.244 * [taylor]: Taking taylor expansion of PI in k 3.244 * [backup-simplify]: Simplify PI into PI 3.244 * [taylor]: Taking taylor expansion of n in k 3.244 * [backup-simplify]: Simplify n into n 3.245 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.245 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.245 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.245 * [backup-simplify]: Simplify (+ 1 0) into 1 3.245 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.245 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.245 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 3.246 * [backup-simplify]: Simplify (/ +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))))))) 3.246 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 3.246 * [taylor]: Taking taylor expansion of +nan.0 in n 3.246 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.246 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 3.246 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 3.246 * [taylor]: Taking taylor expansion of 0.5 in n 3.246 * [backup-simplify]: Simplify 0.5 into 0.5 3.246 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 3.246 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.246 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.246 * [taylor]: Taking taylor expansion of k in n 3.246 * [backup-simplify]: Simplify k into k 3.246 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.246 * [taylor]: Taking taylor expansion of 1.0 in n 3.246 * [backup-simplify]: Simplify 1.0 into 1.0 3.246 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.246 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.246 * [taylor]: Taking taylor expansion of -2.0 in n 3.246 * [backup-simplify]: Simplify -2.0 into -2.0 3.246 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.246 * [taylor]: Taking taylor expansion of PI in n 3.246 * [backup-simplify]: Simplify PI into PI 3.246 * [taylor]: Taking taylor expansion of n in n 3.246 * [backup-simplify]: Simplify 0 into 0 3.246 * [backup-simplify]: Simplify 1 into 1 3.246 * [backup-simplify]: Simplify (/ PI 1) into PI 3.247 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.247 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.247 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.248 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.249 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 3.250 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 3.250 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 3.251 * [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)))))) 3.252 * [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)))))) 3.252 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.254 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.254 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) 3.254 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) in n 3.255 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 3.255 * [taylor]: Taking taylor expansion of +nan.0 in n 3.255 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.255 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 3.255 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 3.255 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 3.255 * [taylor]: Taking taylor expansion of 0.5 in n 3.255 * [backup-simplify]: Simplify 0.5 into 0.5 3.255 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 3.255 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.255 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.255 * [taylor]: Taking taylor expansion of k in n 3.255 * [backup-simplify]: Simplify k into k 3.255 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.255 * [taylor]: Taking taylor expansion of 1.0 in n 3.255 * [backup-simplify]: Simplify 1.0 into 1.0 3.255 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.255 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.255 * [taylor]: Taking taylor expansion of -2.0 in n 3.255 * [backup-simplify]: Simplify -2.0 into -2.0 3.255 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.255 * [taylor]: Taking taylor expansion of PI in n 3.255 * [backup-simplify]: Simplify PI into PI 3.255 * [taylor]: Taking taylor expansion of n in n 3.255 * [backup-simplify]: Simplify 0 into 0 3.255 * [backup-simplify]: Simplify 1 into 1 3.255 * [backup-simplify]: Simplify (/ PI 1) into PI 3.256 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.256 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.256 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.257 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.258 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 3.258 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 3.259 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 3.260 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 3.261 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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)))))) 3.261 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) 3.262 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) 3.263 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.263 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.264 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.264 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.264 * [backup-simplify]: Simplify (+ 0 0) into 0 3.265 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.266 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.267 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 3.268 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.270 * [backup-simplify]: Simplify (- (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))) into 0 3.270 * [backup-simplify]: Simplify 0 into 0 3.271 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.273 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.279 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) 3.279 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) in n 3.279 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 3.279 * [taylor]: Taking taylor expansion of +nan.0 in n 3.279 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.279 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 3.279 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 3.279 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 3.279 * [taylor]: Taking taylor expansion of 0.5 in n 3.279 * [backup-simplify]: Simplify 0.5 into 0.5 3.279 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 3.279 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.279 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.279 * [taylor]: Taking taylor expansion of k in n 3.279 * [backup-simplify]: Simplify k into k 3.279 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.279 * [taylor]: Taking taylor expansion of 1.0 in n 3.279 * [backup-simplify]: Simplify 1.0 into 1.0 3.279 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.279 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.279 * [taylor]: Taking taylor expansion of -2.0 in n 3.279 * [backup-simplify]: Simplify -2.0 into -2.0 3.279 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.279 * [taylor]: Taking taylor expansion of PI in n 3.280 * [backup-simplify]: Simplify PI into PI 3.280 * [taylor]: Taking taylor expansion of n in n 3.280 * [backup-simplify]: Simplify 0 into 0 3.280 * [backup-simplify]: Simplify 1 into 1 3.280 * [backup-simplify]: Simplify (/ PI 1) into PI 3.280 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.281 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.281 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.282 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.283 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 3.283 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 3.284 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 3.285 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 3.286 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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)))))) 3.287 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) 3.287 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) 3.290 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (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 (/ 1 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) (- (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))))) 3.290 * * * [progress]: simplifying candidates 3.296 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (log1p (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (- (log 1.0) (- (log (sqrt k)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))) (- (log 1.0) (- (log (sqrt k)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))) (- (log 1.0) (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))) (- (log 1.0) (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))) (- (log 1.0) (- (log (sqrt k)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (- (log 1.0) (log (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (log (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (exp (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (* (* 1.0 1.0) 1.0) (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (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))))) (/ (* (* 1.0 1.0) 1.0) (* (* (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (cbrt (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (cbrt (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (* (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (- 1.0) (- (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (/ (cbrt 1.0) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (/ (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) (cbrt 1.0)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 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(pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (* (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (sqrt (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (sqrt (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (- (sqrt h1)) (- (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (/ (* (cbrt (sqrt h1)) (cbrt (sqrt h1))) (pow (* h0 h4) (/ (- h2 h1) h0))) (/ (cbrt (sqrt h1)) (pow h3 (/ (- h2 h1) h0))) (/ (* (cbrt (sqrt h1)) (cbrt (sqrt h1))) (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (/ (cbrt (sqrt h1)) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (* (cbrt (sqrt h1)) (cbrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (cbrt (sqrt h1)) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (* (cbrt (sqrt h1)) (cbrt (sqrt h1))) 1) (/ (cbrt (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (/ (* (cbrt 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h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (/ (sqrt (sqrt h1)) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt (sqrt h1)) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt (sqrt h1)) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt (sqrt h1)) 1) (/ (sqrt (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (/ (sqrt (sqrt h1)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (/ (sqrt (sqrt h1)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (/ (sqrt 1) (pow (* h0 h4) (/ (- h2 h1) h0))) (/ (sqrt h1) (pow h3 (/ (- h2 h1) h0))) (/ (sqrt 1) (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (/ (sqrt h1) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt 1) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt h1) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt 1) 1) (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (/ (sqrt 1) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (/ (sqrt (sqrt h1)) (pow (* h0 h4) (/ (- h2 h1) h0))) (/ (sqrt (sqrt h1)) (pow h3 (/ (- h2 h1) h0))) (/ (sqrt (sqrt h1)) (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (/ (sqrt (sqrt h1)) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt (sqrt h1)) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt (sqrt h1)) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt (sqrt h1)) 1) (/ (sqrt (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (/ (sqrt (sqrt h1)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (/ (sqrt (sqrt h1)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (/ 1 (pow (* h0 h4) (/ (- h2 h1) h0))) (/ (sqrt h1) (pow h3 (/ (- h2 h1) h0))) (/ 1 (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (/ (sqrt h1) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ 1 (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt h1) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ 1 1) (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (/ 1 (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (/ 1 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (sqrt h1)) (/ (sqrt h1) (pow (* h0 h4) (/ (- h2 h1) h0))) (/ (sqrt h1) (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (/ (sqrt h1) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (/ (sqrt h1) 1) (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (cbrt (sqrt h1))) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (sqrt (cbrt h1))) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (sqrt (sqrt h1))) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (sqrt h1)) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (sqrt (sqrt h1))) (/ (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (sqrt h1)) (/ (sqrt h1) (pow (* (* h0 h4) h3) (/ h2 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 (* (* (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)))))))))))) (- (+ (* h9 (* (pow h1 2) (pow (/ 1 (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2)))) h5))) (- (+ (* h9 (* (* (pow h1 3) (pow (log (* h0 h4)) 2)) (pow (/ 1 (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2)))) h5))) (- (+ (* h9 (* (pow h1 3) (pow (/ 1 (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2)))) h5))) (- (+ (* h9 (* (* (pow h1 3) (pow (log (* h0 h4)) 2)) (pow (/ 1 (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2)))) h5))) (- (+ (* h9 (* (* (pow h1 3) (log (* h0 h4))) (pow (/ 1 (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2)))) h5))) (- (+ (* h9 (* h1 (pow (/ 1 (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2)))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log (* h0 h4))) (pow (/ 1 (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2)))) h5))) (- (+ (* h9 (* (* (pow h1 3) (log h3)) (pow (/ 1 (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2)))) h5))) (- (+ (* h9 (* (* (pow h1 3) (pow (log h3) 2)) (pow (/ 1 (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2)))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log h3)) (pow (/ 1 (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2)))) h5))) (- (* h9 (* (* (pow h1 3) (* (log (* h0 h4)) (log h3))) (pow (/ 1 (* (pow h4 h2) (* (pow h0 h2) (pow h3 h2)))) h5)))))))))))))))))))))))) (- (+ (* h9 (/ 1 (* h1 (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1))))))) (- (+ (* h9 (/ 1 (* (pow h1 2) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1))))))) (- (* h9 (/ 1 (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1))))))))))) (- (+ (* h9 (/ 1 (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))))) (- (+ (* h9 (/ 1 (* h1 (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3))))))))) (- (* h9 (/ 1 (* (pow h1 2) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))))))))))) 3.315 * * [simplify]: iteration 0 : 1582 enodes (cost 4271 ) 3.339 * * [simplify]: iteration 1 : 5001 enodes (cost 4099 ) 3.355 * * * [progress]: adding candidates to table 4.160 * * [progress]: iteration 4 / 4 4.160 * * * [progress]: picking best candidate 4.186 * * * * [pick]: Picked # 4.186 * * * [progress]: localizing error 4.201 * * * [progress]: generating rewritten candidates 4.201 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 4.230 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 4.255 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1) 4.272 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1) 4.301 * * * [progress]: generating series expansions 4.301 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 4.301 * [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))) 4.301 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 4.301 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 4.301 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.302 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.302 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 4.302 * [taylor]: Taking taylor expansion of 0.25 in k 4.302 * [backup-simplify]: Simplify 0.25 into 0.25 4.302 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.302 * [taylor]: Taking taylor expansion of 1.0 in k 4.302 * [backup-simplify]: Simplify 1.0 into 1.0 4.302 * [taylor]: Taking taylor expansion of k in k 4.302 * [backup-simplify]: Simplify 0 into 0 4.302 * [backup-simplify]: Simplify 1 into 1 4.302 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.302 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.302 * [taylor]: Taking taylor expansion of 2.0 in k 4.302 * [backup-simplify]: Simplify 2.0 into 2.0 4.302 * [taylor]: Taking taylor expansion of (* n PI) in k 4.302 * [taylor]: Taking taylor expansion of n in k 4.302 * [backup-simplify]: Simplify n into n 4.302 * [taylor]: Taking taylor expansion of PI in k 4.302 * [backup-simplify]: Simplify PI into PI 4.302 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.302 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.302 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.302 * [backup-simplify]: Simplify (- 0) into 0 4.302 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.303 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 4.303 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 4.303 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 4.303 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.303 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.303 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.303 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.303 * [taylor]: Taking taylor expansion of 0.25 in n 4.303 * [backup-simplify]: Simplify 0.25 into 0.25 4.303 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.303 * [taylor]: Taking taylor expansion of 1.0 in n 4.303 * [backup-simplify]: Simplify 1.0 into 1.0 4.303 * [taylor]: Taking taylor expansion of k in n 4.303 * [backup-simplify]: Simplify k into k 4.303 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.303 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.303 * [taylor]: Taking taylor expansion of 2.0 in n 4.303 * [backup-simplify]: Simplify 2.0 into 2.0 4.303 * [taylor]: Taking taylor expansion of (* n PI) in n 4.303 * [taylor]: Taking taylor expansion of n in n 4.303 * [backup-simplify]: Simplify 0 into 0 4.303 * [backup-simplify]: Simplify 1 into 1 4.303 * [taylor]: Taking taylor expansion of PI in n 4.303 * [backup-simplify]: Simplify PI into PI 4.304 * [backup-simplify]: Simplify (* 0 PI) into 0 4.304 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.305 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.306 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.306 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.306 * [backup-simplify]: Simplify (- k) into (- k) 4.306 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.306 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.307 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.308 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.309 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.309 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.309 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.309 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.309 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.309 * [taylor]: Taking taylor expansion of 0.25 in n 4.309 * [backup-simplify]: Simplify 0.25 into 0.25 4.309 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.309 * [taylor]: Taking taylor expansion of 1.0 in n 4.309 * [backup-simplify]: Simplify 1.0 into 1.0 4.309 * [taylor]: Taking taylor expansion of k in n 4.309 * [backup-simplify]: Simplify k into k 4.309 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.309 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.309 * [taylor]: Taking taylor expansion of 2.0 in n 4.309 * [backup-simplify]: Simplify 2.0 into 2.0 4.309 * [taylor]: Taking taylor expansion of (* n PI) in n 4.309 * [taylor]: Taking taylor expansion of n in n 4.309 * [backup-simplify]: Simplify 0 into 0 4.309 * [backup-simplify]: Simplify 1 into 1 4.309 * [taylor]: Taking taylor expansion of PI in n 4.309 * [backup-simplify]: Simplify PI into PI 4.309 * [backup-simplify]: Simplify (* 0 PI) into 0 4.310 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.311 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.311 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.312 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.312 * [backup-simplify]: Simplify (- k) into (- k) 4.312 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.312 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.313 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.314 * [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)))) 4.314 * [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))))) 4.315 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.315 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.315 * [taylor]: Taking taylor expansion of 0.25 in k 4.315 * [backup-simplify]: Simplify 0.25 into 0.25 4.315 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.315 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.315 * [taylor]: Taking taylor expansion of 1.0 in k 4.315 * [backup-simplify]: Simplify 1.0 into 1.0 4.315 * [taylor]: Taking taylor expansion of k in k 4.315 * [backup-simplify]: Simplify 0 into 0 4.315 * [backup-simplify]: Simplify 1 into 1 4.315 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.315 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.315 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.315 * [taylor]: Taking taylor expansion of 2.0 in k 4.315 * [backup-simplify]: Simplify 2.0 into 2.0 4.315 * [taylor]: Taking taylor expansion of PI in k 4.315 * [backup-simplify]: Simplify PI into PI 4.315 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.316 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.316 * [taylor]: Taking taylor expansion of (log n) in k 4.316 * [taylor]: Taking taylor expansion of n in k 4.316 * [backup-simplify]: Simplify n into n 4.316 * [backup-simplify]: Simplify (log n) into (log n) 4.316 * [backup-simplify]: Simplify (- 0) into 0 4.316 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.317 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.318 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.318 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 4.319 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.320 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.320 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.321 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.322 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.322 * [backup-simplify]: Simplify (- 0) into 0 4.322 * [backup-simplify]: Simplify (+ 0 0) into 0 4.323 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 4.323 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.324 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.325 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.325 * [taylor]: Taking taylor expansion of 0 in k 4.325 * [backup-simplify]: Simplify 0 into 0 4.325 * [backup-simplify]: Simplify 0 into 0 4.326 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.327 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.327 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.328 * [backup-simplify]: Simplify (+ 0 0) into 0 4.328 * [backup-simplify]: Simplify (- 1) into -1 4.328 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.329 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.330 * [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)))) 4.332 * [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)))))) 4.334 * [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)))))) 4.335 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.335 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.337 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.337 * [backup-simplify]: Simplify (- 0) into 0 4.338 * [backup-simplify]: Simplify (+ 0 0) into 0 4.338 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.339 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.340 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.341 * [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 4.341 * [taylor]: Taking taylor expansion of 0 in k 4.341 * [backup-simplify]: Simplify 0 into 0 4.341 * [backup-simplify]: Simplify 0 into 0 4.341 * [backup-simplify]: Simplify 0 into 0 4.342 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.344 * [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 4.345 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.345 * [backup-simplify]: Simplify (+ 0 0) into 0 4.345 * [backup-simplify]: Simplify (- 0) into 0 4.346 * [backup-simplify]: Simplify (+ 0 0) into 0 4.347 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.348 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.351 * [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))))) 4.354 * [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))))) 4.360 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 4.360 * [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)))) 4.360 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 4.360 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 4.361 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.361 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.361 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 4.361 * [taylor]: Taking taylor expansion of 0.25 in k 4.361 * [backup-simplify]: Simplify 0.25 into 0.25 4.361 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.361 * [taylor]: Taking taylor expansion of 1.0 in k 4.361 * [backup-simplify]: Simplify 1.0 into 1.0 4.361 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.361 * [taylor]: Taking taylor expansion of k in k 4.361 * [backup-simplify]: Simplify 0 into 0 4.361 * [backup-simplify]: Simplify 1 into 1 4.361 * [backup-simplify]: Simplify (/ 1 1) into 1 4.361 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.361 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.361 * [taylor]: Taking taylor expansion of 2.0 in k 4.361 * [backup-simplify]: Simplify 2.0 into 2.0 4.361 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.361 * [taylor]: Taking taylor expansion of PI in k 4.361 * [backup-simplify]: Simplify PI into PI 4.361 * [taylor]: Taking taylor expansion of n in k 4.361 * [backup-simplify]: Simplify n into n 4.361 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.361 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.361 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.361 * [backup-simplify]: Simplify (- 1) into -1 4.362 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.362 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 4.362 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 4.362 * [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))))) 4.362 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.362 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.362 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.362 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.362 * [taylor]: Taking taylor expansion of 0.25 in n 4.362 * [backup-simplify]: Simplify 0.25 into 0.25 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) 4.363 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.363 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.363 * [taylor]: Taking taylor expansion of 2.0 in n 4.363 * [backup-simplify]: Simplify 2.0 into 2.0 4.363 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.363 * [taylor]: Taking taylor expansion of PI in n 4.363 * [backup-simplify]: Simplify PI into PI 4.363 * [taylor]: Taking taylor expansion of n in n 4.363 * [backup-simplify]: Simplify 0 into 0 4.363 * [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 (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.365 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.366 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.367 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.367 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.367 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.367 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.367 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.367 * [taylor]: Taking taylor expansion of 0.25 in n 4.367 * [backup-simplify]: Simplify 0.25 into 0.25 4.367 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.367 * [taylor]: Taking taylor expansion of 1.0 in n 4.367 * [backup-simplify]: Simplify 1.0 into 1.0 4.367 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.367 * [taylor]: Taking taylor expansion of k in n 4.367 * [backup-simplify]: Simplify k into k 4.367 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.367 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.367 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.367 * [taylor]: Taking taylor expansion of 2.0 in n 4.367 * [backup-simplify]: Simplify 2.0 into 2.0 4.367 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.367 * [taylor]: Taking taylor expansion of PI in n 4.367 * [backup-simplify]: Simplify PI into PI 4.367 * [taylor]: Taking taylor expansion of n in n 4.367 * [backup-simplify]: Simplify 0 into 0 4.367 * [backup-simplify]: Simplify 1 into 1 4.367 * [backup-simplify]: Simplify (/ PI 1) into PI 4.374 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.375 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.375 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.375 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.375 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.376 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.376 * [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)))) 4.377 * [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))))) 4.377 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.377 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.377 * [taylor]: Taking taylor expansion of 0.25 in k 4.377 * [backup-simplify]: Simplify 0.25 into 0.25 4.377 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.377 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.377 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.377 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.377 * [taylor]: Taking taylor expansion of 2.0 in k 4.377 * [backup-simplify]: Simplify 2.0 into 2.0 4.377 * [taylor]: Taking taylor expansion of PI in k 4.377 * [backup-simplify]: Simplify PI into PI 4.378 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.378 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.378 * [taylor]: Taking taylor expansion of (log n) in k 4.378 * [taylor]: Taking taylor expansion of n in k 4.378 * [backup-simplify]: Simplify n into n 4.378 * [backup-simplify]: Simplify (log n) into (log n) 4.378 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.379 * [taylor]: Taking taylor expansion of 1.0 in k 4.379 * [backup-simplify]: Simplify 1.0 into 1.0 4.379 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.379 * [taylor]: Taking taylor expansion of k in k 4.379 * [backup-simplify]: Simplify 0 into 0 4.379 * [backup-simplify]: Simplify 1 into 1 4.379 * [backup-simplify]: Simplify (/ 1 1) into 1 4.379 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.380 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.380 * [backup-simplify]: Simplify (- 1) into -1 4.380 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.381 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.381 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 4.382 * [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))))) 4.383 * [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))))) 4.383 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.384 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.385 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.385 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.385 * [backup-simplify]: Simplify (- 0) into 0 4.385 * [backup-simplify]: Simplify (+ 0 0) into 0 4.386 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.387 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.387 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.388 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.388 * [taylor]: Taking taylor expansion of 0 in k 4.388 * [backup-simplify]: Simplify 0 into 0 4.388 * [backup-simplify]: Simplify 0 into 0 4.388 * [backup-simplify]: Simplify 0 into 0 4.389 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.390 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.391 * [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 4.391 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.392 * [backup-simplify]: Simplify (- 0) into 0 4.392 * [backup-simplify]: Simplify (+ 0 0) into 0 4.392 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.393 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.394 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.396 * [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 4.396 * [taylor]: Taking taylor expansion of 0 in k 4.396 * [backup-simplify]: Simplify 0 into 0 4.396 * [backup-simplify]: Simplify 0 into 0 4.396 * [backup-simplify]: Simplify 0 into 0 4.396 * [backup-simplify]: Simplify 0 into 0 4.397 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.397 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.400 * [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 4.400 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.401 * [backup-simplify]: Simplify (- 0) into 0 4.401 * [backup-simplify]: Simplify (+ 0 0) into 0 4.401 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.402 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.403 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.405 * [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 4.405 * [taylor]: Taking taylor expansion of 0 in k 4.405 * [backup-simplify]: Simplify 0 into 0 4.405 * [backup-simplify]: Simplify 0 into 0 4.406 * [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)))) 4.406 * [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))) 4.406 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 4.406 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 4.406 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.406 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.406 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 4.407 * [taylor]: Taking taylor expansion of 0.25 in k 4.407 * [backup-simplify]: Simplify 0.25 into 0.25 4.407 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.407 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.407 * [taylor]: Taking taylor expansion of k in k 4.407 * [backup-simplify]: Simplify 0 into 0 4.407 * [backup-simplify]: Simplify 1 into 1 4.407 * [backup-simplify]: Simplify (/ 1 1) into 1 4.407 * [taylor]: Taking taylor expansion of 1.0 in k 4.407 * [backup-simplify]: Simplify 1.0 into 1.0 4.407 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.407 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.407 * [taylor]: Taking taylor expansion of -2.0 in k 4.407 * [backup-simplify]: Simplify -2.0 into -2.0 4.407 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.407 * [taylor]: Taking taylor expansion of PI in k 4.407 * [backup-simplify]: Simplify PI into PI 4.407 * [taylor]: Taking taylor expansion of n in k 4.407 * [backup-simplify]: Simplify n into n 4.407 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.407 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.407 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.407 * [backup-simplify]: Simplify (+ 1 0) into 1 4.408 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 4.408 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 4.408 * [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)))))) 4.408 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.408 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.408 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.408 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.408 * [taylor]: Taking taylor expansion of 0.25 in n 4.408 * [backup-simplify]: Simplify 0.25 into 0.25 4.408 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.408 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.408 * [taylor]: Taking taylor expansion of k in n 4.408 * [backup-simplify]: Simplify k into k 4.408 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.408 * [taylor]: Taking taylor expansion of 1.0 in n 4.408 * [backup-simplify]: Simplify 1.0 into 1.0 4.408 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.408 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.408 * [taylor]: Taking taylor expansion of -2.0 in n 4.408 * [backup-simplify]: Simplify -2.0 into -2.0 4.408 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.408 * [taylor]: Taking taylor expansion of PI in n 4.408 * [backup-simplify]: Simplify PI into PI 4.408 * [taylor]: Taking taylor expansion of n in n 4.408 * [backup-simplify]: Simplify 0 into 0 4.408 * [backup-simplify]: Simplify 1 into 1 4.409 * [backup-simplify]: Simplify (/ PI 1) into PI 4.409 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.409 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.410 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.410 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.410 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.411 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.412 * [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))))) 4.412 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.412 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.412 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.412 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.412 * [taylor]: Taking taylor expansion of 0.25 in n 4.412 * [backup-simplify]: Simplify 0.25 into 0.25 4.412 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.412 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.412 * [taylor]: Taking taylor expansion of k in n 4.412 * [backup-simplify]: Simplify k into k 4.412 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.412 * [taylor]: Taking taylor expansion of 1.0 in n 4.412 * [backup-simplify]: Simplify 1.0 into 1.0 4.412 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.412 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.412 * [taylor]: Taking taylor expansion of -2.0 in n 4.412 * [backup-simplify]: Simplify -2.0 into -2.0 4.412 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.412 * [taylor]: Taking taylor expansion of PI in n 4.412 * [backup-simplify]: Simplify PI into PI 4.412 * [taylor]: Taking taylor expansion of n in n 4.412 * [backup-simplify]: Simplify 0 into 0 4.412 * [backup-simplify]: Simplify 1 into 1 4.413 * [backup-simplify]: Simplify (/ PI 1) into PI 4.413 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.414 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.414 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.414 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.415 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.415 * [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)))) 4.416 * [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))))) 4.416 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.416 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.416 * [taylor]: Taking taylor expansion of 0.25 in k 4.416 * [backup-simplify]: Simplify 0.25 into 0.25 4.416 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.416 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.416 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.416 * [taylor]: Taking taylor expansion of k in k 4.416 * [backup-simplify]: Simplify 0 into 0 4.416 * [backup-simplify]: Simplify 1 into 1 4.416 * [backup-simplify]: Simplify (/ 1 1) into 1 4.416 * [taylor]: Taking taylor expansion of 1.0 in k 4.417 * [backup-simplify]: Simplify 1.0 into 1.0 4.417 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.417 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.417 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.417 * [taylor]: Taking taylor expansion of -2.0 in k 4.417 * [backup-simplify]: Simplify -2.0 into -2.0 4.417 * [taylor]: Taking taylor expansion of PI in k 4.417 * [backup-simplify]: Simplify PI into PI 4.417 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.418 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.418 * [taylor]: Taking taylor expansion of (log n) in k 4.418 * [taylor]: Taking taylor expansion of n in k 4.418 * [backup-simplify]: Simplify n into n 4.418 * [backup-simplify]: Simplify (log n) into (log n) 4.418 * [backup-simplify]: Simplify (+ 1 0) into 1 4.418 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.419 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.419 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.420 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 4.421 * [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))))) 4.421 * [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))))) 4.422 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.422 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.423 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.423 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.424 * [backup-simplify]: Simplify (+ 0 0) into 0 4.424 * [backup-simplify]: Simplify (+ (* 0.25 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 (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.427 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.427 * [taylor]: Taking taylor expansion of 0 in k 4.427 * [backup-simplify]: Simplify 0 into 0 4.427 * [backup-simplify]: Simplify 0 into 0 4.427 * [backup-simplify]: Simplify 0 into 0 4.427 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.428 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.430 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 4.430 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.430 * [backup-simplify]: Simplify (+ 0 0) into 0 4.431 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.432 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.433 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.434 * [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 4.434 * [taylor]: Taking taylor expansion of 0 in k 4.434 * [backup-simplify]: Simplify 0 into 0 4.434 * [backup-simplify]: Simplify 0 into 0 4.434 * [backup-simplify]: Simplify 0 into 0 4.434 * [backup-simplify]: Simplify 0 into 0 4.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.435 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.438 * [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 4.438 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.439 * [backup-simplify]: Simplify (+ 0 0) into 0 4.439 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.440 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.441 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.443 * [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 4.443 * [taylor]: Taking taylor expansion of 0 in k 4.443 * [backup-simplify]: Simplify 0 into 0 4.443 * [backup-simplify]: Simplify 0 into 0 4.444 * [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)))))) 4.444 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 4.444 * [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))) 4.444 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 4.444 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 4.444 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.444 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.444 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 4.444 * [taylor]: Taking taylor expansion of 0.25 in k 4.444 * [backup-simplify]: Simplify 0.25 into 0.25 4.444 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.444 * [taylor]: Taking taylor expansion of 1.0 in k 4.445 * [backup-simplify]: Simplify 1.0 into 1.0 4.445 * [taylor]: Taking taylor expansion of k in k 4.445 * [backup-simplify]: Simplify 0 into 0 4.445 * [backup-simplify]: Simplify 1 into 1 4.445 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.445 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.445 * [taylor]: Taking taylor expansion of 2.0 in k 4.445 * [backup-simplify]: Simplify 2.0 into 2.0 4.445 * [taylor]: Taking taylor expansion of (* n PI) in k 4.445 * [taylor]: Taking taylor expansion of n in k 4.445 * [backup-simplify]: Simplify n into n 4.445 * [taylor]: Taking taylor expansion of PI in k 4.445 * [backup-simplify]: Simplify PI into PI 4.445 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.445 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.445 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.445 * [backup-simplify]: Simplify (- 0) into 0 4.446 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.446 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 4.446 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 4.446 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 4.446 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.446 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.446 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.446 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.446 * [taylor]: Taking taylor expansion of 0.25 in n 4.446 * [backup-simplify]: Simplify 0.25 into 0.25 4.446 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.446 * [taylor]: Taking taylor expansion of 1.0 in n 4.446 * [backup-simplify]: Simplify 1.0 into 1.0 4.446 * [taylor]: Taking taylor expansion of k in n 4.446 * [backup-simplify]: Simplify k into k 4.446 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.446 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.446 * [taylor]: Taking taylor expansion of 2.0 in n 4.446 * [backup-simplify]: Simplify 2.0 into 2.0 4.446 * [taylor]: Taking taylor expansion of (* n PI) in n 4.446 * [taylor]: Taking taylor expansion of n in n 4.446 * [backup-simplify]: Simplify 0 into 0 4.446 * [backup-simplify]: Simplify 1 into 1 4.446 * [taylor]: Taking taylor expansion of PI in n 4.446 * [backup-simplify]: Simplify PI into PI 4.447 * [backup-simplify]: Simplify (* 0 PI) into 0 4.447 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.448 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.449 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.449 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.449 * [backup-simplify]: Simplify (- k) into (- k) 4.449 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.449 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.450 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.451 * [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)))) 4.452 * [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))))) 4.452 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.452 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.452 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.452 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.452 * [taylor]: Taking taylor expansion of 0.25 in n 4.452 * [backup-simplify]: Simplify 0.25 into 0.25 4.452 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.452 * [taylor]: Taking taylor expansion of 1.0 in n 4.452 * [backup-simplify]: Simplify 1.0 into 1.0 4.452 * [taylor]: Taking taylor expansion of k in n 4.452 * [backup-simplify]: Simplify k into k 4.452 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.452 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.452 * [taylor]: Taking taylor expansion of 2.0 in n 4.452 * [backup-simplify]: Simplify 2.0 into 2.0 4.452 * [taylor]: Taking taylor expansion of (* n PI) in n 4.452 * [taylor]: Taking taylor expansion of n in n 4.452 * [backup-simplify]: Simplify 0 into 0 4.452 * [backup-simplify]: Simplify 1 into 1 4.452 * [taylor]: Taking taylor expansion of PI in n 4.452 * [backup-simplify]: Simplify PI into PI 4.452 * [backup-simplify]: Simplify (* 0 PI) into 0 4.452 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.453 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.454 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.455 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.455 * [backup-simplify]: Simplify (- k) into (- k) 4.455 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.455 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.456 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.457 * [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)))) 4.457 * [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))))) 4.457 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.457 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.458 * [taylor]: Taking taylor expansion of 0.25 in k 4.458 * [backup-simplify]: Simplify 0.25 into 0.25 4.458 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.458 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.458 * [taylor]: Taking taylor expansion of 1.0 in k 4.458 * [backup-simplify]: Simplify 1.0 into 1.0 4.458 * [taylor]: Taking taylor expansion of k in k 4.458 * [backup-simplify]: Simplify 0 into 0 4.458 * [backup-simplify]: Simplify 1 into 1 4.458 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.458 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.458 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.458 * [taylor]: Taking taylor expansion of 2.0 in k 4.458 * [backup-simplify]: Simplify 2.0 into 2.0 4.458 * [taylor]: Taking taylor expansion of PI in k 4.458 * [backup-simplify]: Simplify PI into PI 4.458 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.459 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.459 * [taylor]: Taking taylor expansion of (log n) in k 4.459 * [taylor]: Taking taylor expansion of n in k 4.459 * [backup-simplify]: Simplify n into n 4.459 * [backup-simplify]: Simplify (log n) into (log n) 4.459 * [backup-simplify]: Simplify (- 0) into 0 4.459 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.460 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.461 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.461 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 4.462 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.463 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.463 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.464 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.465 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.465 * [backup-simplify]: Simplify (- 0) into 0 4.465 * [backup-simplify]: Simplify (+ 0 0) into 0 4.465 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 4.473 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.474 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.475 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.475 * [taylor]: Taking taylor expansion of 0 in k 4.475 * [backup-simplify]: Simplify 0 into 0 4.475 * [backup-simplify]: Simplify 0 into 0 4.475 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.476 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.477 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.477 * [backup-simplify]: Simplify (+ 0 0) into 0 4.477 * [backup-simplify]: Simplify (- 1) into -1 4.477 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.478 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.480 * [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)))) 4.482 * [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)))))) 4.483 * [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)))))) 4.484 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.485 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.486 * [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 4.487 * [backup-simplify]: Simplify (- 0) into 0 4.487 * [backup-simplify]: Simplify (+ 0 0) into 0 4.487 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.488 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.489 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.491 * [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 4.491 * [taylor]: Taking taylor expansion of 0 in k 4.491 * [backup-simplify]: Simplify 0 into 0 4.491 * [backup-simplify]: Simplify 0 into 0 4.491 * [backup-simplify]: Simplify 0 into 0 4.491 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.493 * [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 4.494 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.494 * [backup-simplify]: Simplify (+ 0 0) into 0 4.494 * [backup-simplify]: Simplify (- 0) into 0 4.495 * [backup-simplify]: Simplify (+ 0 0) into 0 4.496 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.498 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.500 * [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))))) 4.503 * [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))))) 4.509 * [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)))))) 4.510 * [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)))) 4.510 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 4.510 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 4.510 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.510 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.510 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 4.510 * [taylor]: Taking taylor expansion of 0.25 in k 4.510 * [backup-simplify]: Simplify 0.25 into 0.25 4.510 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.510 * [taylor]: Taking taylor expansion of 1.0 in k 4.510 * [backup-simplify]: Simplify 1.0 into 1.0 4.510 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.510 * [taylor]: Taking taylor expansion of k in k 4.510 * [backup-simplify]: Simplify 0 into 0 4.510 * [backup-simplify]: Simplify 1 into 1 4.510 * [backup-simplify]: Simplify (/ 1 1) into 1 4.510 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.510 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.510 * [taylor]: Taking taylor expansion of 2.0 in k 4.510 * [backup-simplify]: Simplify 2.0 into 2.0 4.510 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.510 * [taylor]: Taking taylor expansion of PI in k 4.510 * [backup-simplify]: Simplify PI into PI 4.510 * [taylor]: Taking taylor expansion of n in k 4.510 * [backup-simplify]: Simplify n into n 4.510 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.510 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.510 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.511 * [backup-simplify]: Simplify (- 1) into -1 4.511 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.511 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 4.511 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 4.511 * [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))))) 4.511 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.511 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.511 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.511 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.511 * [taylor]: Taking taylor expansion of 0.25 in n 4.511 * [backup-simplify]: Simplify 0.25 into 0.25 4.511 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.511 * [taylor]: Taking taylor expansion of 1.0 in n 4.511 * [backup-simplify]: Simplify 1.0 into 1.0 4.511 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.511 * [taylor]: Taking taylor expansion of k in n 4.511 * [backup-simplify]: Simplify k into k 4.512 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.512 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.512 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.512 * [taylor]: Taking taylor expansion of 2.0 in n 4.512 * [backup-simplify]: Simplify 2.0 into 2.0 4.512 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.512 * [taylor]: Taking taylor expansion of PI in n 4.512 * [backup-simplify]: Simplify PI into PI 4.512 * [taylor]: Taking taylor expansion of n in n 4.512 * [backup-simplify]: Simplify 0 into 0 4.512 * [backup-simplify]: Simplify 1 into 1 4.512 * [backup-simplify]: Simplify (/ PI 1) into PI 4.512 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.513 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.513 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.513 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.513 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.514 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.515 * [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)))) 4.515 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.515 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.515 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.515 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.515 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.515 * [taylor]: Taking taylor expansion of 0.25 in n 4.515 * [backup-simplify]: Simplify 0.25 into 0.25 4.515 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.515 * [taylor]: Taking taylor expansion of 1.0 in n 4.516 * [backup-simplify]: Simplify 1.0 into 1.0 4.516 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.516 * [taylor]: Taking taylor expansion of k in n 4.516 * [backup-simplify]: Simplify k into k 4.516 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.516 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.516 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.516 * [taylor]: Taking taylor expansion of 2.0 in n 4.516 * [backup-simplify]: Simplify 2.0 into 2.0 4.516 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.516 * [taylor]: Taking taylor expansion of PI in n 4.516 * [backup-simplify]: Simplify PI into PI 4.516 * [taylor]: Taking taylor expansion of n in n 4.516 * [backup-simplify]: Simplify 0 into 0 4.516 * [backup-simplify]: Simplify 1 into 1 4.516 * [backup-simplify]: Simplify (/ PI 1) into PI 4.516 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.517 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.517 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.517 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.517 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.518 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.519 * [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)))) 4.519 * [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))))) 4.520 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.520 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.520 * [taylor]: Taking taylor expansion of 0.25 in k 4.520 * [backup-simplify]: Simplify 0.25 into 0.25 4.520 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.520 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.520 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.520 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.520 * [taylor]: Taking taylor expansion of 2.0 in k 4.520 * [backup-simplify]: Simplify 2.0 into 2.0 4.520 * [taylor]: Taking taylor expansion of PI in k 4.520 * [backup-simplify]: Simplify PI into PI 4.520 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.521 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.521 * [taylor]: Taking taylor expansion of (log n) in k 4.521 * [taylor]: Taking taylor expansion of n in k 4.521 * [backup-simplify]: Simplify n into n 4.521 * [backup-simplify]: Simplify (log n) into (log n) 4.521 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.521 * [taylor]: Taking taylor expansion of 1.0 in k 4.521 * [backup-simplify]: Simplify 1.0 into 1.0 4.521 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.521 * [taylor]: Taking taylor expansion of k in k 4.521 * [backup-simplify]: Simplify 0 into 0 4.521 * [backup-simplify]: Simplify 1 into 1 4.521 * [backup-simplify]: Simplify (/ 1 1) into 1 4.521 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.522 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.522 * [backup-simplify]: Simplify (- 1) into -1 4.522 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.523 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.524 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 4.524 * [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))))) 4.525 * [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))))) 4.526 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.526 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.527 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.527 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.527 * [backup-simplify]: Simplify (- 0) into 0 4.528 * [backup-simplify]: Simplify (+ 0 0) into 0 4.528 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.529 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.529 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.531 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.531 * [taylor]: Taking taylor expansion of 0 in k 4.531 * [backup-simplify]: Simplify 0 into 0 4.531 * [backup-simplify]: Simplify 0 into 0 4.531 * [backup-simplify]: Simplify 0 into 0 4.531 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.532 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.534 * [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 4.534 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.534 * [backup-simplify]: Simplify (- 0) into 0 4.534 * [backup-simplify]: Simplify (+ 0 0) into 0 4.535 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.536 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.537 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.538 * [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 4.538 * [taylor]: Taking taylor expansion of 0 in k 4.538 * [backup-simplify]: Simplify 0 into 0 4.538 * [backup-simplify]: Simplify 0 into 0 4.538 * [backup-simplify]: Simplify 0 into 0 4.538 * [backup-simplify]: Simplify 0 into 0 4.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.539 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.542 * [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 4.542 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.543 * [backup-simplify]: Simplify (- 0) into 0 4.543 * [backup-simplify]: Simplify (+ 0 0) into 0 4.544 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.544 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.546 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.547 * [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 4.547 * [taylor]: Taking taylor expansion of 0 in k 4.547 * [backup-simplify]: Simplify 0 into 0 4.547 * [backup-simplify]: Simplify 0 into 0 4.548 * [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)))) 4.549 * [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))) 4.549 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 4.549 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 4.549 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.549 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.549 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 4.549 * [taylor]: Taking taylor expansion of 0.25 in k 4.549 * [backup-simplify]: Simplify 0.25 into 0.25 4.549 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.549 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.549 * [taylor]: Taking taylor expansion of k in k 4.549 * [backup-simplify]: Simplify 0 into 0 4.549 * [backup-simplify]: Simplify 1 into 1 4.549 * [backup-simplify]: Simplify (/ 1 1) into 1 4.549 * [taylor]: Taking taylor expansion of 1.0 in k 4.549 * [backup-simplify]: Simplify 1.0 into 1.0 4.549 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.549 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.549 * [taylor]: Taking taylor expansion of -2.0 in k 4.549 * [backup-simplify]: Simplify -2.0 into -2.0 4.549 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.549 * [taylor]: Taking taylor expansion of PI in k 4.549 * [backup-simplify]: Simplify PI into PI 4.549 * [taylor]: Taking taylor expansion of n in k 4.549 * [backup-simplify]: Simplify n into n 4.549 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.549 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.550 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.550 * [backup-simplify]: Simplify (+ 1 0) into 1 4.550 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 4.550 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 4.550 * [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)))))) 4.550 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.550 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.550 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.550 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.550 * [taylor]: Taking taylor expansion of 0.25 in n 4.550 * [backup-simplify]: Simplify 0.25 into 0.25 4.550 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.550 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.550 * [taylor]: Taking taylor expansion of k in n 4.550 * [backup-simplify]: Simplify k into k 4.550 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.551 * [taylor]: Taking taylor expansion of 1.0 in n 4.551 * [backup-simplify]: Simplify 1.0 into 1.0 4.551 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.551 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.551 * [taylor]: Taking taylor expansion of -2.0 in n 4.551 * [backup-simplify]: Simplify -2.0 into -2.0 4.551 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.551 * [taylor]: Taking taylor expansion of PI in n 4.551 * [backup-simplify]: Simplify PI into PI 4.551 * [taylor]: Taking taylor expansion of n in n 4.551 * [backup-simplify]: Simplify 0 into 0 4.551 * [backup-simplify]: Simplify 1 into 1 4.551 * [backup-simplify]: Simplify (/ PI 1) into PI 4.551 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.552 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.552 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.552 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.553 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.554 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.554 * [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))))) 4.554 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.554 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.554 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.554 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.554 * [taylor]: Taking taylor expansion of 0.25 in n 4.554 * [backup-simplify]: Simplify 0.25 into 0.25 4.554 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.554 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.554 * [taylor]: Taking taylor expansion of k in n 4.554 * [backup-simplify]: Simplify k into k 4.554 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.555 * [taylor]: Taking taylor expansion of 1.0 in n 4.555 * [backup-simplify]: Simplify 1.0 into 1.0 4.555 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.555 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.555 * [taylor]: Taking taylor expansion of -2.0 in n 4.555 * [backup-simplify]: Simplify -2.0 into -2.0 4.555 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.555 * [taylor]: Taking taylor expansion of PI in n 4.555 * [backup-simplify]: Simplify PI into PI 4.555 * [taylor]: Taking taylor expansion of n in n 4.555 * [backup-simplify]: Simplify 0 into 0 4.555 * [backup-simplify]: Simplify 1 into 1 4.555 * [backup-simplify]: Simplify (/ PI 1) into PI 4.555 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.556 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.556 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.556 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.557 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.558 * [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)))) 4.558 * [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))))) 4.558 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.558 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.558 * [taylor]: Taking taylor expansion of 0.25 in k 4.558 * [backup-simplify]: Simplify 0.25 into 0.25 4.558 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.558 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.559 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.559 * [taylor]: Taking taylor expansion of k in k 4.559 * [backup-simplify]: Simplify 0 into 0 4.559 * [backup-simplify]: Simplify 1 into 1 4.559 * [backup-simplify]: Simplify (/ 1 1) into 1 4.559 * [taylor]: Taking taylor expansion of 1.0 in k 4.559 * [backup-simplify]: Simplify 1.0 into 1.0 4.559 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.559 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.559 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.559 * [taylor]: Taking taylor expansion of -2.0 in k 4.559 * [backup-simplify]: Simplify -2.0 into -2.0 4.559 * [taylor]: Taking taylor expansion of PI in k 4.559 * [backup-simplify]: Simplify PI into PI 4.559 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.560 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.560 * [taylor]: Taking taylor expansion of (log n) in k 4.560 * [taylor]: Taking taylor expansion of n in k 4.560 * [backup-simplify]: Simplify n into n 4.560 * [backup-simplify]: Simplify (log n) into (log n) 4.560 * [backup-simplify]: Simplify (+ 1 0) into 1 4.560 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.561 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.561 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.562 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 4.563 * [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))))) 4.564 * [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))))) 4.570 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.571 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.572 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.572 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.572 * [backup-simplify]: Simplify (+ 0 0) into 0 4.573 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.574 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.574 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.576 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.576 * [taylor]: Taking taylor expansion of 0 in k 4.576 * [backup-simplify]: Simplify 0 into 0 4.576 * [backup-simplify]: Simplify 0 into 0 4.576 * [backup-simplify]: Simplify 0 into 0 4.577 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.577 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.579 * [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 4.579 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.579 * [backup-simplify]: Simplify (+ 0 0) into 0 4.580 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.581 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.582 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.583 * [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 4.583 * [taylor]: Taking taylor expansion of 0 in k 4.583 * [backup-simplify]: Simplify 0 into 0 4.583 * [backup-simplify]: Simplify 0 into 0 4.583 * [backup-simplify]: Simplify 0 into 0 4.583 * [backup-simplify]: Simplify 0 into 0 4.584 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.585 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.587 * [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 4.588 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.588 * [backup-simplify]: Simplify (+ 0 0) into 0 4.589 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.589 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.591 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.592 * [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 4.592 * [taylor]: Taking taylor expansion of 0 in k 4.592 * [backup-simplify]: Simplify 0 into 0 4.592 * [backup-simplify]: Simplify 0 into 0 4.593 * [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)))))) 4.593 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1) 4.594 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.594 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.594 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.594 * [taylor]: Taking taylor expansion of 2.0 in n 4.594 * [backup-simplify]: Simplify 2.0 into 2.0 4.594 * [taylor]: Taking taylor expansion of (* n PI) in n 4.594 * [taylor]: Taking taylor expansion of n in n 4.594 * [backup-simplify]: Simplify 0 into 0 4.594 * [backup-simplify]: Simplify 1 into 1 4.594 * [taylor]: Taking taylor expansion of PI in n 4.594 * [backup-simplify]: Simplify PI into PI 4.594 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.594 * [taylor]: Taking taylor expansion of 2.0 in n 4.594 * [backup-simplify]: Simplify 2.0 into 2.0 4.594 * [taylor]: Taking taylor expansion of (* n PI) in n 4.594 * [taylor]: Taking taylor expansion of n in n 4.594 * [backup-simplify]: Simplify 0 into 0 4.594 * [backup-simplify]: Simplify 1 into 1 4.594 * [taylor]: Taking taylor expansion of PI in n 4.594 * [backup-simplify]: Simplify PI into PI 4.594 * [backup-simplify]: Simplify (* 0 PI) into 0 4.594 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.594 * [backup-simplify]: Simplify 0 into 0 4.595 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.597 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.597 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.597 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.598 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.598 * [backup-simplify]: Simplify 0 into 0 4.599 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.599 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.599 * [backup-simplify]: Simplify 0 into 0 4.600 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.601 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.601 * [backup-simplify]: Simplify 0 into 0 4.602 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.602 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 4.602 * [backup-simplify]: Simplify 0 into 0 4.603 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.604 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 4.604 * [backup-simplify]: Simplify 0 into 0 4.605 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 4.606 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 4.606 * [backup-simplify]: Simplify 0 into 0 4.607 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.607 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 4.607 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.607 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.607 * [taylor]: Taking taylor expansion of 2.0 in n 4.607 * [backup-simplify]: Simplify 2.0 into 2.0 4.607 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.607 * [taylor]: Taking taylor expansion of PI in n 4.607 * [backup-simplify]: Simplify PI into PI 4.607 * [taylor]: Taking taylor expansion of n in n 4.607 * [backup-simplify]: Simplify 0 into 0 4.607 * [backup-simplify]: Simplify 1 into 1 4.607 * [backup-simplify]: Simplify (/ PI 1) into PI 4.607 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.607 * [taylor]: Taking taylor expansion of 2.0 in n 4.607 * [backup-simplify]: Simplify 2.0 into 2.0 4.607 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.607 * [taylor]: Taking taylor expansion of PI in n 4.607 * [backup-simplify]: Simplify PI into PI 4.607 * [taylor]: Taking taylor expansion of n in n 4.607 * [backup-simplify]: Simplify 0 into 0 4.607 * [backup-simplify]: Simplify 1 into 1 4.608 * [backup-simplify]: Simplify (/ PI 1) into PI 4.608 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.608 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.609 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.609 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.609 * [backup-simplify]: Simplify 0 into 0 4.610 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.610 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.611 * [backup-simplify]: Simplify 0 into 0 4.611 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.612 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.612 * [backup-simplify]: Simplify 0 into 0 4.612 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.613 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.613 * [backup-simplify]: Simplify 0 into 0 4.614 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.615 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.615 * [backup-simplify]: Simplify 0 into 0 4.615 * [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 4.616 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.616 * [backup-simplify]: Simplify 0 into 0 4.617 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 4.617 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 4.617 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.617 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.617 * [taylor]: Taking taylor expansion of -2.0 in n 4.617 * [backup-simplify]: Simplify -2.0 into -2.0 4.617 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.617 * [taylor]: Taking taylor expansion of PI in n 4.617 * [backup-simplify]: Simplify PI into PI 4.617 * [taylor]: Taking taylor expansion of n in n 4.617 * [backup-simplify]: Simplify 0 into 0 4.617 * [backup-simplify]: Simplify 1 into 1 4.617 * [backup-simplify]: Simplify (/ PI 1) into PI 4.617 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.617 * [taylor]: Taking taylor expansion of -2.0 in n 4.617 * [backup-simplify]: Simplify -2.0 into -2.0 4.617 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.617 * [taylor]: Taking taylor expansion of PI in n 4.617 * [backup-simplify]: Simplify PI into PI 4.617 * [taylor]: Taking taylor expansion of n in n 4.617 * [backup-simplify]: Simplify 0 into 0 4.617 * [backup-simplify]: Simplify 1 into 1 4.618 * [backup-simplify]: Simplify (/ PI 1) into PI 4.618 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.618 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.619 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.619 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.619 * [backup-simplify]: Simplify 0 into 0 4.620 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.620 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.621 * [backup-simplify]: Simplify 0 into 0 4.621 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.622 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.622 * [backup-simplify]: Simplify 0 into 0 4.622 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.623 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.623 * [backup-simplify]: Simplify 0 into 0 4.624 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.625 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.625 * [backup-simplify]: Simplify 0 into 0 4.625 * [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 4.626 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.626 * [backup-simplify]: Simplify 0 into 0 4.626 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 4.627 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1) 4.627 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.627 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.627 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.627 * [taylor]: Taking taylor expansion of 2.0 in n 4.627 * [backup-simplify]: Simplify 2.0 into 2.0 4.627 * [taylor]: Taking taylor expansion of (* n PI) in n 4.627 * [taylor]: Taking taylor expansion of n in n 4.627 * [backup-simplify]: Simplify 0 into 0 4.627 * [backup-simplify]: Simplify 1 into 1 4.627 * [taylor]: Taking taylor expansion of PI in n 4.627 * [backup-simplify]: Simplify PI into PI 4.627 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.627 * [taylor]: Taking taylor expansion of 2.0 in n 4.627 * [backup-simplify]: Simplify 2.0 into 2.0 4.627 * [taylor]: Taking taylor expansion of (* n PI) in n 4.627 * [taylor]: Taking taylor expansion of n in n 4.627 * [backup-simplify]: Simplify 0 into 0 4.627 * [backup-simplify]: Simplify 1 into 1 4.627 * [taylor]: Taking taylor expansion of PI in n 4.627 * [backup-simplify]: Simplify PI into PI 4.627 * [backup-simplify]: Simplify (* 0 PI) into 0 4.628 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.628 * [backup-simplify]: Simplify 0 into 0 4.629 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.630 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.630 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.630 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.631 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.631 * [backup-simplify]: Simplify 0 into 0 4.632 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.632 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.632 * [backup-simplify]: Simplify 0 into 0 4.633 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.634 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.634 * [backup-simplify]: Simplify 0 into 0 4.635 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.635 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 4.635 * [backup-simplify]: Simplify 0 into 0 4.636 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.637 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 4.637 * [backup-simplify]: Simplify 0 into 0 4.638 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 4.639 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 4.639 * [backup-simplify]: Simplify 0 into 0 4.640 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.640 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 4.640 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.640 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.640 * [taylor]: Taking taylor expansion of 2.0 in n 4.640 * [backup-simplify]: Simplify 2.0 into 2.0 4.640 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.640 * [taylor]: Taking taylor expansion of PI in n 4.640 * [backup-simplify]: Simplify PI into PI 4.640 * [taylor]: Taking taylor expansion of n in n 4.640 * [backup-simplify]: Simplify 0 into 0 4.640 * [backup-simplify]: Simplify 1 into 1 4.641 * [backup-simplify]: Simplify (/ PI 1) into PI 4.641 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.641 * [taylor]: Taking taylor expansion of 2.0 in n 4.641 * [backup-simplify]: Simplify 2.0 into 2.0 4.641 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.641 * [taylor]: Taking taylor expansion of PI in n 4.641 * [backup-simplify]: Simplify PI into PI 4.641 * [taylor]: Taking taylor expansion of n in n 4.641 * [backup-simplify]: Simplify 0 into 0 4.641 * [backup-simplify]: Simplify 1 into 1 4.641 * [backup-simplify]: Simplify (/ PI 1) into PI 4.641 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.642 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.642 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.643 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.643 * [backup-simplify]: Simplify 0 into 0 4.643 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.644 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.644 * [backup-simplify]: Simplify 0 into 0 4.644 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.645 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.645 * [backup-simplify]: Simplify 0 into 0 4.646 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.647 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.647 * [backup-simplify]: Simplify 0 into 0 4.647 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.648 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.648 * [backup-simplify]: Simplify 0 into 0 4.649 * [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 4.650 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.650 * [backup-simplify]: Simplify 0 into 0 4.650 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 4.650 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 4.651 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.651 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.651 * [taylor]: Taking taylor expansion of -2.0 in n 4.651 * [backup-simplify]: Simplify -2.0 into -2.0 4.651 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.651 * [taylor]: Taking taylor expansion of PI in n 4.651 * [backup-simplify]: Simplify PI into PI 4.651 * [taylor]: Taking taylor expansion of n in n 4.651 * [backup-simplify]: Simplify 0 into 0 4.651 * [backup-simplify]: Simplify 1 into 1 4.651 * [backup-simplify]: Simplify (/ PI 1) into PI 4.651 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.651 * [taylor]: Taking taylor expansion of -2.0 in n 4.651 * [backup-simplify]: Simplify -2.0 into -2.0 4.651 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.651 * [taylor]: Taking taylor expansion of PI in n 4.651 * [backup-simplify]: Simplify PI into PI 4.651 * [taylor]: Taking taylor expansion of n in n 4.651 * [backup-simplify]: Simplify 0 into 0 4.651 * [backup-simplify]: Simplify 1 into 1 4.651 * [backup-simplify]: Simplify (/ PI 1) into PI 4.652 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.652 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.653 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.653 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.653 * [backup-simplify]: Simplify 0 into 0 4.654 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.654 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.654 * [backup-simplify]: Simplify 0 into 0 4.655 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.655 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.655 * [backup-simplify]: Simplify 0 into 0 4.656 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.657 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.657 * [backup-simplify]: Simplify 0 into 0 4.657 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.658 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.658 * [backup-simplify]: Simplify 0 into 0 4.665 * [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 4.666 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.666 * [backup-simplify]: Simplify 0 into 0 4.667 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 4.667 * * * [progress]: simplifying candidates 4.670 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 4.671 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (log1p (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (/ (- h2 h1) h0) 2)) (* (+ (log (* h0 h4)) (log h3)) (/ (/ (- h2 h1) h0) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (- h2 h1) h0) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ h2 h0) 2)) (pow (* (* h0 h4) h3) (/ (/ h1 h0) 2)) (pow (* (* h0 h4) h3) (* (cbrt (/ (/ (- h2 h1) h0) 2)) (cbrt (/ (/ (- h2 h1) h0) 2)))) (pow (* (* h0 h4) h3) (sqrt (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) 1)) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ 1 (sqrt 2))) (pow (* (* h0 h4) h3) (/ 1 1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (- h2 h1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (- h2 h1) 1)) (pow (* (* h0 h4) h3) 1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* h0 h4) (/ (/ (- h2 h1) h0) 2)) (pow h3 (/ (/ (- h2 h1) h0) 2)) (log (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (exp (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (expm1 (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (log1p (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (/ (- h2 h1) h0) 2)) (* (+ (log (* h0 h4)) (log h3)) (/ (/ (- h2 h1) h0) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (- h2 h1) h0) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (* 1 (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ h2 h0) 2)) (pow (* (* h0 h4) h3) (/ (/ h1 h0) 2)) (pow (* (* h0 h4) h3) (* (cbrt (/ (/ (- h2 h1) h0) 2)) (cbrt (/ (/ (- h2 h1) h0) 2)))) (pow (* (* h0 h4) h3) (sqrt (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (* (cbrt (/ (- h2 h1) h0)) (cbrt (/ (- h2 h1) h0))) 1)) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- 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h0) 2) 2)) (expm1 (* (* h0 h4) h3)) (log1p (* (* h0 h4) h3)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (expm1 (* (* h0 h4) h3)) (log1p (* (* h0 h4) h3)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) 4.679 * * [simplify]: iteration 0 : 703 enodes (cost 1718 ) 4.690 * * [simplify]: iteration 1 : 2797 enodes (cost 1652 ) 4.732 * * [simplify]: iteration 2 : 5001 enodes (cost 1636 ) 4.740 * * * [progress]: adding candidates to table 5.461 * [progress]: [Phase 3 of 3] Extracting. 5.461 * * [regime]: Finding splitpoints for: (# # # # # # # # #) 5.463 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 5.463 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # # #) 5.505 * * * * [regimes]: Trying to branch on n from (# # # # # # # # #) 5.544 * * * * [regimes]: Trying to branch on k from (# # # # # # # # #) 5.583 * * * [regime]: Found split indices: #