10.999 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.090 * * * [progress]: [2/2] Setting up program. 0.093 * [progress]: [Phase 2 of 3] Improving. 0.093 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.093 * [simplify]: Sending expressions to egg_math: (* (/ h0 (sqrt h1)) (pow (* (* h2 h3) h4) (/ (- h0 h1) h2))) 0.095 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.096 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.098 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.101 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.106 * * [simplify]: iteration 4 : 1044 enodes (cost 8 ) 0.128 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.129 * * [progress]: iteration 1 / 4 0.129 * * * [progress]: picking best candidate 0.131 * * * * [pick]: Picked # 0.131 * * * [progress]: localizing error 0.144 * * * [progress]: generating rewritten candidates 0.144 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.167 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.173 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 0.190 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.234 * * * [progress]: generating series expansions 0.234 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.235 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 0.235 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.235 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.235 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.235 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.235 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.235 * [taylor]: Taking taylor expansion of 0.5 in k 0.235 * [backup-simplify]: Simplify 0.5 into 0.5 0.235 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.235 * [taylor]: Taking taylor expansion of 1.0 in k 0.235 * [backup-simplify]: Simplify 1.0 into 1.0 0.235 * [taylor]: Taking taylor expansion of k in k 0.235 * [backup-simplify]: Simplify 0 into 0 0.235 * [backup-simplify]: Simplify 1 into 1 0.235 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.235 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.235 * [taylor]: Taking taylor expansion of 2.0 in k 0.235 * [backup-simplify]: Simplify 2.0 into 2.0 0.235 * [taylor]: Taking taylor expansion of (* n PI) in k 0.235 * [taylor]: Taking taylor expansion of n in k 0.235 * [backup-simplify]: Simplify n into n 0.235 * [taylor]: Taking taylor expansion of PI in k 0.235 * [backup-simplify]: Simplify PI into PI 0.235 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.235 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.235 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.236 * [backup-simplify]: Simplify (- 0) into 0 0.236 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.236 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.236 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.236 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.236 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.236 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.236 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.236 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.236 * [taylor]: Taking taylor expansion of 0.5 in n 0.236 * [backup-simplify]: Simplify 0.5 into 0.5 0.236 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.236 * [taylor]: Taking taylor expansion of 1.0 in n 0.236 * [backup-simplify]: Simplify 1.0 into 1.0 0.236 * [taylor]: Taking taylor expansion of k in n 0.236 * [backup-simplify]: Simplify k into k 0.236 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.236 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.236 * [taylor]: Taking taylor expansion of 2.0 in n 0.236 * [backup-simplify]: Simplify 2.0 into 2.0 0.237 * [taylor]: Taking taylor expansion of (* n PI) in n 0.237 * [taylor]: Taking taylor expansion of n in n 0.237 * [backup-simplify]: Simplify 0 into 0 0.237 * [backup-simplify]: Simplify 1 into 1 0.237 * [taylor]: Taking taylor expansion of PI in n 0.237 * [backup-simplify]: Simplify PI into PI 0.237 * [backup-simplify]: Simplify (* 0 PI) into 0 0.237 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.238 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.239 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.239 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.239 * [backup-simplify]: Simplify (- k) into (- k) 0.239 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.240 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.240 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.241 * [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)))) 0.242 * [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))))) 0.242 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.242 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.242 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.242 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.242 * [taylor]: Taking taylor expansion of 0.5 in n 0.242 * [backup-simplify]: Simplify 0.5 into 0.5 0.242 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.242 * [taylor]: Taking taylor expansion of 1.0 in n 0.242 * [backup-simplify]: Simplify 1.0 into 1.0 0.242 * [taylor]: Taking taylor expansion of k in n 0.242 * [backup-simplify]: Simplify k into k 0.242 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.242 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.242 * [taylor]: Taking taylor expansion of 2.0 in n 0.242 * [backup-simplify]: Simplify 2.0 into 2.0 0.242 * [taylor]: Taking taylor expansion of (* n PI) in n 0.242 * [taylor]: Taking taylor expansion of n in n 0.242 * [backup-simplify]: Simplify 0 into 0 0.242 * [backup-simplify]: Simplify 1 into 1 0.242 * [taylor]: Taking taylor expansion of PI in n 0.242 * [backup-simplify]: Simplify PI into PI 0.242 * [backup-simplify]: Simplify (* 0 PI) into 0 0.242 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.243 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.244 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.245 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.245 * [backup-simplify]: Simplify (- k) into (- k) 0.245 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.245 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.246 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.246 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.247 * [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))))) 0.247 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.247 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.247 * [taylor]: Taking taylor expansion of 0.5 in k 0.247 * [backup-simplify]: Simplify 0.5 into 0.5 0.247 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.247 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.247 * [taylor]: Taking taylor expansion of 1.0 in k 0.247 * [backup-simplify]: Simplify 1.0 into 1.0 0.247 * [taylor]: Taking taylor expansion of k in k 0.247 * [backup-simplify]: Simplify 0 into 0 0.247 * [backup-simplify]: Simplify 1 into 1 0.247 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.247 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.247 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.247 * [taylor]: Taking taylor expansion of 2.0 in k 0.247 * [backup-simplify]: Simplify 2.0 into 2.0 0.247 * [taylor]: Taking taylor expansion of PI in k 0.247 * [backup-simplify]: Simplify PI into PI 0.248 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.248 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.248 * [taylor]: Taking taylor expansion of (log n) in k 0.248 * [taylor]: Taking taylor expansion of n in k 0.248 * [backup-simplify]: Simplify n into n 0.248 * [backup-simplify]: Simplify (log n) into (log n) 0.249 * [backup-simplify]: Simplify (- 0) into 0 0.249 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.249 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.250 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.251 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.252 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.252 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.253 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.253 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.254 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.254 * [backup-simplify]: Simplify (- 0) into 0 0.255 * [backup-simplify]: Simplify (+ 0 0) into 0 0.255 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 0.256 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.256 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.257 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.257 * [taylor]: Taking taylor expansion of 0 in k 0.257 * [backup-simplify]: Simplify 0 into 0 0.257 * [backup-simplify]: Simplify 0 into 0 0.258 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.259 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.259 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.259 * [backup-simplify]: Simplify (+ 0 0) into 0 0.260 * [backup-simplify]: Simplify (- 1) into -1 0.260 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.261 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.262 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 0.264 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0.265 * [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 0.267 * [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 0.269 * [backup-simplify]: Simplify (- 0) into 0 0.269 * [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 0.273 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.273 * [taylor]: Taking taylor expansion of 0 in k 0.273 * [backup-simplify]: Simplify 0 into 0 0.273 * [backup-simplify]: Simplify 0 into 0 0.273 * [backup-simplify]: Simplify 0 into 0 0.273 * [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)))))) 0.290 * [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)))) 0.290 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.290 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.290 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.290 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.290 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.290 * [taylor]: Taking taylor expansion of 0.5 in k 0.290 * [backup-simplify]: Simplify 0.5 into 0.5 0.290 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.290 * [taylor]: Taking taylor expansion of 1.0 in k 0.290 * [backup-simplify]: Simplify 1.0 into 1.0 0.290 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.290 * [taylor]: Taking taylor expansion of k in k 0.290 * [backup-simplify]: Simplify 0 into 0 0.290 * [backup-simplify]: Simplify 1 into 1 0.291 * [backup-simplify]: Simplify (/ 1 1) into 1 0.291 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.291 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.291 * [taylor]: Taking taylor expansion of 2.0 in k 0.291 * [backup-simplify]: Simplify 2.0 into 2.0 0.291 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.291 * [taylor]: Taking taylor expansion of PI in k 0.291 * [backup-simplify]: Simplify PI into PI 0.291 * [taylor]: Taking taylor expansion of n in k 0.291 * [backup-simplify]: Simplify n into n 0.291 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.291 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.291 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.291 * [backup-simplify]: Simplify (- 1) into -1 0.291 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.292 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.292 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.292 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 0.292 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.292 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.292 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.292 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.292 * [taylor]: Taking taylor expansion of 0.5 in n 0.292 * [backup-simplify]: Simplify 0.5 into 0.5 0.292 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.292 * [taylor]: Taking taylor expansion of 1.0 in n 0.292 * [backup-simplify]: Simplify 1.0 into 1.0 0.292 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.292 * [taylor]: Taking taylor expansion of k in n 0.292 * [backup-simplify]: Simplify k into k 0.292 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.292 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.292 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.292 * [taylor]: Taking taylor expansion of 2.0 in n 0.292 * [backup-simplify]: Simplify 2.0 into 2.0 0.292 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.292 * [taylor]: Taking taylor expansion of PI in n 0.292 * [backup-simplify]: Simplify PI into PI 0.292 * [taylor]: Taking taylor expansion of n in n 0.292 * [backup-simplify]: Simplify 0 into 0 0.292 * [backup-simplify]: Simplify 1 into 1 0.293 * [backup-simplify]: Simplify (/ PI 1) into PI 0.293 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.293 * [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))) 0.294 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.295 * [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)))) 0.296 * [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))))) 0.296 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.296 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.296 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.296 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.296 * [taylor]: Taking taylor expansion of 0.5 in n 0.296 * [backup-simplify]: Simplify 0.5 into 0.5 0.296 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.296 * [taylor]: Taking taylor expansion of 1.0 in n 0.296 * [backup-simplify]: Simplify 1.0 into 1.0 0.296 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.296 * [taylor]: Taking taylor expansion of k in n 0.296 * [backup-simplify]: Simplify k into k 0.296 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.296 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.296 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.296 * [taylor]: Taking taylor expansion of 2.0 in n 0.296 * [backup-simplify]: Simplify 2.0 into 2.0 0.296 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.296 * [taylor]: Taking taylor expansion of PI in n 0.296 * [backup-simplify]: Simplify PI into PI 0.296 * [taylor]: Taking taylor expansion of n in n 0.296 * [backup-simplify]: Simplify 0 into 0 0.296 * [backup-simplify]: Simplify 1 into 1 0.297 * [backup-simplify]: Simplify (/ PI 1) into PI 0.297 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.297 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.297 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.297 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.298 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.298 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.299 * [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)))) 0.300 * [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))))) 0.300 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.300 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.300 * [taylor]: Taking taylor expansion of 0.5 in k 0.300 * [backup-simplify]: Simplify 0.5 into 0.5 0.300 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.300 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.300 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.300 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.300 * [taylor]: Taking taylor expansion of 2.0 in k 0.300 * [backup-simplify]: Simplify 2.0 into 2.0 0.300 * [taylor]: Taking taylor expansion of PI in k 0.300 * [backup-simplify]: Simplify PI into PI 0.300 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.301 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.301 * [taylor]: Taking taylor expansion of (log n) in k 0.301 * [taylor]: Taking taylor expansion of n in k 0.301 * [backup-simplify]: Simplify n into n 0.301 * [backup-simplify]: Simplify (log n) into (log n) 0.301 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.301 * [taylor]: Taking taylor expansion of 1.0 in k 0.301 * [backup-simplify]: Simplify 1.0 into 1.0 0.301 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.301 * [taylor]: Taking taylor expansion of k in k 0.301 * [backup-simplify]: Simplify 0 into 0 0.301 * [backup-simplify]: Simplify 1 into 1 0.301 * [backup-simplify]: Simplify (/ 1 1) into 1 0.301 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.302 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.302 * [backup-simplify]: Simplify (- 1) into -1 0.302 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.303 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.304 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 0.308 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.309 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.310 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.311 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.311 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.311 * [backup-simplify]: Simplify (- 0) into 0 0.311 * [backup-simplify]: Simplify (+ 0 0) into 0 0.311 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.312 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.313 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.314 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.314 * [taylor]: Taking taylor expansion of 0 in k 0.314 * [backup-simplify]: Simplify 0 into 0 0.314 * [backup-simplify]: Simplify 0 into 0 0.314 * [backup-simplify]: Simplify 0 into 0 0.315 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.315 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.317 * [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 0.317 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.317 * [backup-simplify]: Simplify (- 0) into 0 0.317 * [backup-simplify]: Simplify (+ 0 0) into 0 0.318 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 0.318 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.319 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 0.321 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.321 * [taylor]: Taking taylor expansion of 0 in k 0.321 * [backup-simplify]: Simplify 0 into 0 0.321 * [backup-simplify]: Simplify 0 into 0 0.321 * [backup-simplify]: Simplify 0 into 0 0.321 * [backup-simplify]: Simplify 0 into 0 0.321 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.322 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.325 * [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 0.325 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.325 * [backup-simplify]: Simplify (- 0) into 0 0.325 * [backup-simplify]: Simplify (+ 0 0) into 0 0.326 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 0.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.328 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 0.329 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 0.329 * [taylor]: Taking taylor expansion of 0 in k 0.329 * [backup-simplify]: Simplify 0 into 0 0.330 * [backup-simplify]: Simplify 0 into 0 0.330 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 0.331 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 0.331 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.331 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.331 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.331 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.331 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.331 * [taylor]: Taking taylor expansion of 0.5 in k 0.331 * [backup-simplify]: Simplify 0.5 into 0.5 0.331 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.331 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.331 * [taylor]: Taking taylor expansion of k in k 0.331 * [backup-simplify]: Simplify 0 into 0 0.331 * [backup-simplify]: Simplify 1 into 1 0.331 * [backup-simplify]: Simplify (/ 1 1) into 1 0.331 * [taylor]: Taking taylor expansion of 1.0 in k 0.331 * [backup-simplify]: Simplify 1.0 into 1.0 0.331 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.331 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.331 * [taylor]: Taking taylor expansion of -2.0 in k 0.331 * [backup-simplify]: Simplify -2.0 into -2.0 0.331 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.331 * [taylor]: Taking taylor expansion of PI in k 0.331 * [backup-simplify]: Simplify PI into PI 0.331 * [taylor]: Taking taylor expansion of n in k 0.331 * [backup-simplify]: Simplify n into n 0.332 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.332 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.332 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.332 * [backup-simplify]: Simplify (+ 1 0) into 1 0.332 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.332 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.332 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 0.332 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.332 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.332 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.332 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.332 * [taylor]: Taking taylor expansion of 0.5 in n 0.332 * [backup-simplify]: Simplify 0.5 into 0.5 0.332 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.332 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.333 * [taylor]: Taking taylor expansion of k in n 0.333 * [backup-simplify]: Simplify k into k 0.333 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.333 * [taylor]: Taking taylor expansion of 1.0 in n 0.333 * [backup-simplify]: Simplify 1.0 into 1.0 0.333 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.333 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.333 * [taylor]: Taking taylor expansion of -2.0 in n 0.333 * [backup-simplify]: Simplify -2.0 into -2.0 0.333 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.333 * [taylor]: Taking taylor expansion of PI in n 0.333 * [backup-simplify]: Simplify PI into PI 0.333 * [taylor]: Taking taylor expansion of n in n 0.333 * [backup-simplify]: Simplify 0 into 0 0.333 * [backup-simplify]: Simplify 1 into 1 0.333 * [backup-simplify]: Simplify (/ PI 1) into PI 0.333 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.334 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.334 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.334 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.335 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.336 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.336 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.336 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.336 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.336 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.336 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.336 * [taylor]: Taking taylor expansion of 0.5 in n 0.336 * [backup-simplify]: Simplify 0.5 into 0.5 0.336 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.336 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.336 * [taylor]: Taking taylor expansion of k in n 0.336 * [backup-simplify]: Simplify k into k 0.337 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.337 * [taylor]: Taking taylor expansion of 1.0 in n 0.337 * [backup-simplify]: Simplify 1.0 into 1.0 0.337 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.337 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.337 * [taylor]: Taking taylor expansion of -2.0 in n 0.337 * [backup-simplify]: Simplify -2.0 into -2.0 0.337 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.337 * [taylor]: Taking taylor expansion of PI in n 0.337 * [backup-simplify]: Simplify PI into PI 0.337 * [taylor]: Taking taylor expansion of n in n 0.337 * [backup-simplify]: Simplify 0 into 0 0.337 * [backup-simplify]: Simplify 1 into 1 0.337 * [backup-simplify]: Simplify (/ PI 1) into PI 0.337 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.338 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.338 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.338 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.339 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.339 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.340 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.340 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.340 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.340 * [taylor]: Taking taylor expansion of 0.5 in k 0.340 * [backup-simplify]: Simplify 0.5 into 0.5 0.340 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.340 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.340 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.340 * [taylor]: Taking taylor expansion of k in k 0.340 * [backup-simplify]: Simplify 0 into 0 0.340 * [backup-simplify]: Simplify 1 into 1 0.341 * [backup-simplify]: Simplify (/ 1 1) into 1 0.341 * [taylor]: Taking taylor expansion of 1.0 in k 0.341 * [backup-simplify]: Simplify 1.0 into 1.0 0.341 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.341 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.341 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.341 * [taylor]: Taking taylor expansion of -2.0 in k 0.341 * [backup-simplify]: Simplify -2.0 into -2.0 0.341 * [taylor]: Taking taylor expansion of PI in k 0.341 * [backup-simplify]: Simplify PI into PI 0.341 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.342 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.342 * [taylor]: Taking taylor expansion of (log n) in k 0.342 * [taylor]: Taking taylor expansion of n in k 0.342 * [backup-simplify]: Simplify n into n 0.342 * [backup-simplify]: Simplify (log n) into (log n) 0.342 * [backup-simplify]: Simplify (+ 1 0) into 1 0.342 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.343 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 0.343 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 0.344 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 0.345 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.345 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.346 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.346 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.347 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.347 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.347 * [backup-simplify]: Simplify (+ 0 0) into 0 0.348 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 0.348 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.349 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.350 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.350 * [taylor]: Taking taylor expansion of 0 in k 0.350 * [backup-simplify]: Simplify 0 into 0 0.350 * [backup-simplify]: Simplify 0 into 0 0.350 * [backup-simplify]: Simplify 0 into 0 0.351 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.351 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.353 * [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 0.353 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.353 * [backup-simplify]: Simplify (+ 0 0) into 0 0.354 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 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)) 0.356 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 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 2) 2)) (* (/ (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 into 0 0.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.358 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.361 * [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 0.361 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.362 * [backup-simplify]: Simplify (+ 0 0) into 0 0.362 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.363 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.364 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 0.366 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 0.366 * [taylor]: Taking taylor expansion of 0 in k 0.366 * [backup-simplify]: Simplify 0 into 0 0.366 * [backup-simplify]: Simplify 0 into 0 0.367 * [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)))))) 0.367 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.367 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.367 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.367 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.367 * [taylor]: Taking taylor expansion of 1.0 in k 0.367 * [backup-simplify]: Simplify 1.0 into 1.0 0.367 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.367 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.367 * [taylor]: Taking taylor expansion of k in k 0.367 * [backup-simplify]: Simplify 0 into 0 0.367 * [backup-simplify]: Simplify 1 into 1 0.367 * [backup-simplify]: Simplify (/ 1 1) into 1 0.367 * [backup-simplify]: Simplify (sqrt 0) into 0 0.368 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.368 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.368 * [taylor]: Taking taylor expansion of 1.0 in k 0.368 * [backup-simplify]: Simplify 1.0 into 1.0 0.368 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.368 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.368 * [taylor]: Taking taylor expansion of k in k 0.368 * [backup-simplify]: Simplify 0 into 0 0.368 * [backup-simplify]: Simplify 1 into 1 0.368 * [backup-simplify]: Simplify (/ 1 1) into 1 0.369 * [backup-simplify]: Simplify (sqrt 0) into 0 0.369 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.370 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.370 * [backup-simplify]: Simplify 0 into 0 0.370 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.371 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.371 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.373 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.374 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.374 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.374 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.376 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.378 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.378 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.379 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 0.379 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 0.379 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.379 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.379 * [taylor]: Taking taylor expansion of 1.0 in k 0.379 * [backup-simplify]: Simplify 1.0 into 1.0 0.379 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.379 * [taylor]: Taking taylor expansion of k in k 0.379 * [backup-simplify]: Simplify 0 into 0 0.379 * [backup-simplify]: Simplify 1 into 1 0.379 * [backup-simplify]: Simplify (sqrt 0) into 0 0.380 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.380 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.380 * [taylor]: Taking taylor expansion of 1.0 in k 0.380 * [backup-simplify]: Simplify 1.0 into 1.0 0.380 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.380 * [taylor]: Taking taylor expansion of k in k 0.380 * [backup-simplify]: Simplify 0 into 0 0.380 * [backup-simplify]: Simplify 1 into 1 0.380 * [backup-simplify]: Simplify (sqrt 0) into 0 0.381 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.381 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.381 * [backup-simplify]: Simplify 0 into 0 0.382 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.382 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.384 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.385 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.385 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.387 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.388 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.389 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.390 * [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)))))))) 0.390 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.390 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.390 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.390 * [taylor]: Taking taylor expansion of 1.0 in k 0.390 * [backup-simplify]: Simplify 1.0 into 1.0 0.390 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.390 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.390 * [taylor]: Taking taylor expansion of -1 in k 0.390 * [backup-simplify]: Simplify -1 into -1 0.390 * [taylor]: Taking taylor expansion of k in k 0.390 * [backup-simplify]: Simplify 0 into 0 0.390 * [backup-simplify]: Simplify 1 into 1 0.390 * [backup-simplify]: Simplify (/ -1 1) into -1 0.390 * [backup-simplify]: Simplify (sqrt 0) into 0 0.391 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.391 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.391 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.391 * [taylor]: Taking taylor expansion of 1.0 in k 0.391 * [backup-simplify]: Simplify 1.0 into 1.0 0.391 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.391 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.391 * [taylor]: Taking taylor expansion of -1 in k 0.391 * [backup-simplify]: Simplify -1 into -1 0.391 * [taylor]: Taking taylor expansion of k in k 0.392 * [backup-simplify]: Simplify 0 into 0 0.392 * [backup-simplify]: Simplify 1 into 1 0.392 * [backup-simplify]: Simplify (/ -1 1) into -1 0.392 * [backup-simplify]: Simplify (sqrt 0) into 0 0.396 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.397 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.397 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.397 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.399 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.400 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 0.400 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.403 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.405 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 0.406 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.406 * [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))))) 0.406 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 0.407 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.407 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.407 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.407 * [taylor]: Taking taylor expansion of 2.0 in n 0.407 * [backup-simplify]: Simplify 2.0 into 2.0 0.407 * [taylor]: Taking taylor expansion of (* n PI) in n 0.407 * [taylor]: Taking taylor expansion of n in n 0.407 * [backup-simplify]: Simplify 0 into 0 0.407 * [backup-simplify]: Simplify 1 into 1 0.407 * [taylor]: Taking taylor expansion of PI in n 0.407 * [backup-simplify]: Simplify PI into PI 0.407 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.407 * [taylor]: Taking taylor expansion of 2.0 in n 0.407 * [backup-simplify]: Simplify 2.0 into 2.0 0.407 * [taylor]: Taking taylor expansion of (* n PI) in n 0.407 * [taylor]: Taking taylor expansion of n in n 0.407 * [backup-simplify]: Simplify 0 into 0 0.407 * [backup-simplify]: Simplify 1 into 1 0.407 * [taylor]: Taking taylor expansion of PI in n 0.407 * [backup-simplify]: Simplify PI into PI 0.407 * [backup-simplify]: Simplify (* 0 PI) into 0 0.408 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.408 * [backup-simplify]: Simplify 0 into 0 0.408 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.409 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.409 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.410 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.411 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.411 * [backup-simplify]: Simplify 0 into 0 0.411 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.412 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.412 * [backup-simplify]: Simplify 0 into 0 0.412 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.413 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.413 * [backup-simplify]: Simplify 0 into 0 0.414 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.415 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 0.415 * [backup-simplify]: Simplify 0 into 0 0.416 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.416 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.416 * [backup-simplify]: Simplify 0 into 0 0.417 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.418 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.418 * [backup-simplify]: Simplify 0 into 0 0.419 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.419 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 0.419 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.419 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.419 * [taylor]: Taking taylor expansion of 2.0 in n 0.419 * [backup-simplify]: Simplify 2.0 into 2.0 0.419 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.419 * [taylor]: Taking taylor expansion of PI in n 0.419 * [backup-simplify]: Simplify PI into PI 0.419 * [taylor]: Taking taylor expansion of n in n 0.419 * [backup-simplify]: Simplify 0 into 0 0.419 * [backup-simplify]: Simplify 1 into 1 0.420 * [backup-simplify]: Simplify (/ PI 1) into PI 0.420 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.420 * [taylor]: Taking taylor expansion of 2.0 in n 0.420 * [backup-simplify]: Simplify 2.0 into 2.0 0.420 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.420 * [taylor]: Taking taylor expansion of PI in n 0.420 * [backup-simplify]: Simplify PI into PI 0.420 * [taylor]: Taking taylor expansion of n in n 0.420 * [backup-simplify]: Simplify 0 into 0 0.420 * [backup-simplify]: Simplify 1 into 1 0.420 * [backup-simplify]: Simplify (/ PI 1) into PI 0.420 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.421 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.421 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.421 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.421 * [backup-simplify]: Simplify 0 into 0 0.422 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.423 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.423 * [backup-simplify]: Simplify 0 into 0 0.423 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.424 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.424 * [backup-simplify]: Simplify 0 into 0 0.424 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.425 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.425 * [backup-simplify]: Simplify 0 into 0 0.426 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.426 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.426 * [backup-simplify]: Simplify 0 into 0 0.427 * [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 0.428 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.428 * [backup-simplify]: Simplify 0 into 0 0.428 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.429 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.429 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.429 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.429 * [taylor]: Taking taylor expansion of -2.0 in n 0.429 * [backup-simplify]: Simplify -2.0 into -2.0 0.429 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.429 * [taylor]: Taking taylor expansion of PI in n 0.429 * [backup-simplify]: Simplify PI into PI 0.429 * [taylor]: Taking taylor expansion of n in n 0.429 * [backup-simplify]: Simplify 0 into 0 0.429 * [backup-simplify]: Simplify 1 into 1 0.429 * [backup-simplify]: Simplify (/ PI 1) into PI 0.429 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.429 * [taylor]: Taking taylor expansion of -2.0 in n 0.429 * [backup-simplify]: Simplify -2.0 into -2.0 0.429 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.429 * [taylor]: Taking taylor expansion of PI in n 0.429 * [backup-simplify]: Simplify PI into PI 0.429 * [taylor]: Taking taylor expansion of n in n 0.429 * [backup-simplify]: Simplify 0 into 0 0.429 * [backup-simplify]: Simplify 1 into 1 0.429 * [backup-simplify]: Simplify (/ PI 1) into PI 0.430 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.430 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.431 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.431 * [backup-simplify]: Simplify 0 into 0 0.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.432 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 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)) (* 0 (/ 0 1)))) into 0 0.433 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 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)) (* 0 (/ 0 1)))) into 0 0.435 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.435 * [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)) (* 0 (/ 0 1)))) into 0 0.436 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 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)) (* 0 (/ 0 1)))) into 0 0.437 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.438 * [backup-simplify]: Simplify 0 into 0 0.438 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.438 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.438 * [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))))) 0.438 * [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 0.438 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.439 * [taylor]: Taking taylor expansion of 1.0 in n 0.439 * [backup-simplify]: Simplify 1.0 into 1.0 0.439 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.439 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.439 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.439 * [taylor]: Taking taylor expansion of k in n 0.439 * [backup-simplify]: Simplify k into k 0.439 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.439 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 0.439 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.439 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 0.439 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.439 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.439 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.439 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.439 * [taylor]: Taking taylor expansion of 0.5 in n 0.439 * [backup-simplify]: Simplify 0.5 into 0.5 0.439 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.439 * [taylor]: Taking taylor expansion of 1.0 in n 0.439 * [backup-simplify]: Simplify 1.0 into 1.0 0.439 * [taylor]: Taking taylor expansion of k in n 0.439 * [backup-simplify]: Simplify k into k 0.439 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.439 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.439 * [taylor]: Taking taylor expansion of 2.0 in n 0.439 * [backup-simplify]: Simplify 2.0 into 2.0 0.439 * [taylor]: Taking taylor expansion of (* n PI) in n 0.439 * [taylor]: Taking taylor expansion of n in n 0.439 * [backup-simplify]: Simplify 0 into 0 0.439 * [backup-simplify]: Simplify 1 into 1 0.439 * [taylor]: Taking taylor expansion of PI in n 0.439 * [backup-simplify]: Simplify PI into PI 0.439 * [backup-simplify]: Simplify (* 0 PI) into 0 0.440 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.440 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.441 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.442 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.442 * [backup-simplify]: Simplify (- k) into (- k) 0.442 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.442 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.443 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.443 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.444 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.444 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.444 * [taylor]: Taking taylor expansion of 1.0 in k 0.444 * [backup-simplify]: Simplify 1.0 into 1.0 0.444 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.444 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.444 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.444 * [taylor]: Taking taylor expansion of k in k 0.444 * [backup-simplify]: Simplify 0 into 0 0.444 * [backup-simplify]: Simplify 1 into 1 0.445 * [backup-simplify]: Simplify (/ 1 1) into 1 0.445 * [backup-simplify]: Simplify (sqrt 0) into 0 0.446 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.446 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.446 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.446 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.446 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.446 * [taylor]: Taking taylor expansion of 0.5 in k 0.446 * [backup-simplify]: Simplify 0.5 into 0.5 0.446 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.446 * [taylor]: Taking taylor expansion of 1.0 in k 0.446 * [backup-simplify]: Simplify 1.0 into 1.0 0.446 * [taylor]: Taking taylor expansion of k in k 0.446 * [backup-simplify]: Simplify 0 into 0 0.446 * [backup-simplify]: Simplify 1 into 1 0.446 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.446 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.446 * [taylor]: Taking taylor expansion of 2.0 in k 0.446 * [backup-simplify]: Simplify 2.0 into 2.0 0.446 * [taylor]: Taking taylor expansion of (* n PI) in k 0.446 * [taylor]: Taking taylor expansion of n in k 0.446 * [backup-simplify]: Simplify n into n 0.446 * [taylor]: Taking taylor expansion of PI in k 0.446 * [backup-simplify]: Simplify PI into PI 0.446 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.446 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.446 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.446 * [backup-simplify]: Simplify (- 0) into 0 0.447 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.447 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.447 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.447 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.447 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.447 * [taylor]: Taking taylor expansion of 1.0 in k 0.447 * [backup-simplify]: Simplify 1.0 into 1.0 0.447 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.447 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.447 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.447 * [taylor]: Taking taylor expansion of k in k 0.447 * [backup-simplify]: Simplify 0 into 0 0.447 * [backup-simplify]: Simplify 1 into 1 0.447 * [backup-simplify]: Simplify (/ 1 1) into 1 0.447 * [backup-simplify]: Simplify (sqrt 0) into 0 0.448 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.448 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.448 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.448 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.448 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.448 * [taylor]: Taking taylor expansion of 0.5 in k 0.448 * [backup-simplify]: Simplify 0.5 into 0.5 0.448 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.448 * [taylor]: Taking taylor expansion of 1.0 in k 0.448 * [backup-simplify]: Simplify 1.0 into 1.0 0.448 * [taylor]: Taking taylor expansion of k in k 0.448 * [backup-simplify]: Simplify 0 into 0 0.448 * [backup-simplify]: Simplify 1 into 1 0.448 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.448 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.448 * [taylor]: Taking taylor expansion of 2.0 in k 0.448 * [backup-simplify]: Simplify 2.0 into 2.0 0.448 * [taylor]: Taking taylor expansion of (* n PI) in k 0.449 * [taylor]: Taking taylor expansion of n in k 0.449 * [backup-simplify]: Simplify n into n 0.449 * [taylor]: Taking taylor expansion of PI in k 0.449 * [backup-simplify]: Simplify PI into PI 0.449 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.449 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.449 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.449 * [backup-simplify]: Simplify (- 0) into 0 0.449 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.449 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.449 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.450 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.450 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 0.450 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.450 * [taylor]: Taking taylor expansion of 0 in n 0.450 * [backup-simplify]: Simplify 0 into 0 0.450 * [backup-simplify]: Simplify 0 into 0 0.450 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 0.451 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 0.451 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 0.452 * [backup-simplify]: Simplify (- 1) into -1 0.452 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.453 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 0.453 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 0.453 * [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))) 0.454 * [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))) 0.456 * [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))) 0.456 * [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 0.456 * [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 0.456 * [taylor]: Taking taylor expansion of +nan.0 in n 0.456 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.456 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.456 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.456 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.456 * [taylor]: Taking taylor expansion of 0.5 in n 0.456 * [backup-simplify]: Simplify 0.5 into 0.5 0.456 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.456 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.456 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.456 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.456 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.456 * [taylor]: Taking taylor expansion of 1.0 in n 0.456 * [backup-simplify]: Simplify 1.0 into 1.0 0.456 * [taylor]: Taking taylor expansion of (log PI) in n 0.456 * [taylor]: Taking taylor expansion of PI in n 0.456 * [backup-simplify]: Simplify PI into PI 0.456 * [backup-simplify]: Simplify (log PI) into (log PI) 0.457 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.458 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.458 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.458 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.458 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.458 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.458 * [taylor]: Taking taylor expansion of 1.0 in n 0.458 * [backup-simplify]: Simplify 1.0 into 1.0 0.458 * [taylor]: Taking taylor expansion of (log n) in n 0.458 * [taylor]: Taking taylor expansion of n in n 0.458 * [backup-simplify]: Simplify 0 into 0 0.458 * [backup-simplify]: Simplify 1 into 1 0.458 * [backup-simplify]: Simplify (log 1) into 0 0.459 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.459 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.459 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.459 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.459 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.459 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.459 * [taylor]: Taking taylor expansion of 1.0 in n 0.459 * [backup-simplify]: Simplify 1.0 into 1.0 0.459 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.459 * [taylor]: Taking taylor expansion of 2.0 in n 0.459 * [backup-simplify]: Simplify 2.0 into 2.0 0.459 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.460 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.461 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.461 * [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) 0.462 * [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) 0.463 * [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)) 0.463 * [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))) 0.464 * [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) 0.465 * [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)) 0.466 * [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))) 0.467 * [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))) 0.467 * [backup-simplify]: Simplify 0 into 0 0.467 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 0.468 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 0.469 * [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 0.469 * [backup-simplify]: Simplify (- 0) into 0 0.469 * [backup-simplify]: Simplify (+ 0 0) into 0 0.470 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.470 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 0.471 * [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))) 0.471 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.473 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.475 * [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)))))))) 0.478 * [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)))))))) 0.478 * [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 0.478 * [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 0.478 * [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 0.478 * [taylor]: Taking taylor expansion of +nan.0 in n 0.478 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.478 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.478 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.478 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.478 * [taylor]: Taking taylor expansion of 0.5 in n 0.478 * [backup-simplify]: Simplify 0.5 into 0.5 0.478 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.478 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.478 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.478 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.478 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.478 * [taylor]: Taking taylor expansion of 1.0 in n 0.478 * [backup-simplify]: Simplify 1.0 into 1.0 0.478 * [taylor]: Taking taylor expansion of (log PI) in n 0.478 * [taylor]: Taking taylor expansion of PI in n 0.478 * [backup-simplify]: Simplify PI into PI 0.479 * [backup-simplify]: Simplify (log PI) into (log PI) 0.479 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.480 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.480 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.480 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.480 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.480 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.480 * [taylor]: Taking taylor expansion of 1.0 in n 0.480 * [backup-simplify]: Simplify 1.0 into 1.0 0.480 * [taylor]: Taking taylor expansion of (log n) in n 0.480 * [taylor]: Taking taylor expansion of n in n 0.480 * [backup-simplify]: Simplify 0 into 0 0.480 * [backup-simplify]: Simplify 1 into 1 0.481 * [backup-simplify]: Simplify (log 1) into 0 0.481 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.481 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.481 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.481 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.481 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.481 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.481 * [taylor]: Taking taylor expansion of 1.0 in n 0.481 * [backup-simplify]: Simplify 1.0 into 1.0 0.481 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.481 * [taylor]: Taking taylor expansion of 2.0 in n 0.481 * [backup-simplify]: Simplify 2.0 into 2.0 0.482 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.482 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.483 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.483 * [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) 0.484 * [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) 0.485 * [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)) 0.489 * [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))) 0.490 * [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) 0.490 * [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 0.490 * [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 0.490 * [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 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 (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.490 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.490 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 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 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.490 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.490 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.490 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.490 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.490 * [taylor]: Taking taylor expansion of 1.0 in n 0.490 * [backup-simplify]: Simplify 1.0 into 1.0 0.491 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.491 * [taylor]: Taking taylor expansion of 2.0 in n 0.491 * [backup-simplify]: Simplify 2.0 into 2.0 0.491 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.491 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.492 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.492 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.492 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.492 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.492 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.492 * [taylor]: Taking taylor expansion of 1.0 in n 0.492 * [backup-simplify]: Simplify 1.0 into 1.0 0.492 * [taylor]: Taking taylor expansion of (log PI) in n 0.492 * [taylor]: Taking taylor expansion of PI in n 0.492 * [backup-simplify]: Simplify PI into PI 0.493 * [backup-simplify]: Simplify (log PI) into (log PI) 0.493 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.494 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.494 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.494 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.494 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.494 * [taylor]: Taking taylor expansion of 1.0 in n 0.494 * [backup-simplify]: Simplify 1.0 into 1.0 0.494 * [taylor]: Taking taylor expansion of (log n) in n 0.494 * [taylor]: Taking taylor expansion of n in n 0.494 * [backup-simplify]: Simplify 0 into 0 0.494 * [backup-simplify]: Simplify 1 into 1 0.495 * [backup-simplify]: Simplify (log 1) into 0 0.495 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.495 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.495 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.495 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.496 * [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) 0.497 * [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)) 0.498 * [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))) 0.498 * [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) 0.498 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.499 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) 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 * [taylor]: Taking taylor expansion of (* n PI) in n 0.499 * [taylor]: Taking taylor expansion of n in n 0.499 * [backup-simplify]: Simplify 0 into 0 0.499 * [backup-simplify]: Simplify 1 into 1 0.499 * [taylor]: Taking taylor expansion of PI in n 0.499 * [backup-simplify]: Simplify PI into PI 0.499 * [backup-simplify]: Simplify (* 0 PI) into 0 0.499 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.500 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.501 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.501 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.502 * [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)) 0.503 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.505 * [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)) 0.506 * [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))) 0.508 * [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)))))) 0.511 * [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)))))))) 0.514 * [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)))))))) 0.518 * [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)))))))) 0.519 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 0.519 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 0.520 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 0.521 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 0.521 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.521 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.522 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 0.522 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 0.523 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 0.524 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 0.524 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 0.525 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 0.526 * [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 0.528 * [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 0.529 * [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 0.530 * [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 0.530 * [backup-simplify]: Simplify (- 0) into 0 0.530 * [backup-simplify]: Simplify 0 into 0 0.530 * [backup-simplify]: Simplify 0 into 0 0.531 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.532 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 0.534 * [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 0.534 * [backup-simplify]: Simplify (- 0) into 0 0.534 * [backup-simplify]: Simplify (+ 0 0) into 0 0.535 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 0.536 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 0.537 * [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))) 0.537 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.539 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.543 * [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)))))))) 0.549 * [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)))))))) 0.549 * [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 0.549 * [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 0.549 * [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 0.549 * [taylor]: Taking taylor expansion of +nan.0 in n 0.549 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.549 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.549 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.549 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.549 * [taylor]: Taking taylor expansion of 0.5 in n 0.549 * [backup-simplify]: Simplify 0.5 into 0.5 0.549 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.549 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.549 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.549 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.549 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.549 * [taylor]: Taking taylor expansion of 1.0 in n 0.549 * [backup-simplify]: Simplify 1.0 into 1.0 0.549 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.549 * [taylor]: Taking taylor expansion of 2.0 in n 0.549 * [backup-simplify]: Simplify 2.0 into 2.0 0.549 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.550 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.551 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.551 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.551 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.551 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.551 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.551 * [taylor]: Taking taylor expansion of 1.0 in n 0.551 * [backup-simplify]: Simplify 1.0 into 1.0 0.551 * [taylor]: Taking taylor expansion of (log n) in n 0.551 * [taylor]: Taking taylor expansion of n in n 0.551 * [backup-simplify]: Simplify 0 into 0 0.551 * [backup-simplify]: Simplify 1 into 1 0.551 * [backup-simplify]: Simplify (log 1) into 0 0.551 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.551 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.551 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.551 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.552 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.552 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.552 * [taylor]: Taking taylor expansion of 1.0 in n 0.552 * [backup-simplify]: Simplify 1.0 into 1.0 0.552 * [taylor]: Taking taylor expansion of (log PI) in n 0.552 * [taylor]: Taking taylor expansion of PI in n 0.552 * [backup-simplify]: Simplify PI into PI 0.552 * [backup-simplify]: Simplify (log PI) into (log PI) 0.552 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.553 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.554 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.555 * [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) 0.555 * [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)) 0.556 * [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))) 0.557 * [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) 0.557 * [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 0.557 * [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 0.557 * [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 0.557 * [taylor]: Taking taylor expansion of +nan.0 in n 0.557 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.557 * [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 0.557 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.557 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.557 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.557 * [taylor]: Taking taylor expansion of 0.5 in n 0.557 * [backup-simplify]: Simplify 0.5 into 0.5 0.557 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.557 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.557 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.557 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.557 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.557 * [taylor]: Taking taylor expansion of 1.0 in n 0.557 * [backup-simplify]: Simplify 1.0 into 1.0 0.557 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.558 * [taylor]: Taking taylor expansion of 2.0 in n 0.558 * [backup-simplify]: Simplify 2.0 into 2.0 0.558 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.558 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.559 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.559 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.559 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.559 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.559 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.559 * [taylor]: Taking taylor expansion of 1.0 in n 0.559 * [backup-simplify]: Simplify 1.0 into 1.0 0.559 * [taylor]: Taking taylor expansion of (log PI) in n 0.559 * [taylor]: Taking taylor expansion of PI in n 0.559 * [backup-simplify]: Simplify PI into PI 0.560 * [backup-simplify]: Simplify (log PI) into (log PI) 0.560 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.561 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.561 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.561 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.561 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.561 * [taylor]: Taking taylor expansion of 1.0 in n 0.561 * [backup-simplify]: Simplify 1.0 into 1.0 0.561 * [taylor]: Taking taylor expansion of (log n) in n 0.561 * [taylor]: Taking taylor expansion of n in n 0.561 * [backup-simplify]: Simplify 0 into 0 0.561 * [backup-simplify]: Simplify 1 into 1 0.561 * [backup-simplify]: Simplify (log 1) into 0 0.562 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.562 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.562 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.562 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.563 * [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) 0.564 * [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)) 0.565 * [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))) 0.566 * [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) 0.566 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.566 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.566 * [taylor]: Taking taylor expansion of 2.0 in n 0.566 * [backup-simplify]: Simplify 2.0 into 2.0 0.566 * [taylor]: Taking taylor expansion of (* n PI) in n 0.566 * [taylor]: Taking taylor expansion of n in n 0.566 * [backup-simplify]: Simplify 0 into 0 0.566 * [backup-simplify]: Simplify 1 into 1 0.566 * [taylor]: Taking taylor expansion of PI in n 0.566 * [backup-simplify]: Simplify PI into PI 0.566 * [backup-simplify]: Simplify (* 0 PI) into 0 0.566 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.567 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.568 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.569 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.569 * [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 0.569 * [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 0.569 * [taylor]: Taking taylor expansion of +nan.0 in n 0.569 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.569 * [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 0.569 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.569 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.569 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.569 * [taylor]: Taking taylor expansion of 0.5 in n 0.569 * [backup-simplify]: Simplify 0.5 into 0.5 0.569 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.569 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.569 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.569 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.569 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.569 * [taylor]: Taking taylor expansion of 1.0 in n 0.569 * [backup-simplify]: Simplify 1.0 into 1.0 0.569 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.569 * [taylor]: Taking taylor expansion of 2.0 in n 0.569 * [backup-simplify]: Simplify 2.0 into 2.0 0.569 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.570 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.571 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.571 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.571 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.571 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.571 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) 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 PI) in n 0.571 * [taylor]: Taking taylor expansion of PI in n 0.571 * [backup-simplify]: Simplify PI into PI 0.571 * [backup-simplify]: Simplify (log PI) into (log PI) 0.572 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.572 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.573 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.573 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.573 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) 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 n) in n 0.573 * [taylor]: Taking taylor expansion of n in n 0.573 * [backup-simplify]: Simplify 0 into 0 0.573 * [backup-simplify]: Simplify 1 into 1 0.573 * [backup-simplify]: Simplify (log 1) into 0 0.573 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.573 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.573 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.574 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.574 * [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) 0.575 * [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)) 0.576 * [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))) 0.577 * [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) 0.577 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.577 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.577 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.577 * [taylor]: Taking taylor expansion of 2.0 in n 0.577 * [backup-simplify]: Simplify 2.0 into 2.0 0.577 * [taylor]: Taking taylor expansion of (* n PI) in n 0.577 * [taylor]: Taking taylor expansion of n in n 0.577 * [backup-simplify]: Simplify 0 into 0 0.577 * [backup-simplify]: Simplify 1 into 1 0.577 * [taylor]: Taking taylor expansion of PI in n 0.577 * [backup-simplify]: Simplify PI into PI 0.577 * [backup-simplify]: Simplify (* 0 PI) into 0 0.577 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.578 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.579 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.580 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.581 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.582 * [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)) 0.587 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.589 * [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)) 0.590 * [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))) 0.591 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.592 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.593 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 0.595 * [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)) 0.597 * [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))) 0.598 * [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)))))))) 0.605 * [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)))))))))))) 0.613 * [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)))))))))))) 0.622 * [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)))))))))))))) 0.631 * [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)))))))))))))) 0.640 * [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)))))))))))))) 0.655 * [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 (* (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)))))))))))))))))))))) 0.655 * [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)))))) 0.655 * [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 0.655 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.655 * [taylor]: Taking taylor expansion of 1.0 in n 0.655 * [backup-simplify]: Simplify 1.0 into 1.0 0.655 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.655 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.655 * [taylor]: Taking taylor expansion of k in n 0.655 * [backup-simplify]: Simplify k into k 0.655 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 0.655 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 0.656 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.656 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.656 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.656 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.656 * [taylor]: Taking taylor expansion of 0.5 in n 0.656 * [backup-simplify]: Simplify 0.5 into 0.5 0.656 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.656 * [taylor]: Taking taylor expansion of 1.0 in n 0.656 * [backup-simplify]: Simplify 1.0 into 1.0 0.656 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.656 * [taylor]: Taking taylor expansion of k in n 0.656 * [backup-simplify]: Simplify k into k 0.656 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.656 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.656 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.656 * [taylor]: Taking taylor expansion of 2.0 in n 0.656 * [backup-simplify]: Simplify 2.0 into 2.0 0.656 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.656 * [taylor]: Taking taylor expansion of PI in n 0.656 * [backup-simplify]: Simplify PI into PI 0.656 * [taylor]: Taking taylor expansion of n in n 0.656 * [backup-simplify]: Simplify 0 into 0 0.656 * [backup-simplify]: Simplify 1 into 1 0.656 * [backup-simplify]: Simplify (/ PI 1) into PI 0.656 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.657 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.657 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.657 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.657 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.658 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.659 * [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)))) 0.659 * [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))))) 0.659 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.660 * [taylor]: Taking taylor expansion of 1.0 in k 0.660 * [backup-simplify]: Simplify 1.0 into 1.0 0.660 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.660 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.660 * [taylor]: Taking taylor expansion of k in k 0.660 * [backup-simplify]: Simplify 0 into 0 0.660 * [backup-simplify]: Simplify 1 into 1 0.660 * [backup-simplify]: Simplify (sqrt 0) into 0 0.661 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.661 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.661 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.661 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.661 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.661 * [taylor]: Taking taylor expansion of 0.5 in k 0.661 * [backup-simplify]: Simplify 0.5 into 0.5 0.661 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.661 * [taylor]: Taking taylor expansion of 1.0 in k 0.661 * [backup-simplify]: Simplify 1.0 into 1.0 0.661 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.661 * [taylor]: Taking taylor expansion of k in k 0.661 * [backup-simplify]: Simplify 0 into 0 0.661 * [backup-simplify]: Simplify 1 into 1 0.661 * [backup-simplify]: Simplify (/ 1 1) into 1 0.661 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.661 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.661 * [taylor]: Taking taylor expansion of 2.0 in k 0.661 * [backup-simplify]: Simplify 2.0 into 2.0 0.661 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.661 * [taylor]: Taking taylor expansion of PI in k 0.661 * [backup-simplify]: Simplify PI into PI 0.661 * [taylor]: Taking taylor expansion of n in k 0.661 * [backup-simplify]: Simplify n into n 0.661 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.661 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.661 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.662 * [backup-simplify]: Simplify (- 1) into -1 0.662 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.662 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.662 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.662 * [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))))) 0.662 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.662 * [taylor]: Taking taylor expansion of 1.0 in k 0.662 * [backup-simplify]: Simplify 1.0 into 1.0 0.662 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.662 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.662 * [taylor]: Taking taylor expansion of k in k 0.662 * [backup-simplify]: Simplify 0 into 0 0.662 * [backup-simplify]: Simplify 1 into 1 0.663 * [backup-simplify]: Simplify (sqrt 0) into 0 0.663 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.663 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.664 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.664 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.664 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.664 * [taylor]: Taking taylor expansion of 0.5 in k 0.664 * [backup-simplify]: Simplify 0.5 into 0.5 0.664 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.664 * [taylor]: Taking taylor expansion of 1.0 in k 0.664 * [backup-simplify]: Simplify 1.0 into 1.0 0.664 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.664 * [taylor]: Taking taylor expansion of k in k 0.664 * [backup-simplify]: Simplify 0 into 0 0.664 * [backup-simplify]: Simplify 1 into 1 0.664 * [backup-simplify]: Simplify (/ 1 1) into 1 0.664 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.664 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.664 * [taylor]: Taking taylor expansion of 2.0 in k 0.664 * [backup-simplify]: Simplify 2.0 into 2.0 0.664 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.664 * [taylor]: Taking taylor expansion of PI in k 0.664 * [backup-simplify]: Simplify PI into PI 0.664 * [taylor]: Taking taylor expansion of n in k 0.664 * [backup-simplify]: Simplify n into n 0.664 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.664 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.664 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.664 * [backup-simplify]: Simplify (- 1) into -1 0.665 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.665 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.665 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.665 * [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))))) 0.665 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 0.666 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.666 * [taylor]: Taking taylor expansion of 0 in n 0.666 * [backup-simplify]: Simplify 0 into 0 0.666 * [backup-simplify]: Simplify 0 into 0 0.666 * [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))))))) 0.666 * [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))))))) 0.666 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.667 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.667 * [taylor]: Taking taylor expansion of +nan.0 in n 0.667 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.667 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.667 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.667 * [taylor]: Taking taylor expansion of 0.5 in n 0.667 * [backup-simplify]: Simplify 0.5 into 0.5 0.667 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.667 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.667 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.667 * [taylor]: Taking taylor expansion of 2.0 in n 0.667 * [backup-simplify]: Simplify 2.0 into 2.0 0.667 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.667 * [taylor]: Taking taylor expansion of PI in n 0.667 * [backup-simplify]: Simplify PI into PI 0.667 * [taylor]: Taking taylor expansion of n in n 0.667 * [backup-simplify]: Simplify 0 into 0 0.667 * [backup-simplify]: Simplify 1 into 1 0.667 * [backup-simplify]: Simplify (/ PI 1) into PI 0.667 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.668 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.668 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.668 * [taylor]: Taking taylor expansion of 1.0 in n 0.668 * [backup-simplify]: Simplify 1.0 into 1.0 0.668 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.668 * [taylor]: Taking taylor expansion of k in n 0.668 * [backup-simplify]: Simplify k into k 0.668 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.669 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.669 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.669 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.670 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.670 * [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)))) 0.671 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.672 * [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)))))) 0.673 * [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))))))) 0.673 * [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))))))) 0.673 * [backup-simplify]: Simplify 0 into 0 0.679 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.680 * [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))))))) 0.680 * [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))))))) 0.680 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.680 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.680 * [taylor]: Taking taylor expansion of +nan.0 in n 0.680 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.680 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.680 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.680 * [taylor]: Taking taylor expansion of 0.5 in n 0.680 * [backup-simplify]: Simplify 0.5 into 0.5 0.680 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.680 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.680 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.680 * [taylor]: Taking taylor expansion of 2.0 in n 0.680 * [backup-simplify]: Simplify 2.0 into 2.0 0.680 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.680 * [taylor]: Taking taylor expansion of PI in n 0.680 * [backup-simplify]: Simplify PI into PI 0.680 * [taylor]: Taking taylor expansion of n in n 0.680 * [backup-simplify]: Simplify 0 into 0 0.680 * [backup-simplify]: Simplify 1 into 1 0.681 * [backup-simplify]: Simplify (/ PI 1) into PI 0.681 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.682 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.682 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.682 * [taylor]: Taking taylor expansion of 1.0 in n 0.682 * [backup-simplify]: Simplify 1.0 into 1.0 0.682 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.682 * [taylor]: Taking taylor expansion of k in n 0.682 * [backup-simplify]: Simplify k into k 0.682 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.683 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.683 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.683 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.684 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.684 * [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)))) 0.685 * [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))))) 0.686 * [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)))))) 0.687 * [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))))))) 0.687 * [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 (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.688 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.689 * [backup-simplify]: Simplify (- 0) into 0 0.689 * [backup-simplify]: Simplify (+ 0 0) into 0 0.689 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.690 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.691 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.691 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.692 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 0.693 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.694 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 0.694 * [backup-simplify]: Simplify (- 0) into 0 0.694 * [backup-simplify]: Simplify 0 into 0 0.694 * [backup-simplify]: Simplify 0 into 0 0.697 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.697 * [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))))))) 0.698 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 0.698 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.698 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.698 * [taylor]: Taking taylor expansion of +nan.0 in n 0.698 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.698 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.698 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.698 * [taylor]: Taking taylor expansion of 0.5 in n 0.698 * [backup-simplify]: Simplify 0.5 into 0.5 0.698 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.698 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.698 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.698 * [taylor]: Taking taylor expansion of 2.0 in n 0.698 * [backup-simplify]: Simplify 2.0 into 2.0 0.698 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.698 * [taylor]: Taking taylor expansion of PI in n 0.698 * [backup-simplify]: Simplify PI into PI 0.698 * [taylor]: Taking taylor expansion of n in n 0.698 * [backup-simplify]: Simplify 0 into 0 0.699 * [backup-simplify]: Simplify 1 into 1 0.699 * [backup-simplify]: Simplify (/ PI 1) into PI 0.699 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.700 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.700 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.700 * [taylor]: Taking taylor expansion of 1.0 in n 0.700 * [backup-simplify]: Simplify 1.0 into 1.0 0.700 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.700 * [taylor]: Taking taylor expansion of k in n 0.700 * [backup-simplify]: Simplify k into k 0.700 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.701 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.701 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.701 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.701 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.702 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.703 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.703 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 0.704 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.705 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.708 * [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)))))))) 0.708 * [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)))) 0.708 * [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 0.708 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.708 * [taylor]: Taking taylor expansion of 1.0 in n 0.708 * [backup-simplify]: Simplify 1.0 into 1.0 0.708 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.708 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.708 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.708 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.708 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.708 * [taylor]: Taking taylor expansion of 0.5 in n 0.708 * [backup-simplify]: Simplify 0.5 into 0.5 0.708 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.708 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.708 * [taylor]: Taking taylor expansion of k in n 0.708 * [backup-simplify]: Simplify k into k 0.708 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.708 * [taylor]: Taking taylor expansion of 1.0 in n 0.709 * [backup-simplify]: Simplify 1.0 into 1.0 0.709 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.709 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.709 * [taylor]: Taking taylor expansion of -2.0 in n 0.709 * [backup-simplify]: Simplify -2.0 into -2.0 0.709 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.709 * [taylor]: Taking taylor expansion of PI in n 0.709 * [backup-simplify]: Simplify PI into PI 0.709 * [taylor]: Taking taylor expansion of n in n 0.709 * [backup-simplify]: Simplify 0 into 0 0.709 * [backup-simplify]: Simplify 1 into 1 0.709 * [backup-simplify]: Simplify (/ PI 1) into PI 0.709 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.710 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.710 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.710 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.711 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.711 * [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)))) 0.712 * [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))))) 0.712 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.712 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.712 * [taylor]: Taking taylor expansion of -1 in n 0.712 * [backup-simplify]: Simplify -1 into -1 0.712 * [taylor]: Taking taylor expansion of k in n 0.712 * [backup-simplify]: Simplify k into k 0.712 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 0.712 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 0.712 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 0.712 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 0.713 * [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))) 0.713 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.713 * [taylor]: Taking taylor expansion of 1.0 in k 0.713 * [backup-simplify]: Simplify 1.0 into 1.0 0.713 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.713 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.713 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.713 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.713 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.713 * [taylor]: Taking taylor expansion of 0.5 in k 0.713 * [backup-simplify]: Simplify 0.5 into 0.5 0.713 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.713 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.713 * [taylor]: Taking taylor expansion of k in k 0.713 * [backup-simplify]: Simplify 0 into 0 0.713 * [backup-simplify]: Simplify 1 into 1 0.714 * [backup-simplify]: Simplify (/ 1 1) into 1 0.714 * [taylor]: Taking taylor expansion of 1.0 in k 0.714 * [backup-simplify]: Simplify 1.0 into 1.0 0.714 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.714 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.714 * [taylor]: Taking taylor expansion of -2.0 in k 0.714 * [backup-simplify]: Simplify -2.0 into -2.0 0.714 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.714 * [taylor]: Taking taylor expansion of PI in k 0.714 * [backup-simplify]: Simplify PI into PI 0.714 * [taylor]: Taking taylor expansion of n in k 0.714 * [backup-simplify]: Simplify n into n 0.714 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.714 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.714 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.714 * [backup-simplify]: Simplify (+ 1 0) into 1 0.715 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.715 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.715 * [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)))))) 0.715 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.715 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.715 * [taylor]: Taking taylor expansion of -1 in k 0.715 * [backup-simplify]: Simplify -1 into -1 0.715 * [taylor]: Taking taylor expansion of k in k 0.715 * [backup-simplify]: Simplify 0 into 0 0.715 * [backup-simplify]: Simplify 1 into 1 0.715 * [backup-simplify]: Simplify (/ -1 1) into -1 0.715 * [backup-simplify]: Simplify (sqrt 0) into 0 0.716 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.716 * [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))))))) 0.716 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.716 * [taylor]: Taking taylor expansion of 1.0 in k 0.716 * [backup-simplify]: Simplify 1.0 into 1.0 0.716 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.716 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.716 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.716 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.716 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.716 * [taylor]: Taking taylor expansion of 0.5 in k 0.716 * [backup-simplify]: Simplify 0.5 into 0.5 0.716 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.716 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.716 * [taylor]: Taking taylor expansion of k in k 0.717 * [backup-simplify]: Simplify 0 into 0 0.717 * [backup-simplify]: Simplify 1 into 1 0.717 * [backup-simplify]: Simplify (/ 1 1) into 1 0.717 * [taylor]: Taking taylor expansion of 1.0 in k 0.717 * [backup-simplify]: Simplify 1.0 into 1.0 0.717 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.717 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.717 * [taylor]: Taking taylor expansion of -2.0 in k 0.717 * [backup-simplify]: Simplify -2.0 into -2.0 0.717 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.717 * [taylor]: Taking taylor expansion of PI in k 0.717 * [backup-simplify]: Simplify PI into PI 0.717 * [taylor]: Taking taylor expansion of n in k 0.717 * [backup-simplify]: Simplify n into n 0.717 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.717 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.717 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.717 * [backup-simplify]: Simplify (+ 1 0) into 1 0.718 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.718 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.718 * [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)))))) 0.718 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.718 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.718 * [taylor]: Taking taylor expansion of -1 in k 0.718 * [backup-simplify]: Simplify -1 into -1 0.718 * [taylor]: Taking taylor expansion of k in k 0.718 * [backup-simplify]: Simplify 0 into 0 0.718 * [backup-simplify]: Simplify 1 into 1 0.718 * [backup-simplify]: Simplify (/ -1 1) into -1 0.718 * [backup-simplify]: Simplify (sqrt 0) into 0 0.719 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.719 * [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))))))) 0.719 * [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))))))) 0.719 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.719 * [taylor]: Taking taylor expansion of +nan.0 in n 0.720 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.720 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.720 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.720 * [taylor]: Taking taylor expansion of 0.5 in n 0.720 * [backup-simplify]: Simplify 0.5 into 0.5 0.720 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.720 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.720 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.720 * [taylor]: Taking taylor expansion of k in n 0.720 * [backup-simplify]: Simplify k into k 0.720 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.720 * [taylor]: Taking taylor expansion of 1.0 in n 0.720 * [backup-simplify]: Simplify 1.0 into 1.0 0.720 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.720 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.720 * [taylor]: Taking taylor expansion of -2.0 in n 0.720 * [backup-simplify]: Simplify -2.0 into -2.0 0.720 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.720 * [taylor]: Taking taylor expansion of PI in n 0.720 * [backup-simplify]: Simplify PI into PI 0.720 * [taylor]: Taking taylor expansion of n in n 0.720 * [backup-simplify]: Simplify 0 into 0 0.720 * [backup-simplify]: Simplify 1 into 1 0.720 * [backup-simplify]: Simplify (/ PI 1) into PI 0.720 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.721 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.721 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.722 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.723 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.723 * [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)))) 0.724 * [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))))) 0.725 * [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)))))) 0.725 * [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)))))) 0.726 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.728 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.728 * [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)))))))) 0.728 * [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)))))))) 0.729 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.729 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.729 * [taylor]: Taking taylor expansion of +nan.0 in n 0.729 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.729 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.729 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.729 * [taylor]: Taking taylor expansion of 0.5 in n 0.729 * [backup-simplify]: Simplify 0.5 into 0.5 0.729 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.729 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.729 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.729 * [taylor]: Taking taylor expansion of k in n 0.729 * [backup-simplify]: Simplify k into k 0.729 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.729 * [taylor]: Taking taylor expansion of 1.0 in n 0.729 * [backup-simplify]: Simplify 1.0 into 1.0 0.729 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.729 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.729 * [taylor]: Taking taylor expansion of -2.0 in n 0.729 * [backup-simplify]: Simplify -2.0 into -2.0 0.729 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.729 * [taylor]: Taking taylor expansion of PI in n 0.729 * [backup-simplify]: Simplify PI into PI 0.729 * [taylor]: Taking taylor expansion of n in n 0.729 * [backup-simplify]: Simplify 0 into 0 0.729 * [backup-simplify]: Simplify 1 into 1 0.729 * [backup-simplify]: Simplify (/ PI 1) into PI 0.730 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.730 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.730 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.731 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.732 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.733 * [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)))) 0.733 * [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))))) 0.734 * [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)))))) 0.735 * [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))))))) 0.735 * [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))))))) 0.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.736 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.737 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.737 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.738 * [backup-simplify]: Simplify (+ 0 0) into 0 0.738 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.739 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.740 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 0.741 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.742 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 0.742 * [backup-simplify]: Simplify 0 into 0 0.743 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.745 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 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)) (* (- (* +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))))))))) (* 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))))))) 0.756 * [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)))))))))))) 0.756 * * * [progress]: simplifying candidates 0.759 * [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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h3)) (/ (sqrt h4) h3) (expm1 (* (* h0 h1) h2)) (log1p (* (* h0 h1) h2)) (* (* h0 h1) h2) (* (* h0 h1) h2) (+ (+ (log h0) (log h1)) (log h2)) (+ (log (* h0 h1)) (log h2)) (log (* (* h0 h1) h2)) (exp (* (* h0 h1) h2)) (* (* (* (* h0 h0) h0) (* (* h1 h1) h1)) (* (* h2 h2) h2)) (* (* (* (* h0 h1) (* h0 h1)) (* h0 h1)) (* (* h2 h2) h2)) (* (cbrt (* (* h0 h1) h2)) (cbrt (* (* h0 h1) h2))) (cbrt (* (* h0 h1) h2)) (* (* (* (* h0 h1) h2) (* (* h0 h1) h2)) (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (* (* h0 h1) (* (cbrt h2) (cbrt h2))) (* (* h0 h1) (sqrt h2)) (* (* h0 h1) 1) (* h1 h2) (expm1 (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (log1p (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (+ (- (log h3) (log (sqrt h4))) (* (+ (+ (log h0) (log h1)) (log h2)) (/ (- h3 h4) h0))) (+ (- (log h3) (log (sqrt h4))) (* (+ (log (* h0 h1)) (log h2)) (/ (- h3 h4) h0))) (+ (- (log h3) (log (sqrt h4))) (* (log (* (* h0 h1) h2)) (/ (- h3 h4) h0))) (+ (- (log h3) (log (sqrt h4))) (* (log (* (* h0 h1) h2)) (/ (- h3 h4) h0))) (+ (- (log h3) (log (sqrt h4))) (log (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (+ (log (/ h3 (sqrt h4))) (* (+ (+ (log h0) (log h1)) (log h2)) (/ (- h3 h4) h0))) (+ (log (/ h3 (sqrt h4))) (* (+ (log (* h0 h1)) (log h2)) (/ (- h3 h4) h0))) (+ (log (/ h3 (sqrt h4))) (* (log (* (* h0 h1) h2)) (/ (- h3 h4) h0))) (+ (log (/ h3 (sqrt h4))) (* (log (* (* h0 h1) h2)) (/ (- h3 h4) h0))) (+ (log (/ h3 (sqrt h4))) (log (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (log (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (exp (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ (* (* h3 h3) h3) (* (* (sqrt h4) (sqrt h4)) (sqrt h4))) (* (* (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (* (* (/ h3 (sqrt h4)) (/ h3 (sqrt h4))) (/ h3 (sqrt h4))) (* (* (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (cbrt (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (cbrt (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))))) (cbrt (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (* (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (sqrt (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (sqrt (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* h3 (pow (* (* h0 h1) h2) (/ h3 h0))) (* (sqrt h4) (pow (* (* h0 h1) h2) (/ h4 h0))) (* (sqrt (/ h3 (sqrt h4))) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (sqrt (/ h3 (sqrt h4))) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (sqrt (/ h3 (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (sqrt (/ h3 (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (/ h3 (sqrt h4)) (pow (* h0 h1) (/ (- h3 h4) h0))) (* (/ h3 (sqrt h4)) (* (cbrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (cbrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))))) (* (/ h3 (sqrt h4)) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ h3 (sqrt h4)) 1) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (cbrt (/ h3 (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (sqrt (/ h3 (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (cbrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (sqrt (cbrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (cbrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (sqrt (cbrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (cbrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt (cbrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ 1 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ h3 h0))) (* h3 (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (- (+ (* h5 (* (pow h4 2) (* (pow (log (* h0 h1)) 2) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (* h5 (* (pow h4 2) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2)))) (+ (* h7 (* (pow h4 2) (* (log (* h0 h1)) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2))))) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (* h6 (* h4 (* (log (* h0 h1)) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (* h6 (* h4 (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2)))))) (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (- (+ (* h9 h4) (- (+ (* h9 (pow h4 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- (* h9 (/ 1 (pow h4 3)))))))) (- (+ (* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- h9))))) (* h0 (* h2 h1)) (* h0 (* h2 h1)) (* h0 (* h2 h1)) (- (+ (* h9 (* (* (pow h4 2) (pow (log (* h0 h1)) 2)) (pow (* (pow h0 h3) (* (pow h2 h3) (pow h1 h3))) h6))) (- (+ (* h9 (* (* (pow h4 2) (log (* h0 h1))) (pow (* (pow h1 h3) (* (pow h2 h3) (pow h0 h3))) h6))) (- (+ (* h9 (* (* (pow h4 2) (* (log (* h0 h1)) (log h2))) (pow (* (pow h1 h3) (* (pow h0 h3) (pow h2 h3))) h6))) (- (+ (* h9 (* (* (pow h4 2) (log h2)) (pow (* (pow h0 h3) (* (pow h1 h3) (pow h2 h3))) h6))) (- (+ (* h9 (* (* h4 (log (* h0 h1))) (pow (* (pow h0 h3) (* (pow h2 h3) (pow h1 h3))) h6))) (- (+ (* h9 (* (* (pow h4 2) (pow (log h2) 2)) (pow (* (pow h0 h3) (* (pow h1 h3) (pow h2 h3))) h6))) (- (+ (* h9 (* (* h4 (log h2)) (pow (* (pow h0 h3) (* (pow h1 h3) (pow h2 h3))) h6))) (- (+ (* h9 (pow (* (pow h0 h3) (* (pow h2 h3) (pow h1 h3))) h6)) (- (+ (* h9 (* (pow h4 2) (pow (* (pow h1 h3) (* (pow h2 h3) (pow h0 h3))) h6))) (- (* h9 (* h4 (pow (* (pow h0 h3) (* (pow h2 h3) (pow h1 h3))) h6)))))))))))))))))))))) (- (+ (* h9 (/ (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (pow h4 3))) (- (+ (* h9 (/ (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) h4)) (- (* h9 (/ (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (pow h4 2)))))))) (- (+ (* h9 (/ (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) h4)) (- (+ (* h9 (/ (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (pow h4 2))) (- (* h9 (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))))))))) 0.769 * * [simplify]: iteration 0 : 981 enodes (cost 1502 ) 0.785 * * [simplify]: iteration 1 : 4021 enodes (cost 1398 ) 0.848 * * [simplify]: iteration 2 : 5003 enodes (cost 1383 ) 0.858 * * * [progress]: adding candidates to table 1.278 * * [progress]: iteration 2 / 4 1.278 * * * [progress]: picking best candidate 1.305 * * * * [pick]: Picked # 1.305 * * * [progress]: localizing error 1.320 * * * [progress]: generating rewritten candidates 1.320 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 1.344 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 1.370 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 1.376 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1) 1.407 * * * [progress]: generating series expansions 1.408 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 1.408 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 1.408 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 1.408 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 1.408 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.408 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.408 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 1.408 * [taylor]: Taking taylor expansion of 0.25 in k 1.408 * [backup-simplify]: Simplify 0.25 into 0.25 1.408 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.408 * [taylor]: Taking taylor expansion of 1.0 in k 1.408 * [backup-simplify]: Simplify 1.0 into 1.0 1.408 * [taylor]: Taking taylor expansion of k in k 1.408 * [backup-simplify]: Simplify 0 into 0 1.408 * [backup-simplify]: Simplify 1 into 1 1.408 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.408 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.409 * [taylor]: Taking taylor expansion of 2.0 in k 1.409 * [backup-simplify]: Simplify 2.0 into 2.0 1.409 * [taylor]: Taking taylor expansion of (* n PI) in k 1.409 * [taylor]: Taking taylor expansion of n in k 1.409 * [backup-simplify]: Simplify n into n 1.409 * [taylor]: Taking taylor expansion of PI in k 1.409 * [backup-simplify]: Simplify PI into PI 1.409 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.409 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.409 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.409 * [backup-simplify]: Simplify (- 0) into 0 1.409 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.410 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 1.410 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 1.410 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 1.410 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.410 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.410 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.410 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.410 * [taylor]: Taking taylor expansion of 0.25 in n 1.410 * [backup-simplify]: Simplify 0.25 into 0.25 1.410 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.410 * [taylor]: Taking taylor expansion of 1.0 in n 1.410 * [backup-simplify]: Simplify 1.0 into 1.0 1.410 * [taylor]: Taking taylor expansion of k in n 1.410 * [backup-simplify]: Simplify k into k 1.410 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.410 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.410 * [taylor]: Taking taylor expansion of 2.0 in n 1.410 * [backup-simplify]: Simplify 2.0 into 2.0 1.410 * [taylor]: Taking taylor expansion of (* n PI) in n 1.410 * [taylor]: Taking taylor expansion of n in n 1.410 * [backup-simplify]: Simplify 0 into 0 1.410 * [backup-simplify]: Simplify 1 into 1 1.410 * [taylor]: Taking taylor expansion of PI in n 1.410 * [backup-simplify]: Simplify PI into PI 1.410 * [backup-simplify]: Simplify (* 0 PI) into 0 1.411 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.411 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.412 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.413 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.413 * [backup-simplify]: Simplify (- k) into (- k) 1.413 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.413 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.414 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.414 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.415 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.415 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.415 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.415 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.415 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.415 * [taylor]: Taking taylor expansion of 0.25 in n 1.415 * [backup-simplify]: Simplify 0.25 into 0.25 1.415 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.415 * [taylor]: Taking taylor expansion of 1.0 in n 1.415 * [backup-simplify]: Simplify 1.0 into 1.0 1.415 * [taylor]: Taking taylor expansion of k in n 1.415 * [backup-simplify]: Simplify k into k 1.415 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.415 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.415 * [taylor]: Taking taylor expansion of 2.0 in n 1.415 * [backup-simplify]: Simplify 2.0 into 2.0 1.415 * [taylor]: Taking taylor expansion of (* n PI) in n 1.415 * [taylor]: Taking taylor expansion of n in n 1.415 * [backup-simplify]: Simplify 0 into 0 1.416 * [backup-simplify]: Simplify 1 into 1 1.416 * [taylor]: Taking taylor expansion of PI in n 1.416 * [backup-simplify]: Simplify PI into PI 1.416 * [backup-simplify]: Simplify (* 0 PI) into 0 1.416 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.417 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.418 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.418 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.418 * [backup-simplify]: Simplify (- k) into (- k) 1.418 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.418 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.419 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.420 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.421 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.421 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.421 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.421 * [taylor]: Taking taylor expansion of 0.25 in k 1.421 * [backup-simplify]: Simplify 0.25 into 0.25 1.421 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.421 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.421 * [taylor]: Taking taylor expansion of 1.0 in k 1.421 * [backup-simplify]: Simplify 1.0 into 1.0 1.421 * [taylor]: Taking taylor expansion of k in k 1.421 * [backup-simplify]: Simplify 0 into 0 1.421 * [backup-simplify]: Simplify 1 into 1 1.421 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.421 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.421 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.421 * [taylor]: Taking taylor expansion of 2.0 in k 1.421 * [backup-simplify]: Simplify 2.0 into 2.0 1.421 * [taylor]: Taking taylor expansion of PI in k 1.421 * [backup-simplify]: Simplify PI into PI 1.422 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.422 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.422 * [taylor]: Taking taylor expansion of (log n) in k 1.422 * [taylor]: Taking taylor expansion of n in k 1.422 * [backup-simplify]: Simplify n into n 1.422 * [backup-simplify]: Simplify (log n) into (log n) 1.423 * [backup-simplify]: Simplify (- 0) into 0 1.423 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.424 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.424 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.425 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 1.425 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.426 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.427 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.427 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.428 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.428 * [backup-simplify]: Simplify (- 0) into 0 1.429 * [backup-simplify]: Simplify (+ 0 0) into 0 1.429 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 1.430 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.430 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.431 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.431 * [taylor]: Taking taylor expansion of 0 in k 1.431 * [backup-simplify]: Simplify 0 into 0 1.431 * [backup-simplify]: Simplify 0 into 0 1.432 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.433 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.433 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.434 * [backup-simplify]: Simplify (+ 0 0) into 0 1.434 * [backup-simplify]: Simplify (- 1) into -1 1.434 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.435 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.436 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1.438 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.440 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.440 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.441 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.443 * [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 1.443 * [backup-simplify]: Simplify (- 0) into 0 1.443 * [backup-simplify]: Simplify (+ 0 0) into 0 1.443 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.444 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.445 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.446 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.446 * [taylor]: Taking taylor expansion of 0 in k 1.446 * [backup-simplify]: Simplify 0 into 0 1.447 * [backup-simplify]: Simplify 0 into 0 1.447 * [backup-simplify]: Simplify 0 into 0 1.447 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.449 * [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 1.450 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.450 * [backup-simplify]: Simplify (+ 0 0) into 0 1.451 * [backup-simplify]: Simplify (- 0) into 0 1.451 * [backup-simplify]: Simplify (+ 0 0) into 0 1.452 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.453 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.456 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.459 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.464 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 1.465 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 1.465 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 1.465 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 1.465 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.465 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.465 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 1.465 * [taylor]: Taking taylor expansion of 0.25 in k 1.465 * [backup-simplify]: Simplify 0.25 into 0.25 1.465 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.465 * [taylor]: Taking taylor expansion of 1.0 in k 1.465 * [backup-simplify]: Simplify 1.0 into 1.0 1.465 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.465 * [taylor]: Taking taylor expansion of k in k 1.465 * [backup-simplify]: Simplify 0 into 0 1.465 * [backup-simplify]: Simplify 1 into 1 1.465 * [backup-simplify]: Simplify (/ 1 1) into 1 1.465 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.465 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.465 * [taylor]: Taking taylor expansion of 2.0 in k 1.465 * [backup-simplify]: Simplify 2.0 into 2.0 1.465 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.465 * [taylor]: Taking taylor expansion of PI in k 1.465 * [backup-simplify]: Simplify PI into PI 1.465 * [taylor]: Taking taylor expansion of n in k 1.465 * [backup-simplify]: Simplify n into n 1.465 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.465 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.465 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.466 * [backup-simplify]: Simplify (- 1) into -1 1.466 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.466 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 1.466 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 1.466 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.466 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.466 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.466 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.467 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.467 * [taylor]: Taking taylor expansion of 0.25 in n 1.467 * [backup-simplify]: Simplify 0.25 into 0.25 1.467 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.467 * [taylor]: Taking taylor expansion of 1.0 in n 1.467 * [backup-simplify]: Simplify 1.0 into 1.0 1.467 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.467 * [taylor]: Taking taylor expansion of k in n 1.467 * [backup-simplify]: Simplify k into k 1.467 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.467 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.467 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.467 * [taylor]: Taking taylor expansion of 2.0 in n 1.467 * [backup-simplify]: Simplify 2.0 into 2.0 1.467 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.467 * [taylor]: Taking taylor expansion of PI in n 1.467 * [backup-simplify]: Simplify PI into PI 1.467 * [taylor]: Taking taylor expansion of n in n 1.467 * [backup-simplify]: Simplify 0 into 0 1.467 * [backup-simplify]: Simplify 1 into 1 1.467 * [backup-simplify]: Simplify (/ PI 1) into PI 1.468 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.468 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.468 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.468 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.468 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.469 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.470 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.471 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.471 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.471 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.471 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.471 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.471 * [taylor]: Taking taylor expansion of 0.25 in n 1.471 * [backup-simplify]: Simplify 0.25 into 0.25 1.471 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.471 * [taylor]: Taking taylor expansion of 1.0 in n 1.471 * [backup-simplify]: Simplify 1.0 into 1.0 1.471 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.471 * [taylor]: Taking taylor expansion of k in n 1.471 * [backup-simplify]: Simplify k into k 1.471 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.471 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.471 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.471 * [taylor]: Taking taylor expansion of 2.0 in n 1.471 * [backup-simplify]: Simplify 2.0 into 2.0 1.471 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.471 * [taylor]: Taking taylor expansion of PI in n 1.471 * [backup-simplify]: Simplify PI into PI 1.471 * [taylor]: Taking taylor expansion of n in n 1.471 * [backup-simplify]: Simplify 0 into 0 1.471 * [backup-simplify]: Simplify 1 into 1 1.471 * [backup-simplify]: Simplify (/ PI 1) into PI 1.472 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.472 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.472 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.472 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.472 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.473 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.474 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.474 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.475 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.475 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.475 * [taylor]: Taking taylor expansion of 0.25 in k 1.475 * [backup-simplify]: Simplify 0.25 into 0.25 1.475 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.475 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.475 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.475 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.475 * [taylor]: Taking taylor expansion of 2.0 in k 1.475 * [backup-simplify]: Simplify 2.0 into 2.0 1.475 * [taylor]: Taking taylor expansion of PI in k 1.475 * [backup-simplify]: Simplify PI into PI 1.475 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.476 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.476 * [taylor]: Taking taylor expansion of (log n) in k 1.476 * [taylor]: Taking taylor expansion of n in k 1.476 * [backup-simplify]: Simplify n into n 1.476 * [backup-simplify]: Simplify (log n) into (log n) 1.476 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.476 * [taylor]: Taking taylor expansion of 1.0 in k 1.476 * [backup-simplify]: Simplify 1.0 into 1.0 1.476 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.476 * [taylor]: Taking taylor expansion of k in k 1.476 * [backup-simplify]: Simplify 0 into 0 1.476 * [backup-simplify]: Simplify 1 into 1 1.476 * [backup-simplify]: Simplify (/ 1 1) into 1 1.476 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.477 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.477 * [backup-simplify]: Simplify (- 1) into -1 1.477 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.478 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.478 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 1.479 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.480 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.480 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.481 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.482 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.482 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.482 * [backup-simplify]: Simplify (- 0) into 0 1.482 * [backup-simplify]: Simplify (+ 0 0) into 0 1.483 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.483 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.484 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.485 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.485 * [taylor]: Taking taylor expansion of 0 in k 1.485 * [backup-simplify]: Simplify 0 into 0 1.485 * [backup-simplify]: Simplify 0 into 0 1.485 * [backup-simplify]: Simplify 0 into 0 1.486 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.486 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.488 * [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 1.488 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.488 * [backup-simplify]: Simplify (- 0) into 0 1.489 * [backup-simplify]: Simplify (+ 0 0) into 0 1.489 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.490 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.491 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.492 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.492 * [taylor]: Taking taylor expansion of 0 in k 1.492 * [backup-simplify]: Simplify 0 into 0 1.492 * [backup-simplify]: Simplify 0 into 0 1.492 * [backup-simplify]: Simplify 0 into 0 1.492 * [backup-simplify]: Simplify 0 into 0 1.493 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.493 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.499 * [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 1.500 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.500 * [backup-simplify]: Simplify (- 0) into 0 1.500 * [backup-simplify]: Simplify (+ 0 0) into 0 1.501 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.502 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.503 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.504 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.504 * [taylor]: Taking taylor expansion of 0 in k 1.504 * [backup-simplify]: Simplify 0 into 0 1.504 * [backup-simplify]: Simplify 0 into 0 1.505 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 1.506 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 1.506 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 1.506 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 1.506 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.506 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.506 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 1.506 * [taylor]: Taking taylor expansion of 0.25 in k 1.506 * [backup-simplify]: Simplify 0.25 into 0.25 1.506 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.506 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.506 * [taylor]: Taking taylor expansion of k in k 1.506 * [backup-simplify]: Simplify 0 into 0 1.506 * [backup-simplify]: Simplify 1 into 1 1.506 * [backup-simplify]: Simplify (/ 1 1) into 1 1.506 * [taylor]: Taking taylor expansion of 1.0 in k 1.506 * [backup-simplify]: Simplify 1.0 into 1.0 1.506 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.506 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.506 * [taylor]: Taking taylor expansion of -2.0 in k 1.506 * [backup-simplify]: Simplify -2.0 into -2.0 1.506 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.506 * [taylor]: Taking taylor expansion of PI in k 1.506 * [backup-simplify]: Simplify PI into PI 1.506 * [taylor]: Taking taylor expansion of n in k 1.506 * [backup-simplify]: Simplify n into n 1.506 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.506 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.506 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.507 * [backup-simplify]: Simplify (+ 1 0) into 1 1.507 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 1.507 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 1.507 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.507 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.507 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.507 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.507 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.507 * [taylor]: Taking taylor expansion of 0.25 in n 1.507 * [backup-simplify]: Simplify 0.25 into 0.25 1.507 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.507 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.507 * [taylor]: Taking taylor expansion of k in n 1.507 * [backup-simplify]: Simplify k into k 1.507 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.507 * [taylor]: Taking taylor expansion of 1.0 in n 1.507 * [backup-simplify]: Simplify 1.0 into 1.0 1.507 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.507 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.507 * [taylor]: Taking taylor expansion of -2.0 in n 1.508 * [backup-simplify]: Simplify -2.0 into -2.0 1.508 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.508 * [taylor]: Taking taylor expansion of PI in n 1.508 * [backup-simplify]: Simplify PI into PI 1.508 * [taylor]: Taking taylor expansion of n in n 1.508 * [backup-simplify]: Simplify 0 into 0 1.508 * [backup-simplify]: Simplify 1 into 1 1.508 * [backup-simplify]: Simplify (/ PI 1) into PI 1.508 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.509 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.509 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.509 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.510 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.510 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.511 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.511 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.511 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.511 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.511 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.511 * [taylor]: Taking taylor expansion of 0.25 in n 1.511 * [backup-simplify]: Simplify 0.25 into 0.25 1.511 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.511 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.511 * [taylor]: Taking taylor expansion of k in n 1.511 * [backup-simplify]: Simplify k into k 1.511 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.511 * [taylor]: Taking taylor expansion of 1.0 in n 1.511 * [backup-simplify]: Simplify 1.0 into 1.0 1.511 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.511 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.511 * [taylor]: Taking taylor expansion of -2.0 in n 1.511 * [backup-simplify]: Simplify -2.0 into -2.0 1.511 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.511 * [taylor]: Taking taylor expansion of PI in n 1.511 * [backup-simplify]: Simplify PI into PI 1.511 * [taylor]: Taking taylor expansion of n in n 1.511 * [backup-simplify]: Simplify 0 into 0 1.511 * [backup-simplify]: Simplify 1 into 1 1.512 * [backup-simplify]: Simplify (/ PI 1) into PI 1.512 * [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 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.513 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.514 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.514 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.515 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.515 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.515 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.515 * [taylor]: Taking taylor expansion of 0.25 in k 1.515 * [backup-simplify]: Simplify 0.25 into 0.25 1.515 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.515 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.515 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.515 * [taylor]: Taking taylor expansion of k in k 1.515 * [backup-simplify]: Simplify 0 into 0 1.515 * [backup-simplify]: Simplify 1 into 1 1.515 * [backup-simplify]: Simplify (/ 1 1) into 1 1.515 * [taylor]: Taking taylor expansion of 1.0 in k 1.515 * [backup-simplify]: Simplify 1.0 into 1.0 1.515 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.515 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.516 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.516 * [taylor]: Taking taylor expansion of -2.0 in k 1.516 * [backup-simplify]: Simplify -2.0 into -2.0 1.516 * [taylor]: Taking taylor expansion of PI in k 1.516 * [backup-simplify]: Simplify PI into PI 1.516 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.516 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.516 * [taylor]: Taking taylor expansion of (log n) in k 1.516 * [taylor]: Taking taylor expansion of n in k 1.517 * [backup-simplify]: Simplify n into n 1.517 * [backup-simplify]: Simplify (log n) into (log n) 1.517 * [backup-simplify]: Simplify (+ 1 0) into 1 1.517 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.517 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.518 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.519 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 1.519 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.520 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.521 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.521 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.522 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.522 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.522 * [backup-simplify]: Simplify (+ 0 0) into 0 1.522 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.523 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.524 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.525 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.525 * [taylor]: Taking taylor expansion of 0 in k 1.525 * [backup-simplify]: Simplify 0 into 0 1.525 * [backup-simplify]: Simplify 0 into 0 1.525 * [backup-simplify]: Simplify 0 into 0 1.526 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.526 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.528 * [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 1.528 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.528 * [backup-simplify]: Simplify (+ 0 0) into 0 1.529 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.530 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.530 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.532 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.532 * [taylor]: Taking taylor expansion of 0 in k 1.532 * [backup-simplify]: Simplify 0 into 0 1.532 * [backup-simplify]: Simplify 0 into 0 1.532 * [backup-simplify]: Simplify 0 into 0 1.532 * [backup-simplify]: Simplify 0 into 0 1.532 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.533 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.536 * [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 1.536 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.536 * [backup-simplify]: Simplify (+ 0 0) into 0 1.537 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.538 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.539 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.540 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.540 * [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 (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 1.541 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 1.542 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 1.542 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 1.542 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 1.542 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.542 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.542 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 1.542 * [taylor]: Taking taylor expansion of 0.25 in k 1.542 * [backup-simplify]: Simplify 0.25 into 0.25 1.542 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 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 k in k 1.542 * [backup-simplify]: Simplify 0 into 0 1.542 * [backup-simplify]: Simplify 1 into 1 1.542 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.542 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) 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 (* n PI) in k 1.542 * [taylor]: Taking taylor expansion of n in k 1.542 * [backup-simplify]: Simplify n into n 1.542 * [taylor]: Taking taylor expansion of PI in k 1.542 * [backup-simplify]: Simplify PI into PI 1.542 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.542 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.542 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.542 * [backup-simplify]: Simplify (- 0) into 0 1.543 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.543 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 1.543 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 1.543 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 1.543 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.543 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.543 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.543 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.543 * [taylor]: Taking taylor expansion of 0.25 in n 1.543 * [backup-simplify]: Simplify 0.25 into 0.25 1.543 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 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 k in n 1.543 * [backup-simplify]: Simplify k into k 1.543 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.543 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) 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 (* n PI) in n 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 * [taylor]: Taking taylor expansion of PI in n 1.543 * [backup-simplify]: Simplify PI into PI 1.544 * [backup-simplify]: Simplify (* 0 PI) into 0 1.544 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.545 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.545 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.546 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.546 * [backup-simplify]: Simplify (- k) into (- k) 1.546 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.546 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.547 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.548 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.548 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.548 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.548 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.548 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.548 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.548 * [taylor]: Taking taylor expansion of 0.25 in n 1.548 * [backup-simplify]: Simplify 0.25 into 0.25 1.548 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.548 * [taylor]: Taking taylor expansion of 1.0 in n 1.548 * [backup-simplify]: Simplify 1.0 into 1.0 1.548 * [taylor]: Taking taylor expansion of k in n 1.549 * [backup-simplify]: Simplify k into k 1.549 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.549 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.549 * [taylor]: Taking taylor expansion of 2.0 in n 1.549 * [backup-simplify]: Simplify 2.0 into 2.0 1.549 * [taylor]: Taking taylor expansion of (* n PI) in n 1.549 * [taylor]: Taking taylor expansion of n in n 1.549 * [backup-simplify]: Simplify 0 into 0 1.549 * [backup-simplify]: Simplify 1 into 1 1.549 * [taylor]: Taking taylor expansion of PI in n 1.549 * [backup-simplify]: Simplify PI into PI 1.549 * [backup-simplify]: Simplify (* 0 PI) into 0 1.549 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.550 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.551 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.551 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.551 * [backup-simplify]: Simplify (- k) into (- k) 1.552 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.552 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.553 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.553 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.554 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.554 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.554 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.554 * [taylor]: Taking taylor expansion of 0.25 in k 1.554 * [backup-simplify]: Simplify 0.25 into 0.25 1.554 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.554 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.554 * [taylor]: Taking taylor expansion of 1.0 in k 1.554 * [backup-simplify]: Simplify 1.0 into 1.0 1.554 * [taylor]: Taking taylor expansion of k in k 1.554 * [backup-simplify]: Simplify 0 into 0 1.554 * [backup-simplify]: Simplify 1 into 1 1.554 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.554 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.554 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.554 * [taylor]: Taking taylor expansion of 2.0 in k 1.554 * [backup-simplify]: Simplify 2.0 into 2.0 1.554 * [taylor]: Taking taylor expansion of PI in k 1.555 * [backup-simplify]: Simplify PI into PI 1.555 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.555 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.555 * [taylor]: Taking taylor expansion of (log n) in k 1.555 * [taylor]: Taking taylor expansion of n in k 1.555 * [backup-simplify]: Simplify n into n 1.555 * [backup-simplify]: Simplify (log n) into (log n) 1.556 * [backup-simplify]: Simplify (- 0) into 0 1.556 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.557 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.557 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.558 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 1.558 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.559 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.560 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.560 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.561 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.561 * [backup-simplify]: Simplify (- 0) into 0 1.561 * [backup-simplify]: Simplify (+ 0 0) into 0 1.562 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 1.563 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.563 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.564 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.564 * [taylor]: Taking taylor expansion of 0 in k 1.564 * [backup-simplify]: Simplify 0 into 0 1.564 * [backup-simplify]: Simplify 0 into 0 1.565 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.566 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.566 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.566 * [backup-simplify]: Simplify (+ 0 0) into 0 1.567 * [backup-simplify]: Simplify (- 1) into -1 1.567 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.568 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.569 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1.571 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.572 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 1.573 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.574 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.575 * [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 1.576 * [backup-simplify]: Simplify (- 0) into 0 1.576 * [backup-simplify]: Simplify (+ 0 0) into 0 1.576 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.577 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.578 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.579 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.579 * [taylor]: Taking taylor expansion of 0 in k 1.579 * [backup-simplify]: Simplify 0 into 0 1.579 * [backup-simplify]: Simplify 0 into 0 1.579 * [backup-simplify]: Simplify 0 into 0 1.580 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.581 * [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 1.585 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.586 * [backup-simplify]: Simplify (+ 0 0) into 0 1.586 * [backup-simplify]: Simplify (- 0) into 0 1.586 * [backup-simplify]: Simplify (+ 0 0) into 0 1.587 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.589 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.591 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.594 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 1.599 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 1.600 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 1.600 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 1.600 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 1.600 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.600 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.600 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 1.600 * [taylor]: Taking taylor expansion of 0.25 in k 1.600 * [backup-simplify]: Simplify 0.25 into 0.25 1.600 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.600 * [taylor]: Taking taylor expansion of 1.0 in k 1.600 * [backup-simplify]: Simplify 1.0 into 1.0 1.600 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.600 * [taylor]: Taking taylor expansion of k in k 1.600 * [backup-simplify]: Simplify 0 into 0 1.600 * [backup-simplify]: Simplify 1 into 1 1.600 * [backup-simplify]: Simplify (/ 1 1) into 1 1.600 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.600 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.600 * [taylor]: Taking taylor expansion of 2.0 in k 1.600 * [backup-simplify]: Simplify 2.0 into 2.0 1.600 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.600 * [taylor]: Taking taylor expansion of PI in k 1.601 * [backup-simplify]: Simplify PI into PI 1.601 * [taylor]: Taking taylor expansion of n in k 1.601 * [backup-simplify]: Simplify n into n 1.601 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.601 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.601 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.601 * [backup-simplify]: Simplify (- 1) into -1 1.601 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.601 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 1.602 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 1.602 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.602 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.602 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.602 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.602 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.602 * [taylor]: Taking taylor expansion of 0.25 in n 1.602 * [backup-simplify]: Simplify 0.25 into 0.25 1.602 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.602 * [taylor]: Taking taylor expansion of 1.0 in n 1.602 * [backup-simplify]: Simplify 1.0 into 1.0 1.602 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.602 * [taylor]: Taking taylor expansion of k in n 1.602 * [backup-simplify]: Simplify k into k 1.602 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.602 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.602 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.602 * [taylor]: Taking taylor expansion of 2.0 in n 1.602 * [backup-simplify]: Simplify 2.0 into 2.0 1.602 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.602 * [taylor]: Taking taylor expansion of PI in n 1.602 * [backup-simplify]: Simplify PI into PI 1.602 * [taylor]: Taking taylor expansion of n in n 1.602 * [backup-simplify]: Simplify 0 into 0 1.602 * [backup-simplify]: Simplify 1 into 1 1.603 * [backup-simplify]: Simplify (/ PI 1) into PI 1.603 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.604 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.604 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.604 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.604 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.605 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.605 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.606 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.606 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.606 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.606 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.606 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.606 * [taylor]: Taking taylor expansion of 0.25 in n 1.606 * [backup-simplify]: Simplify 0.25 into 0.25 1.606 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.606 * [taylor]: Taking taylor expansion of 1.0 in n 1.606 * [backup-simplify]: Simplify 1.0 into 1.0 1.606 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.606 * [taylor]: Taking taylor expansion of k in n 1.606 * [backup-simplify]: Simplify k into k 1.606 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.606 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.606 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.606 * [taylor]: Taking taylor expansion of 2.0 in n 1.606 * [backup-simplify]: Simplify 2.0 into 2.0 1.606 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.606 * [taylor]: Taking taylor expansion of PI in n 1.606 * [backup-simplify]: Simplify PI into PI 1.606 * [taylor]: Taking taylor expansion of n in n 1.606 * [backup-simplify]: Simplify 0 into 0 1.606 * [backup-simplify]: Simplify 1 into 1 1.607 * [backup-simplify]: Simplify (/ PI 1) into PI 1.607 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.607 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.608 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.608 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.608 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.608 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.609 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.610 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.610 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.610 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.610 * [taylor]: Taking taylor expansion of 0.25 in k 1.610 * [backup-simplify]: Simplify 0.25 into 0.25 1.610 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.610 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.610 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.610 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.610 * [taylor]: Taking taylor expansion of 2.0 in k 1.610 * [backup-simplify]: Simplify 2.0 into 2.0 1.610 * [taylor]: Taking taylor expansion of PI in k 1.610 * [backup-simplify]: Simplify PI into PI 1.610 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.611 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.611 * [taylor]: Taking taylor expansion of (log n) in k 1.611 * [taylor]: Taking taylor expansion of n in k 1.611 * [backup-simplify]: Simplify n into n 1.611 * [backup-simplify]: Simplify (log n) into (log n) 1.611 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.611 * [taylor]: Taking taylor expansion of 1.0 in k 1.611 * [backup-simplify]: Simplify 1.0 into 1.0 1.611 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.611 * [taylor]: Taking taylor expansion of k in k 1.611 * [backup-simplify]: Simplify 0 into 0 1.611 * [backup-simplify]: Simplify 1 into 1 1.611 * [backup-simplify]: Simplify (/ 1 1) into 1 1.611 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.612 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.612 * [backup-simplify]: Simplify (- 1) into -1 1.613 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.613 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.614 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 1.615 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.615 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.616 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.616 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.617 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.617 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.617 * [backup-simplify]: Simplify (- 0) into 0 1.618 * [backup-simplify]: Simplify (+ 0 0) into 0 1.618 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.619 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.619 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.620 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.620 * [taylor]: Taking taylor expansion of 0 in k 1.621 * [backup-simplify]: Simplify 0 into 0 1.621 * [backup-simplify]: Simplify 0 into 0 1.621 * [backup-simplify]: Simplify 0 into 0 1.621 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.622 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.623 * [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 1.623 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.624 * [backup-simplify]: Simplify (- 0) into 0 1.624 * [backup-simplify]: Simplify (+ 0 0) into 0 1.624 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.625 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.626 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.627 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.627 * [taylor]: Taking taylor expansion of 0 in k 1.627 * [backup-simplify]: Simplify 0 into 0 1.627 * [backup-simplify]: Simplify 0 into 0 1.627 * [backup-simplify]: Simplify 0 into 0 1.627 * [backup-simplify]: Simplify 0 into 0 1.628 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.629 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.631 * [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 1.632 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.632 * [backup-simplify]: Simplify (- 0) into 0 1.632 * [backup-simplify]: Simplify (+ 0 0) into 0 1.633 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.634 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.635 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.636 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.636 * [taylor]: Taking taylor expansion of 0 in k 1.636 * [backup-simplify]: Simplify 0 into 0 1.636 * [backup-simplify]: Simplify 0 into 0 1.637 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 1.637 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 1.637 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 1.637 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 1.637 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.637 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.637 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 1.637 * [taylor]: Taking taylor expansion of 0.25 in k 1.637 * [backup-simplify]: Simplify 0.25 into 0.25 1.638 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.638 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.638 * [taylor]: Taking taylor expansion of k in k 1.638 * [backup-simplify]: Simplify 0 into 0 1.638 * [backup-simplify]: Simplify 1 into 1 1.638 * [backup-simplify]: Simplify (/ 1 1) into 1 1.638 * [taylor]: Taking taylor expansion of 1.0 in k 1.638 * [backup-simplify]: Simplify 1.0 into 1.0 1.638 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.638 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.638 * [taylor]: Taking taylor expansion of -2.0 in k 1.638 * [backup-simplify]: Simplify -2.0 into -2.0 1.638 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.638 * [taylor]: Taking taylor expansion of PI in k 1.638 * [backup-simplify]: Simplify PI into PI 1.638 * [taylor]: Taking taylor expansion of n in k 1.638 * [backup-simplify]: Simplify n into n 1.638 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.638 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.638 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.639 * [backup-simplify]: Simplify (+ 1 0) into 1 1.639 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 1.639 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 1.639 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.639 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.639 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.639 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.639 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.639 * [taylor]: Taking taylor expansion of 0.25 in n 1.639 * [backup-simplify]: Simplify 0.25 into 0.25 1.639 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.639 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.639 * [taylor]: Taking taylor expansion of k in n 1.639 * [backup-simplify]: Simplify k into k 1.639 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.639 * [taylor]: Taking taylor expansion of 1.0 in n 1.639 * [backup-simplify]: Simplify 1.0 into 1.0 1.639 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.639 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.639 * [taylor]: Taking taylor expansion of -2.0 in n 1.639 * [backup-simplify]: Simplify -2.0 into -2.0 1.639 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.639 * [taylor]: Taking taylor expansion of PI in n 1.639 * [backup-simplify]: Simplify PI into PI 1.639 * [taylor]: Taking taylor expansion of n in n 1.639 * [backup-simplify]: Simplify 0 into 0 1.639 * [backup-simplify]: Simplify 1 into 1 1.640 * [backup-simplify]: Simplify (/ PI 1) into PI 1.640 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.641 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.641 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.641 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.642 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.642 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.643 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.643 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.643 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.643 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.643 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.643 * [taylor]: Taking taylor expansion of 0.25 in n 1.643 * [backup-simplify]: Simplify 0.25 into 0.25 1.643 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.643 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.643 * [taylor]: Taking taylor expansion of k in n 1.643 * [backup-simplify]: Simplify k into k 1.643 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.643 * [taylor]: Taking taylor expansion of 1.0 in n 1.643 * [backup-simplify]: Simplify 1.0 into 1.0 1.643 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.643 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.643 * [taylor]: Taking taylor expansion of -2.0 in n 1.643 * [backup-simplify]: Simplify -2.0 into -2.0 1.643 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.643 * [taylor]: Taking taylor expansion of PI in n 1.643 * [backup-simplify]: Simplify PI into PI 1.643 * [taylor]: Taking taylor expansion of n in n 1.643 * [backup-simplify]: Simplify 0 into 0 1.643 * [backup-simplify]: Simplify 1 into 1 1.644 * [backup-simplify]: Simplify (/ PI 1) into PI 1.644 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.644 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.645 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.645 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.645 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.646 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.647 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.647 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.647 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.647 * [taylor]: Taking taylor expansion of 0.25 in k 1.647 * [backup-simplify]: Simplify 0.25 into 0.25 1.647 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.647 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.647 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.647 * [taylor]: Taking taylor expansion of k in k 1.647 * [backup-simplify]: Simplify 0 into 0 1.647 * [backup-simplify]: Simplify 1 into 1 1.647 * [backup-simplify]: Simplify (/ 1 1) into 1 1.647 * [taylor]: Taking taylor expansion of 1.0 in k 1.647 * [backup-simplify]: Simplify 1.0 into 1.0 1.647 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.647 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.647 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.647 * [taylor]: Taking taylor expansion of -2.0 in k 1.647 * [backup-simplify]: Simplify -2.0 into -2.0 1.647 * [taylor]: Taking taylor expansion of PI in k 1.647 * [backup-simplify]: Simplify PI into PI 1.648 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.648 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.648 * [taylor]: Taking taylor expansion of (log n) in k 1.648 * [taylor]: Taking taylor expansion of n in k 1.648 * [backup-simplify]: Simplify n into n 1.648 * [backup-simplify]: Simplify (log n) into (log n) 1.649 * [backup-simplify]: Simplify (+ 1 0) into 1 1.649 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.649 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.650 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.651 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 1.651 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.652 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.652 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.653 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.654 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.654 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.654 * [backup-simplify]: Simplify (+ 0 0) into 0 1.655 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.655 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.656 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.657 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.657 * [taylor]: Taking taylor expansion of 0 in k 1.657 * [backup-simplify]: Simplify 0 into 0 1.657 * [backup-simplify]: Simplify 0 into 0 1.657 * [backup-simplify]: Simplify 0 into 0 1.658 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.658 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.660 * [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 1.660 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.660 * [backup-simplify]: Simplify (+ 0 0) into 0 1.661 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.662 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.662 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.664 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.664 * [taylor]: Taking taylor expansion of 0 in k 1.664 * [backup-simplify]: Simplify 0 into 0 1.664 * [backup-simplify]: Simplify 0 into 0 1.664 * [backup-simplify]: Simplify 0 into 0 1.664 * [backup-simplify]: Simplify 0 into 0 1.664 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.665 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.668 * [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 1.668 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.668 * [backup-simplify]: Simplify (+ 0 0) into 0 1.669 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.670 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.671 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.675 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.675 * [taylor]: Taking taylor expansion of 0 in k 1.675 * [backup-simplify]: Simplify 0 into 0 1.675 * [backup-simplify]: Simplify 0 into 0 1.676 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 1.676 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 1.676 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 1.676 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.676 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.676 * [taylor]: Taking taylor expansion of 1.0 in k 1.676 * [backup-simplify]: Simplify 1.0 into 1.0 1.676 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.676 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.676 * [taylor]: Taking taylor expansion of k in k 1.677 * [backup-simplify]: Simplify 0 into 0 1.677 * [backup-simplify]: Simplify 1 into 1 1.677 * [backup-simplify]: Simplify (/ 1 1) into 1 1.677 * [backup-simplify]: Simplify (sqrt 0) into 0 1.678 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.678 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.678 * [taylor]: Taking taylor expansion of 1.0 in k 1.678 * [backup-simplify]: Simplify 1.0 into 1.0 1.678 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.678 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.678 * [taylor]: Taking taylor expansion of k in k 1.678 * [backup-simplify]: Simplify 0 into 0 1.678 * [backup-simplify]: Simplify 1 into 1 1.678 * [backup-simplify]: Simplify (/ 1 1) into 1 1.678 * [backup-simplify]: Simplify (sqrt 0) into 0 1.679 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.679 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.679 * [backup-simplify]: Simplify 0 into 0 1.680 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.680 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.681 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.682 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.683 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.684 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.684 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.686 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.687 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.687 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.688 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 1.688 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 1.688 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.688 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.688 * [taylor]: Taking taylor expansion of 1.0 in k 1.688 * [backup-simplify]: Simplify 1.0 into 1.0 1.688 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.688 * [taylor]: Taking taylor expansion of k in k 1.688 * [backup-simplify]: Simplify 0 into 0 1.688 * [backup-simplify]: Simplify 1 into 1 1.689 * [backup-simplify]: Simplify (sqrt 0) into 0 1.689 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.689 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.689 * [taylor]: Taking taylor expansion of 1.0 in k 1.690 * [backup-simplify]: Simplify 1.0 into 1.0 1.690 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.690 * [taylor]: Taking taylor expansion of k in k 1.690 * [backup-simplify]: Simplify 0 into 0 1.690 * [backup-simplify]: Simplify 1 into 1 1.690 * [backup-simplify]: Simplify (sqrt 0) into 0 1.690 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.691 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.691 * [backup-simplify]: Simplify 0 into 0 1.692 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.692 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.693 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.694 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.695 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.697 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.698 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.698 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.699 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 1.699 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 1.699 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.699 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.699 * [taylor]: Taking taylor expansion of 1.0 in k 1.699 * [backup-simplify]: Simplify 1.0 into 1.0 1.699 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.699 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.699 * [taylor]: Taking taylor expansion of -1 in k 1.699 * [backup-simplify]: Simplify -1 into -1 1.699 * [taylor]: Taking taylor expansion of k in k 1.699 * [backup-simplify]: Simplify 0 into 0 1.699 * [backup-simplify]: Simplify 1 into 1 1.699 * [backup-simplify]: Simplify (/ -1 1) into -1 1.700 * [backup-simplify]: Simplify (sqrt 0) into 0 1.700 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.701 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.701 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.701 * [taylor]: Taking taylor expansion of 1.0 in k 1.701 * [backup-simplify]: Simplify 1.0 into 1.0 1.701 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.701 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.701 * [taylor]: Taking taylor expansion of -1 in k 1.701 * [backup-simplify]: Simplify -1 into -1 1.701 * [taylor]: Taking taylor expansion of k in k 1.701 * [backup-simplify]: Simplify 0 into 0 1.701 * [backup-simplify]: Simplify 1 into 1 1.701 * [backup-simplify]: Simplify (/ -1 1) into -1 1.701 * [backup-simplify]: Simplify (sqrt 0) into 0 1.702 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.702 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.702 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.703 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.705 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.706 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1.706 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.707 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.709 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.711 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1.711 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.712 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 1.712 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1) 1.712 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.712 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.712 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.712 * [taylor]: Taking taylor expansion of 2.0 in n 1.712 * [backup-simplify]: Simplify 2.0 into 2.0 1.712 * [taylor]: Taking taylor expansion of (* n PI) in n 1.712 * [taylor]: Taking taylor expansion of n in n 1.712 * [backup-simplify]: Simplify 0 into 0 1.712 * [backup-simplify]: Simplify 1 into 1 1.712 * [taylor]: Taking taylor expansion of PI in n 1.712 * [backup-simplify]: Simplify PI into PI 1.712 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.712 * [taylor]: Taking taylor expansion of 2.0 in n 1.712 * [backup-simplify]: Simplify 2.0 into 2.0 1.712 * [taylor]: Taking taylor expansion of (* n PI) in n 1.712 * [taylor]: Taking taylor expansion of n in n 1.712 * [backup-simplify]: Simplify 0 into 0 1.712 * [backup-simplify]: Simplify 1 into 1 1.712 * [taylor]: Taking taylor expansion of PI in n 1.712 * [backup-simplify]: Simplify PI into PI 1.713 * [backup-simplify]: Simplify (* 0 PI) into 0 1.713 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.713 * [backup-simplify]: Simplify 0 into 0 1.714 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.715 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.715 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.716 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.716 * [backup-simplify]: Simplify 0 into 0 1.717 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.718 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.718 * [backup-simplify]: Simplify 0 into 0 1.718 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.719 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.719 * [backup-simplify]: Simplify 0 into 0 1.720 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.721 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.721 * [backup-simplify]: Simplify 0 into 0 1.722 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.723 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.723 * [backup-simplify]: Simplify 0 into 0 1.724 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.724 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.725 * [backup-simplify]: Simplify 0 into 0 1.725 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.725 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.725 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.725 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.725 * [taylor]: Taking taylor expansion of 2.0 in n 1.725 * [backup-simplify]: Simplify 2.0 into 2.0 1.725 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.725 * [taylor]: Taking taylor expansion of PI in n 1.725 * [backup-simplify]: Simplify PI into PI 1.725 * [taylor]: Taking taylor expansion of n in n 1.725 * [backup-simplify]: Simplify 0 into 0 1.725 * [backup-simplify]: Simplify 1 into 1 1.726 * [backup-simplify]: Simplify (/ PI 1) into PI 1.726 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.726 * [taylor]: Taking taylor expansion of 2.0 in n 1.726 * [backup-simplify]: Simplify 2.0 into 2.0 1.726 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.726 * [taylor]: Taking taylor expansion of PI in n 1.726 * [backup-simplify]: Simplify PI into PI 1.726 * [taylor]: Taking taylor expansion of n in n 1.726 * [backup-simplify]: Simplify 0 into 0 1.726 * [backup-simplify]: Simplify 1 into 1 1.726 * [backup-simplify]: Simplify (/ PI 1) into PI 1.726 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.727 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.727 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.728 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.728 * [backup-simplify]: Simplify 0 into 0 1.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.729 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.729 * [backup-simplify]: Simplify 0 into 0 1.729 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.730 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.730 * [backup-simplify]: Simplify 0 into 0 1.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.731 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.731 * [backup-simplify]: Simplify 0 into 0 1.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.732 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.732 * [backup-simplify]: Simplify 0 into 0 1.733 * [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 1.734 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.734 * [backup-simplify]: Simplify 0 into 0 1.734 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.735 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.735 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.735 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.735 * [taylor]: Taking taylor expansion of -2.0 in n 1.735 * [backup-simplify]: Simplify -2.0 into -2.0 1.735 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.735 * [taylor]: Taking taylor expansion of PI in n 1.735 * [backup-simplify]: Simplify PI into PI 1.735 * [taylor]: Taking taylor expansion of n in n 1.735 * [backup-simplify]: Simplify 0 into 0 1.735 * [backup-simplify]: Simplify 1 into 1 1.735 * [backup-simplify]: Simplify (/ PI 1) into PI 1.735 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.735 * [taylor]: Taking taylor expansion of -2.0 in n 1.735 * [backup-simplify]: Simplify -2.0 into -2.0 1.735 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.735 * [taylor]: Taking taylor expansion of PI in n 1.735 * [backup-simplify]: Simplify PI into PI 1.735 * [taylor]: Taking taylor expansion of n in n 1.735 * [backup-simplify]: Simplify 0 into 0 1.735 * [backup-simplify]: Simplify 1 into 1 1.735 * [backup-simplify]: Simplify (/ PI 1) into PI 1.736 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.736 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.737 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.737 * [backup-simplify]: Simplify 0 into 0 1.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.738 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.738 * [backup-simplify]: Simplify 0 into 0 1.739 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.739 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.739 * [backup-simplify]: Simplify 0 into 0 1.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.740 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.740 * [backup-simplify]: Simplify 0 into 0 1.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.742 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.742 * [backup-simplify]: Simplify 0 into 0 1.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.743 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.743 * [backup-simplify]: Simplify 0 into 0 1.744 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.744 * * * [progress]: simplifying candidates 1.747 * [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 (/ 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(/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 1) 1)) (pow (* (* h0 h1) h2) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ 1 (sqrt 2))) (pow (* (* h0 h1) h2) (/ 1 1)) (pow (* (* h0 h1) h2) (/ (- h3 h4) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (- h3 h4) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (- h3 h4) 1)) (pow (* (* h0 h1) h2) 1) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)) (pow (* h0 h1) (/ (/ (- h3 h4) h0) 2)) (pow h2 (/ (/ (- h3 h4) h0) 2)) (log (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (exp (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (cbrt (pow 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(* (* h0 h1) h2) (* (cbrt (/ (/ (- h3 h4) h0) 2)) (cbrt (/ (/ (- h3 h4) h0) 2)))) (pow (* (* h0 h1) h2) (sqrt (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (* (cbrt (/ (- h3 h4) h0)) (cbrt (/ (- h3 h4) h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (* (cbrt (/ (- h3 h4) h0)) (cbrt (/ (- h3 h4) h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (* (cbrt (/ (- h3 h4) h0)) (cbrt (/ (- h3 h4) h0))) 1)) (pow (* (* h0 h1) h2) (/ (sqrt (/ (- h3 h4) h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (sqrt (/ (- h3 h4) h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (sqrt (/ (- h3 h4) h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) 1) 1)) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) 1) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 1) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) 1) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 1) 1)) (pow (* (* h0 h1) h2) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ 1 (sqrt 2))) (pow (* (* h0 h1) h2) (/ 1 1)) (pow (* (* h0 h1) h2) (/ (- h3 h4) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (- h3 h4) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (- h3 h4) 1)) (pow (* (* h0 h1) h2) 1) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)) (pow (* h0 h1) (/ (/ (- h3 h4) h0) 2)) (pow h2 (/ (/ (- h3 h4) h0) 2)) (log (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (exp (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)))) (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (* (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (expm1 (/ h3 (sqrt h4))) (log1p (/ h3 (sqrt h4))) (- (log h3) (log (sqrt h4))) (log (/ h3 (sqrt h4))) (exp (/ h3 (sqrt h4))) (/ (* (* h3 h3) h3) (* (* (sqrt h4) (sqrt h4)) (sqrt h4))) (* (cbrt (/ h3 (sqrt h4))) (cbrt (/ h3 (sqrt h4)))) (cbrt (/ h3 (sqrt h4))) (* (* (/ h3 (sqrt h4)) (/ h3 (sqrt h4))) (/ h3 (sqrt h4))) (sqrt (/ h3 (sqrt h4))) (sqrt (/ h3 (sqrt h4))) (- h3) (- (sqrt h4)) (/ (* (cbrt h3) (cbrt h3)) (* (cbrt (sqrt h4)) (cbrt (sqrt h4)))) (/ (cbrt h3) (cbrt (sqrt h4))) (/ (* (cbrt h3) (cbrt h3)) (sqrt (* (cbrt h4) (cbrt h4)))) (/ (cbrt h3) (sqrt (cbrt h4))) (/ (* (cbrt h3) (cbrt h3)) (sqrt (sqrt h4))) (/ (cbrt h3) (sqrt (sqrt h4))) (/ (* (cbrt h3) (cbrt h3)) (sqrt 1)) (/ (cbrt h3) (sqrt h4)) (/ (* (cbrt h3) (cbrt h3)) (sqrt (sqrt h4))) (/ (cbrt h3) (sqrt (sqrt h4))) (/ (* (cbrt h3) (cbrt h3)) 1) (/ (cbrt h3) (sqrt h4)) (/ (sqrt h3) (* (cbrt (sqrt h4)) (cbrt (sqrt h4)))) (/ (sqrt h3) (cbrt (sqrt h4))) (/ (sqrt h3) (sqrt (* (cbrt h4) (cbrt h4)))) (/ (sqrt h3) (sqrt (cbrt h4))) (/ (sqrt h3) (sqrt (sqrt h4))) (/ (sqrt h3) (sqrt (sqrt h4))) (/ (sqrt h3) (sqrt 1)) (/ (sqrt h3) (sqrt h4)) (/ (sqrt h3) (sqrt (sqrt h4))) (/ (sqrt h3) (sqrt (sqrt h4))) (/ (sqrt h3) 1) (/ (sqrt h3) (sqrt h4)) (/ 1 (* (cbrt (sqrt h4)) (cbrt (sqrt h4)))) (/ h3 (cbrt (sqrt h4))) (/ 1 (sqrt (* (cbrt h4) (cbrt h4)))) (/ h3 (sqrt (cbrt h4))) (/ 1 (sqrt (sqrt h4))) (/ h3 (sqrt (sqrt h4))) (/ 1 (sqrt 1)) (/ h3 (sqrt h4)) (/ 1 (sqrt (sqrt h4))) (/ h3 (sqrt (sqrt h4))) (/ 1 1) (/ h3 (sqrt h4)) (/ 1 (sqrt h4)) (/ (sqrt h4) h3) (/ h3 (* (cbrt (sqrt h4)) (cbrt (sqrt h4)))) (/ h3 (sqrt (* (cbrt h4) (cbrt h4)))) (/ h3 (sqrt (sqrt h4))) (/ h3 (sqrt 1)) (/ h3 (sqrt (sqrt h4))) (/ h3 1) (/ (sqrt h4) (cbrt h3)) (/ (sqrt h4) (sqrt h3)) (/ (sqrt h4) h3) (expm1 (* (* h0 h1) h2)) (log1p (* (* h0 h1) h2)) (* (* h0 h1) h2) (* (* h0 h1) h2) (+ (+ (log h0) (log h1)) (log h2)) (+ (log (* h0 h1)) (log h2)) (log (* (* h0 h1) h2)) (exp (* (* h0 h1) h2)) (* (* (* (* h0 h0) h0) (* (* h1 h1) h1)) (* (* h2 h2) h2)) (* (* (* (* h0 h1) (* h0 h1)) (* h0 h1)) (* (* h2 h2) h2)) (* (cbrt (* (* h0 h1) h2)) (cbrt (* (* h0 h1) h2))) (cbrt (* (* h0 h1) h2)) (* (* (* (* h0 h1) h2) (* (* h0 h1) h2)) (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (* (* h0 h1) (* (cbrt h2) (cbrt h2))) (* (* h0 h1) (sqrt h2)) (* (* h0 h1) 1) (* h1 h2) (- (+ (* h5 (* (pow h4 2) (* (pow (log (* h0 h1)) 2) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (+ (* h7 (* (pow h4 2) (* (log (* h0 h1)) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2))))) (* h5 (* (pow h4 2) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2))))))) (+ (* h6 (* h4 (* (log (* h0 h1)) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (* h6 (* h4 (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2)))))) (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (- (+ (* h5 (* (pow h4 2) (* (pow (log (* h0 h1)) 2) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (+ (* h7 (* (pow h4 2) (* (log (* h0 h1)) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2))))) (* h5 (* (pow h4 2) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2))))))) (+ (* h6 (* h4 (* (log (* h0 h1)) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (* h6 (* h4 (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2)))))) (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (- (+ (* h9 h4) (- (+ (* h9 (pow h4 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- (* h9 (/ 1 (pow h4 3)))))))) (- (+ (* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- h9))))) (* h0 (* h2 h1)) (* h0 (* h2 h1)) (* h0 (* h2 h1)) 1.757 * * [simplify]: iteration 0 : 874 enodes (cost 1888 ) 1.771 * * [simplify]: iteration 1 : 3432 enodes (cost 1810 ) 1.819 * * [simplify]: iteration 2 : 5001 enodes (cost 1792 ) 1.831 * * * [progress]: adding candidates to table 2.548 * * [progress]: iteration 3 / 4 2.548 * * * [progress]: picking best candidate 2.565 * * * * [pick]: Picked # 2.565 * * * [progress]: localizing error 2.582 * * * [progress]: generating rewritten candidates 2.582 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.607 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 2.633 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 2.639 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 2.668 * * * [progress]: generating series expansions 2.668 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.668 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2.668 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.668 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.668 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.668 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.668 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.668 * [taylor]: Taking taylor expansion of 0.25 in k 2.668 * [backup-simplify]: Simplify 0.25 into 0.25 2.668 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.669 * [taylor]: Taking taylor expansion of 1.0 in k 2.669 * [backup-simplify]: Simplify 1.0 into 1.0 2.669 * [taylor]: Taking taylor expansion of k in k 2.669 * [backup-simplify]: Simplify 0 into 0 2.669 * [backup-simplify]: Simplify 1 into 1 2.669 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.669 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.669 * [taylor]: Taking taylor expansion of 2.0 in k 2.669 * [backup-simplify]: Simplify 2.0 into 2.0 2.669 * [taylor]: Taking taylor expansion of (* n PI) in k 2.669 * [taylor]: Taking taylor expansion of n in k 2.669 * [backup-simplify]: Simplify n into n 2.669 * [taylor]: Taking taylor expansion of PI in k 2.669 * [backup-simplify]: Simplify PI into PI 2.669 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.669 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.669 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.669 * [backup-simplify]: Simplify (- 0) into 0 2.669 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.670 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.670 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.670 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.670 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.670 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.670 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.670 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.670 * [taylor]: Taking taylor expansion of 0.25 in n 2.670 * [backup-simplify]: Simplify 0.25 into 0.25 2.670 * [taylor]: Taking taylor expansion of (- 1.0 k) 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 k in n 2.670 * [backup-simplify]: Simplify k into k 2.670 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.670 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.670 * [taylor]: Taking taylor expansion of 2.0 in n 2.670 * [backup-simplify]: Simplify 2.0 into 2.0 2.670 * [taylor]: Taking taylor expansion of (* n PI) 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 * [taylor]: Taking taylor expansion of PI in n 2.670 * [backup-simplify]: Simplify PI into PI 2.670 * [backup-simplify]: Simplify (* 0 PI) into 0 2.671 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.672 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.672 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.673 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.673 * [backup-simplify]: Simplify (- k) into (- k) 2.673 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.673 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.674 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.675 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.675 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.675 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.675 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.675 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.675 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.676 * [taylor]: Taking taylor expansion of 0.25 in n 2.676 * [backup-simplify]: Simplify 0.25 into 0.25 2.676 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.676 * [taylor]: Taking taylor expansion of 1.0 in n 2.676 * [backup-simplify]: Simplify 1.0 into 1.0 2.676 * [taylor]: Taking taylor expansion of k in n 2.676 * [backup-simplify]: Simplify k into k 2.676 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.676 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.676 * [taylor]: Taking taylor expansion of 2.0 in n 2.676 * [backup-simplify]: Simplify 2.0 into 2.0 2.676 * [taylor]: Taking taylor expansion of (* n PI) in n 2.676 * [taylor]: Taking taylor expansion of n in n 2.676 * [backup-simplify]: Simplify 0 into 0 2.676 * [backup-simplify]: Simplify 1 into 1 2.676 * [taylor]: Taking taylor expansion of PI in n 2.676 * [backup-simplify]: Simplify PI into PI 2.676 * [backup-simplify]: Simplify (* 0 PI) into 0 2.676 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.677 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.678 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.678 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.679 * [backup-simplify]: Simplify (- k) into (- k) 2.679 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.679 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.679 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.680 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.681 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.681 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.681 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.681 * [taylor]: Taking taylor expansion of 0.25 in k 2.681 * [backup-simplify]: Simplify 0.25 into 0.25 2.681 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.681 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.681 * [taylor]: Taking taylor expansion of 1.0 in k 2.681 * [backup-simplify]: Simplify 1.0 into 1.0 2.681 * [taylor]: Taking taylor expansion of k in k 2.681 * [backup-simplify]: Simplify 0 into 0 2.681 * [backup-simplify]: Simplify 1 into 1 2.681 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.681 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.681 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.681 * [taylor]: Taking taylor expansion of 2.0 in k 2.681 * [backup-simplify]: Simplify 2.0 into 2.0 2.681 * [taylor]: Taking taylor expansion of PI in k 2.681 * [backup-simplify]: Simplify PI into PI 2.681 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.682 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.682 * [taylor]: Taking taylor expansion of (log n) in k 2.682 * [taylor]: Taking taylor expansion of n in k 2.682 * [backup-simplify]: Simplify n into n 2.682 * [backup-simplify]: Simplify (log n) into (log n) 2.682 * [backup-simplify]: Simplify (- 0) into 0 2.682 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.683 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.684 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.684 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.685 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.686 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.686 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.687 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.688 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.688 * [backup-simplify]: Simplify (- 0) into 0 2.688 * [backup-simplify]: Simplify (+ 0 0) into 0 2.688 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.689 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.690 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.691 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.691 * [taylor]: Taking taylor expansion of 0 in k 2.691 * [backup-simplify]: Simplify 0 into 0 2.691 * [backup-simplify]: Simplify 0 into 0 2.691 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.692 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.693 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.693 * [backup-simplify]: Simplify (+ 0 0) into 0 2.693 * [backup-simplify]: Simplify (- 1) into -1 2.693 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.694 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.695 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2.697 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.699 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.700 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.705 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.706 * [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 2.707 * [backup-simplify]: Simplify (- 0) into 0 2.707 * [backup-simplify]: Simplify (+ 0 0) into 0 2.707 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.708 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.709 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.710 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.710 * [taylor]: Taking taylor expansion of 0 in k 2.710 * [backup-simplify]: Simplify 0 into 0 2.710 * [backup-simplify]: Simplify 0 into 0 2.710 * [backup-simplify]: Simplify 0 into 0 2.711 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.712 * [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 2.713 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.714 * [backup-simplify]: Simplify (+ 0 0) into 0 2.714 * [backup-simplify]: Simplify (- 0) into 0 2.714 * [backup-simplify]: Simplify (+ 0 0) into 0 2.715 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.717 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.719 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.722 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.728 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.728 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2.728 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.728 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.728 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.729 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.729 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.729 * [taylor]: Taking taylor expansion of 0.25 in k 2.729 * [backup-simplify]: Simplify 0.25 into 0.25 2.729 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.729 * [taylor]: Taking taylor expansion of 1.0 in k 2.729 * [backup-simplify]: Simplify 1.0 into 1.0 2.729 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.729 * [taylor]: Taking taylor expansion of k in k 2.729 * [backup-simplify]: Simplify 0 into 0 2.729 * [backup-simplify]: Simplify 1 into 1 2.729 * [backup-simplify]: Simplify (/ 1 1) into 1 2.729 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.729 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.729 * [taylor]: Taking taylor expansion of 2.0 in k 2.729 * [backup-simplify]: Simplify 2.0 into 2.0 2.729 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.729 * [taylor]: Taking taylor expansion of PI in k 2.729 * [backup-simplify]: Simplify PI into PI 2.729 * [taylor]: Taking taylor expansion of n in k 2.729 * [backup-simplify]: Simplify n into n 2.729 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.729 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.729 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.729 * [backup-simplify]: Simplify (- 1) into -1 2.730 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.730 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.730 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.730 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.730 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.730 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.730 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.730 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.730 * [taylor]: Taking taylor expansion of 0.25 in n 2.730 * [backup-simplify]: Simplify 0.25 into 0.25 2.730 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.730 * [taylor]: Taking taylor expansion of 1.0 in n 2.730 * [backup-simplify]: Simplify 1.0 into 1.0 2.730 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.730 * [taylor]: Taking taylor expansion of k in n 2.730 * [backup-simplify]: Simplify k into k 2.730 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.730 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.730 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.730 * [taylor]: Taking taylor expansion of 2.0 in n 2.730 * [backup-simplify]: Simplify 2.0 into 2.0 2.730 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.730 * [taylor]: Taking taylor expansion of PI in n 2.730 * [backup-simplify]: Simplify PI into PI 2.730 * [taylor]: Taking taylor expansion of n in n 2.730 * [backup-simplify]: Simplify 0 into 0 2.730 * [backup-simplify]: Simplify 1 into 1 2.731 * [backup-simplify]: Simplify (/ PI 1) into PI 2.731 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.732 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.732 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.732 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.732 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.733 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.733 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.734 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.734 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.734 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.734 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.734 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.734 * [taylor]: Taking taylor expansion of 0.25 in n 2.734 * [backup-simplify]: Simplify 0.25 into 0.25 2.734 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.734 * [taylor]: Taking taylor expansion of 1.0 in n 2.734 * [backup-simplify]: Simplify 1.0 into 1.0 2.734 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.734 * [taylor]: Taking taylor expansion of k in n 2.734 * [backup-simplify]: Simplify k into k 2.734 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.734 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.734 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.734 * [taylor]: Taking taylor expansion of 2.0 in n 2.734 * [backup-simplify]: Simplify 2.0 into 2.0 2.734 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.734 * [taylor]: Taking taylor expansion of PI in n 2.734 * [backup-simplify]: Simplify PI into PI 2.734 * [taylor]: Taking taylor expansion of n in n 2.734 * [backup-simplify]: Simplify 0 into 0 2.734 * [backup-simplify]: Simplify 1 into 1 2.735 * [backup-simplify]: Simplify (/ PI 1) into PI 2.735 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.735 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.736 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.736 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.736 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.736 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.737 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.738 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.738 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.738 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.738 * [taylor]: Taking taylor expansion of 0.25 in k 2.738 * [backup-simplify]: Simplify 0.25 into 0.25 2.738 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.738 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.738 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.738 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.738 * [taylor]: Taking taylor expansion of 2.0 in k 2.738 * [backup-simplify]: Simplify 2.0 into 2.0 2.738 * [taylor]: Taking taylor expansion of PI in k 2.738 * [backup-simplify]: Simplify PI into PI 2.738 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.739 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.739 * [taylor]: Taking taylor expansion of (log n) in k 2.739 * [taylor]: Taking taylor expansion of n in k 2.739 * [backup-simplify]: Simplify n into n 2.739 * [backup-simplify]: Simplify (log n) into (log n) 2.739 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.739 * [taylor]: Taking taylor expansion of 1.0 in k 2.739 * [backup-simplify]: Simplify 1.0 into 1.0 2.739 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.739 * [taylor]: Taking taylor expansion of k in k 2.739 * [backup-simplify]: Simplify 0 into 0 2.739 * [backup-simplify]: Simplify 1 into 1 2.739 * [backup-simplify]: Simplify (/ 1 1) into 1 2.739 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.740 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.740 * [backup-simplify]: Simplify (- 1) into -1 2.741 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.741 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.742 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.742 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.743 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.745 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.745 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.745 * [backup-simplify]: Simplify (- 0) into 0 2.745 * [backup-simplify]: Simplify (+ 0 0) into 0 2.746 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.747 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.747 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.748 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.748 * [taylor]: Taking taylor expansion of 0 in k 2.748 * [backup-simplify]: Simplify 0 into 0 2.748 * [backup-simplify]: Simplify 0 into 0 2.748 * [backup-simplify]: Simplify 0 into 0 2.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.749 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.751 * [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 2.751 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.751 * [backup-simplify]: Simplify (- 0) into 0 2.752 * [backup-simplify]: Simplify (+ 0 0) into 0 2.752 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.753 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.754 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.755 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.755 * [taylor]: Taking taylor expansion of 0 in k 2.755 * [backup-simplify]: Simplify 0 into 0 2.755 * [backup-simplify]: Simplify 0 into 0 2.755 * [backup-simplify]: Simplify 0 into 0 2.755 * [backup-simplify]: Simplify 0 into 0 2.756 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.756 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.759 * [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 2.759 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.760 * [backup-simplify]: Simplify (- 0) into 0 2.760 * [backup-simplify]: Simplify (+ 0 0) into 0 2.760 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.761 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.762 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.764 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.764 * [taylor]: Taking taylor expansion of 0 in k 2.764 * [backup-simplify]: Simplify 0 into 0 2.764 * [backup-simplify]: Simplify 0 into 0 2.765 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.765 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2.765 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.765 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.765 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.765 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.765 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.765 * [taylor]: Taking taylor expansion of 0.25 in k 2.765 * [backup-simplify]: Simplify 0.25 into 0.25 2.765 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.765 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.765 * [taylor]: Taking taylor expansion of k in k 2.765 * [backup-simplify]: Simplify 0 into 0 2.765 * [backup-simplify]: Simplify 1 into 1 2.765 * [backup-simplify]: Simplify (/ 1 1) into 1 2.765 * [taylor]: Taking taylor expansion of 1.0 in k 2.766 * [backup-simplify]: Simplify 1.0 into 1.0 2.766 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.766 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.766 * [taylor]: Taking taylor expansion of -2.0 in k 2.766 * [backup-simplify]: Simplify -2.0 into -2.0 2.766 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.766 * [taylor]: Taking taylor expansion of PI in k 2.766 * [backup-simplify]: Simplify PI into PI 2.766 * [taylor]: Taking taylor expansion of n in k 2.766 * [backup-simplify]: Simplify n into n 2.766 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.766 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.766 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.766 * [backup-simplify]: Simplify (+ 1 0) into 1 2.766 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.766 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.766 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.767 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.767 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.767 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.767 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.767 * [taylor]: Taking taylor expansion of 0.25 in n 2.767 * [backup-simplify]: Simplify 0.25 into 0.25 2.767 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.767 * [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 1.0 in n 2.767 * [backup-simplify]: Simplify 1.0 into 1.0 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) 1.0) into (+ (/ 1 k) 1.0) 2.768 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.769 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.770 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.770 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.770 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.770 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.770 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.770 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.770 * [taylor]: Taking taylor expansion of 0.25 in n 2.770 * [backup-simplify]: Simplify 0.25 into 0.25 2.770 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.770 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.770 * [taylor]: Taking taylor expansion of k in n 2.770 * [backup-simplify]: Simplify k into k 2.771 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.771 * [taylor]: Taking taylor expansion of 1.0 in n 2.771 * [backup-simplify]: Simplify 1.0 into 1.0 2.771 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.771 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.771 * [taylor]: Taking taylor expansion of -2.0 in n 2.771 * [backup-simplify]: Simplify -2.0 into -2.0 2.771 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.771 * [taylor]: Taking taylor expansion of PI in n 2.771 * [backup-simplify]: Simplify PI into PI 2.771 * [taylor]: Taking taylor expansion of n in n 2.771 * [backup-simplify]: Simplify 0 into 0 2.771 * [backup-simplify]: Simplify 1 into 1 2.771 * [backup-simplify]: Simplify (/ PI 1) into PI 2.771 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.772 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.772 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.772 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.773 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.773 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.774 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.774 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.774 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.774 * [taylor]: Taking taylor expansion of 0.25 in k 2.774 * [backup-simplify]: Simplify 0.25 into 0.25 2.774 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.774 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.774 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.774 * [taylor]: Taking taylor expansion of k in k 2.774 * [backup-simplify]: Simplify 0 into 0 2.774 * [backup-simplify]: Simplify 1 into 1 2.775 * [backup-simplify]: Simplify (/ 1 1) into 1 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 (- (log (* -2.0 PI)) (log n)) in k 2.775 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.775 * [taylor]: Taking taylor expansion of (* -2.0 PI) 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 in k 2.775 * [backup-simplify]: Simplify PI into PI 2.775 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.776 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.776 * [taylor]: Taking taylor expansion of (log n) in k 2.776 * [taylor]: Taking taylor expansion of n in k 2.776 * [backup-simplify]: Simplify n into n 2.776 * [backup-simplify]: Simplify (log n) into (log n) 2.776 * [backup-simplify]: Simplify (+ 1 0) into 1 2.776 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.777 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.777 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.778 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.779 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.779 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.780 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.780 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.781 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.781 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.782 * [backup-simplify]: Simplify (+ 0 0) into 0 2.782 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.783 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.783 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.784 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.784 * [taylor]: Taking taylor expansion of 0 in k 2.784 * [backup-simplify]: Simplify 0 into 0 2.784 * [backup-simplify]: Simplify 0 into 0 2.785 * [backup-simplify]: Simplify 0 into 0 2.785 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.786 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.787 * [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 2.787 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.788 * [backup-simplify]: Simplify (+ 0 0) into 0 2.788 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.789 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.790 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.794 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.794 * [taylor]: Taking taylor expansion of 0 in k 2.794 * [backup-simplify]: Simplify 0 into 0 2.794 * [backup-simplify]: Simplify 0 into 0 2.794 * [backup-simplify]: Simplify 0 into 0 2.794 * [backup-simplify]: Simplify 0 into 0 2.795 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.795 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.798 * [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 2.798 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.799 * [backup-simplify]: Simplify (+ 0 0) into 0 2.799 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.800 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.801 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.803 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.803 * [taylor]: Taking taylor expansion of 0 in k 2.803 * [backup-simplify]: Simplify 0 into 0 2.803 * [backup-simplify]: Simplify 0 into 0 2.804 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.804 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 2.804 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2.804 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.804 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.804 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.804 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.804 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.804 * [taylor]: Taking taylor expansion of 0.25 in k 2.804 * [backup-simplify]: Simplify 0.25 into 0.25 2.804 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.804 * [taylor]: Taking taylor expansion of 1.0 in k 2.804 * [backup-simplify]: Simplify 1.0 into 1.0 2.804 * [taylor]: Taking taylor expansion of k in k 2.804 * [backup-simplify]: Simplify 0 into 0 2.804 * [backup-simplify]: Simplify 1 into 1 2.804 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.804 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.804 * [taylor]: Taking taylor expansion of 2.0 in k 2.805 * [backup-simplify]: Simplify 2.0 into 2.0 2.805 * [taylor]: Taking taylor expansion of (* n PI) in k 2.805 * [taylor]: Taking taylor expansion of n in k 2.805 * [backup-simplify]: Simplify n into n 2.805 * [taylor]: Taking taylor expansion of PI in k 2.805 * [backup-simplify]: Simplify PI into PI 2.805 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.805 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.805 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.805 * [backup-simplify]: Simplify (- 0) into 0 2.805 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.805 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.805 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.806 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.806 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.806 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.806 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.806 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.806 * [taylor]: Taking taylor expansion of 0.25 in n 2.806 * [backup-simplify]: Simplify 0.25 into 0.25 2.806 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.806 * [taylor]: Taking taylor expansion of 1.0 in n 2.806 * [backup-simplify]: Simplify 1.0 into 1.0 2.806 * [taylor]: Taking taylor expansion of k in n 2.806 * [backup-simplify]: Simplify k into k 2.806 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.806 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.806 * [taylor]: Taking taylor expansion of 2.0 in n 2.806 * [backup-simplify]: Simplify 2.0 into 2.0 2.806 * [taylor]: Taking taylor expansion of (* n PI) in n 2.806 * [taylor]: Taking taylor expansion of n in n 2.806 * [backup-simplify]: Simplify 0 into 0 2.806 * [backup-simplify]: Simplify 1 into 1 2.806 * [taylor]: Taking taylor expansion of PI in n 2.806 * [backup-simplify]: Simplify PI into PI 2.806 * [backup-simplify]: Simplify (* 0 PI) into 0 2.806 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.807 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.808 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.809 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.809 * [backup-simplify]: Simplify (- k) into (- k) 2.809 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.809 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.810 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.810 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.811 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.811 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.811 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.811 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.811 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.811 * [taylor]: Taking taylor expansion of 0.25 in n 2.811 * [backup-simplify]: Simplify 0.25 into 0.25 2.811 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.811 * [taylor]: Taking taylor expansion of 1.0 in n 2.811 * [backup-simplify]: Simplify 1.0 into 1.0 2.811 * [taylor]: Taking taylor expansion of k in n 2.811 * [backup-simplify]: Simplify k into k 2.811 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.811 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.811 * [taylor]: Taking taylor expansion of 2.0 in n 2.811 * [backup-simplify]: Simplify 2.0 into 2.0 2.811 * [taylor]: Taking taylor expansion of (* n PI) in n 2.811 * [taylor]: Taking taylor expansion of n in n 2.811 * [backup-simplify]: Simplify 0 into 0 2.811 * [backup-simplify]: Simplify 1 into 1 2.811 * [taylor]: Taking taylor expansion of PI in n 2.811 * [backup-simplify]: Simplify PI into PI 2.812 * [backup-simplify]: Simplify (* 0 PI) into 0 2.812 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.813 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.813 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.814 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.814 * [backup-simplify]: Simplify (- k) into (- k) 2.814 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.814 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.815 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.816 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.816 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.817 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.817 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.817 * [taylor]: Taking taylor expansion of 0.25 in k 2.817 * [backup-simplify]: Simplify 0.25 into 0.25 2.817 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.817 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.817 * [taylor]: Taking taylor expansion of 1.0 in k 2.817 * [backup-simplify]: Simplify 1.0 into 1.0 2.817 * [taylor]: Taking taylor expansion of k in k 2.817 * [backup-simplify]: Simplify 0 into 0 2.817 * [backup-simplify]: Simplify 1 into 1 2.817 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.817 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.817 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.817 * [taylor]: Taking taylor expansion of 2.0 in k 2.817 * [backup-simplify]: Simplify 2.0 into 2.0 2.817 * [taylor]: Taking taylor expansion of PI in k 2.817 * [backup-simplify]: Simplify PI into PI 2.817 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.818 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.818 * [taylor]: Taking taylor expansion of (log n) in k 2.818 * [taylor]: Taking taylor expansion of n in k 2.818 * [backup-simplify]: Simplify n into n 2.818 * [backup-simplify]: Simplify (log n) into (log n) 2.818 * [backup-simplify]: Simplify (- 0) into 0 2.818 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.819 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.819 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.820 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.821 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.821 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.822 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.822 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.823 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.824 * [backup-simplify]: Simplify (- 0) into 0 2.824 * [backup-simplify]: Simplify (+ 0 0) into 0 2.824 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.825 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.826 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.827 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.827 * [taylor]: Taking taylor expansion of 0 in k 2.827 * [backup-simplify]: Simplify 0 into 0 2.827 * [backup-simplify]: Simplify 0 into 0 2.827 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.828 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.829 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.829 * [backup-simplify]: Simplify (+ 0 0) into 0 2.829 * [backup-simplify]: Simplify (- 1) into -1 2.829 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.830 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.831 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2.833 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.835 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.835 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.836 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.838 * [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 2.838 * [backup-simplify]: Simplify (- 0) into 0 2.838 * [backup-simplify]: Simplify (+ 0 0) into 0 2.839 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.839 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.840 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.841 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.841 * [taylor]: Taking taylor expansion of 0 in k 2.841 * [backup-simplify]: Simplify 0 into 0 2.842 * [backup-simplify]: Simplify 0 into 0 2.842 * [backup-simplify]: Simplify 0 into 0 2.842 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.844 * [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 2.845 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.845 * [backup-simplify]: Simplify (+ 0 0) into 0 2.845 * [backup-simplify]: Simplify (- 0) into 0 2.845 * [backup-simplify]: Simplify (+ 0 0) into 0 2.846 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.848 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.850 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.853 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.858 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.859 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2.859 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.859 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.859 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.859 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.859 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.859 * [taylor]: Taking taylor expansion of 0.25 in k 2.859 * [backup-simplify]: Simplify 0.25 into 0.25 2.859 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.859 * [taylor]: Taking taylor expansion of 1.0 in k 2.859 * [backup-simplify]: Simplify 1.0 into 1.0 2.859 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.859 * [taylor]: Taking taylor expansion of k in k 2.859 * [backup-simplify]: Simplify 0 into 0 2.859 * [backup-simplify]: Simplify 1 into 1 2.859 * [backup-simplify]: Simplify (/ 1 1) into 1 2.859 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.859 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.859 * [taylor]: Taking taylor expansion of 2.0 in k 2.859 * [backup-simplify]: Simplify 2.0 into 2.0 2.859 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.859 * [taylor]: Taking taylor expansion of PI in k 2.859 * [backup-simplify]: Simplify PI into PI 2.859 * [taylor]: Taking taylor expansion of n in k 2.859 * [backup-simplify]: Simplify n into n 2.860 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.860 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.860 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.860 * [backup-simplify]: Simplify (- 1) into -1 2.860 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.860 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.860 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.861 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.861 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.861 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.861 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.861 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.861 * [taylor]: Taking taylor expansion of 0.25 in n 2.861 * [backup-simplify]: Simplify 0.25 into 0.25 2.861 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 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 (/ 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 (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 2.861 * [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)) into (- (/ 1 k)) 2.862 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.862 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.863 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.864 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.864 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.864 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.864 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.864 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.864 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.865 * [taylor]: Taking taylor expansion of 0.25 in n 2.865 * [backup-simplify]: Simplify 0.25 into 0.25 2.865 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.865 * [taylor]: Taking taylor expansion of 1.0 in n 2.865 * [backup-simplify]: Simplify 1.0 into 1.0 2.865 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.865 * [taylor]: Taking taylor expansion of k in n 2.865 * [backup-simplify]: Simplify k into k 2.865 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.865 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.865 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.865 * [taylor]: Taking taylor expansion of 2.0 in n 2.865 * [backup-simplify]: Simplify 2.0 into 2.0 2.865 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.865 * [taylor]: Taking taylor expansion of PI in n 2.865 * [backup-simplify]: Simplify PI into PI 2.865 * [taylor]: Taking taylor expansion of n in n 2.865 * [backup-simplify]: Simplify 0 into 0 2.865 * [backup-simplify]: Simplify 1 into 1 2.865 * [backup-simplify]: Simplify (/ PI 1) into PI 2.865 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.866 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.866 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.866 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.866 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.867 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.868 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.868 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.868 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.868 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.868 * [taylor]: Taking taylor expansion of 0.25 in k 2.868 * [backup-simplify]: Simplify 0.25 into 0.25 2.868 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.868 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.868 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.868 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.869 * [taylor]: Taking taylor expansion of 2.0 in k 2.869 * [backup-simplify]: Simplify 2.0 into 2.0 2.869 * [taylor]: Taking taylor expansion of PI in k 2.869 * [backup-simplify]: Simplify PI into PI 2.869 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.869 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.869 * [taylor]: Taking taylor expansion of (log n) in k 2.869 * [taylor]: Taking taylor expansion of n in k 2.869 * [backup-simplify]: Simplify n into n 2.870 * [backup-simplify]: Simplify (log n) into (log n) 2.870 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.870 * [taylor]: Taking taylor expansion of 1.0 in k 2.870 * [backup-simplify]: Simplify 1.0 into 1.0 2.870 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.870 * [taylor]: Taking taylor expansion of k in k 2.870 * [backup-simplify]: Simplify 0 into 0 2.870 * [backup-simplify]: Simplify 1 into 1 2.870 * [backup-simplify]: Simplify (/ 1 1) into 1 2.870 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.870 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.871 * [backup-simplify]: Simplify (- 1) into -1 2.871 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.872 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.872 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.873 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.873 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.874 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.874 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.875 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.876 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.876 * [backup-simplify]: Simplify (- 0) into 0 2.876 * [backup-simplify]: Simplify (+ 0 0) into 0 2.876 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.877 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.878 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.879 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.879 * [taylor]: Taking taylor expansion of 0 in k 2.879 * [backup-simplify]: Simplify 0 into 0 2.879 * [backup-simplify]: Simplify 0 into 0 2.879 * [backup-simplify]: Simplify 0 into 0 2.883 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.883 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.885 * [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 2.885 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.885 * [backup-simplify]: Simplify (- 0) into 0 2.885 * [backup-simplify]: Simplify (+ 0 0) into 0 2.886 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.887 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.888 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.889 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.889 * [taylor]: Taking taylor expansion of 0 in k 2.889 * [backup-simplify]: Simplify 0 into 0 2.889 * [backup-simplify]: Simplify 0 into 0 2.889 * [backup-simplify]: Simplify 0 into 0 2.889 * [backup-simplify]: Simplify 0 into 0 2.890 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.890 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.893 * [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 2.893 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.893 * [backup-simplify]: Simplify (- 0) into 0 2.893 * [backup-simplify]: Simplify (+ 0 0) into 0 2.894 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.895 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.896 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.897 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.897 * [taylor]: Taking taylor expansion of 0 in k 2.897 * [backup-simplify]: Simplify 0 into 0 2.897 * [backup-simplify]: Simplify 0 into 0 2.898 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.899 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2.899 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.899 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.899 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.899 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.899 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.899 * [taylor]: Taking taylor expansion of 0.25 in k 2.899 * [backup-simplify]: Simplify 0.25 into 0.25 2.899 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.899 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.899 * [taylor]: Taking taylor expansion of k in k 2.899 * [backup-simplify]: Simplify 0 into 0 2.899 * [backup-simplify]: Simplify 1 into 1 2.899 * [backup-simplify]: Simplify (/ 1 1) into 1 2.899 * [taylor]: Taking taylor expansion of 1.0 in k 2.899 * [backup-simplify]: Simplify 1.0 into 1.0 2.899 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.899 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.899 * [taylor]: Taking taylor expansion of -2.0 in k 2.899 * [backup-simplify]: Simplify -2.0 into -2.0 2.899 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.899 * [taylor]: Taking taylor expansion of PI in k 2.899 * [backup-simplify]: Simplify PI into PI 2.899 * [taylor]: Taking taylor expansion of n in k 2.899 * [backup-simplify]: Simplify n into n 2.899 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.899 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.899 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.900 * [backup-simplify]: Simplify (+ 1 0) into 1 2.900 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.900 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.900 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.900 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.900 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.900 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.900 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.900 * [taylor]: Taking taylor expansion of 0.25 in n 2.900 * [backup-simplify]: Simplify 0.25 into 0.25 2.900 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.900 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.900 * [taylor]: Taking taylor expansion of k in n 2.900 * [backup-simplify]: Simplify k into k 2.900 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 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 (* -2.0 (/ PI n))) in n 2.900 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.900 * [taylor]: Taking taylor expansion of -2.0 in n 2.900 * [backup-simplify]: Simplify -2.0 into -2.0 2.900 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.900 * [taylor]: Taking taylor expansion of PI in n 2.900 * [backup-simplify]: Simplify PI into PI 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 2.901 * [backup-simplify]: Simplify (/ PI 1) into PI 2.901 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.902 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.902 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.902 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.903 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.903 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.904 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.904 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.904 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.904 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.904 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.904 * [taylor]: Taking taylor expansion of 0.25 in n 2.904 * [backup-simplify]: Simplify 0.25 into 0.25 2.904 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.904 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.904 * [taylor]: Taking taylor expansion of k in n 2.904 * [backup-simplify]: Simplify k into k 2.904 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.904 * [taylor]: Taking taylor expansion of 1.0 in n 2.904 * [backup-simplify]: Simplify 1.0 into 1.0 2.904 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.904 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.904 * [taylor]: Taking taylor expansion of -2.0 in n 2.904 * [backup-simplify]: Simplify -2.0 into -2.0 2.904 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.904 * [taylor]: Taking taylor expansion of PI in n 2.904 * [backup-simplify]: Simplify PI into PI 2.904 * [taylor]: Taking taylor expansion of n in n 2.904 * [backup-simplify]: Simplify 0 into 0 2.904 * [backup-simplify]: Simplify 1 into 1 2.905 * [backup-simplify]: Simplify (/ PI 1) into PI 2.905 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.905 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.906 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.906 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.906 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.907 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.908 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.908 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.908 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.908 * [taylor]: Taking taylor expansion of 0.25 in k 2.908 * [backup-simplify]: Simplify 0.25 into 0.25 2.908 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.908 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.908 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.908 * [taylor]: Taking taylor expansion of k in k 2.908 * [backup-simplify]: Simplify 0 into 0 2.908 * [backup-simplify]: Simplify 1 into 1 2.908 * [backup-simplify]: Simplify (/ 1 1) into 1 2.908 * [taylor]: Taking taylor expansion of 1.0 in k 2.908 * [backup-simplify]: Simplify 1.0 into 1.0 2.908 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.908 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.908 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.908 * [taylor]: Taking taylor expansion of -2.0 in k 2.908 * [backup-simplify]: Simplify -2.0 into -2.0 2.908 * [taylor]: Taking taylor expansion of PI in k 2.908 * [backup-simplify]: Simplify PI into PI 2.909 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.909 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.909 * [taylor]: Taking taylor expansion of (log n) in k 2.909 * [taylor]: Taking taylor expansion of n in k 2.909 * [backup-simplify]: Simplify n into n 2.909 * [backup-simplify]: Simplify (log n) into (log n) 2.910 * [backup-simplify]: Simplify (+ 1 0) into 1 2.910 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.910 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.911 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.912 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.912 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.913 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.914 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.914 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.915 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.915 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.915 * [backup-simplify]: Simplify (+ 0 0) into 0 2.916 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.916 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.917 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.918 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.918 * [taylor]: Taking taylor expansion of 0 in k 2.918 * [backup-simplify]: Simplify 0 into 0 2.918 * [backup-simplify]: Simplify 0 into 0 2.918 * [backup-simplify]: Simplify 0 into 0 2.919 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.919 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.921 * [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 2.921 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.921 * [backup-simplify]: Simplify (+ 0 0) into 0 2.922 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.923 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.923 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.925 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.925 * [taylor]: Taking taylor expansion of 0 in k 2.925 * [backup-simplify]: Simplify 0 into 0 2.925 * [backup-simplify]: Simplify 0 into 0 2.925 * [backup-simplify]: Simplify 0 into 0 2.925 * [backup-simplify]: Simplify 0 into 0 2.925 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.926 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.929 * [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 2.929 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.929 * [backup-simplify]: Simplify (+ 0 0) into 0 2.930 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.931 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.932 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.933 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.933 * [taylor]: Taking taylor expansion of 0 in k 2.933 * [backup-simplify]: Simplify 0 into 0 2.934 * [backup-simplify]: Simplify 0 into 0 2.934 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.934 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 2.934 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 2.934 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.934 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.934 * [taylor]: Taking taylor expansion of 1.0 in k 2.934 * [backup-simplify]: Simplify 1.0 into 1.0 2.934 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.934 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.935 * [taylor]: Taking taylor expansion of k in k 2.935 * [backup-simplify]: Simplify 0 into 0 2.935 * [backup-simplify]: Simplify 1 into 1 2.935 * [backup-simplify]: Simplify (/ 1 1) into 1 2.935 * [backup-simplify]: Simplify (sqrt 0) into 0 2.936 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.936 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.936 * [taylor]: Taking taylor expansion of 1.0 in k 2.936 * [backup-simplify]: Simplify 1.0 into 1.0 2.936 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.936 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.936 * [taylor]: Taking taylor expansion of k in k 2.936 * [backup-simplify]: Simplify 0 into 0 2.936 * [backup-simplify]: Simplify 1 into 1 2.936 * [backup-simplify]: Simplify (/ 1 1) into 1 2.936 * [backup-simplify]: Simplify (sqrt 0) into 0 2.937 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.937 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.937 * [backup-simplify]: Simplify 0 into 0 2.938 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.938 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.939 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.940 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.941 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.942 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.942 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.944 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.945 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.945 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.946 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 2.946 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 2.946 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.946 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.946 * [taylor]: Taking taylor expansion of 1.0 in k 2.946 * [backup-simplify]: Simplify 1.0 into 1.0 2.946 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.946 * [taylor]: Taking taylor expansion of k in k 2.946 * [backup-simplify]: Simplify 0 into 0 2.946 * [backup-simplify]: Simplify 1 into 1 2.947 * [backup-simplify]: Simplify (sqrt 0) into 0 2.947 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.947 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.947 * [taylor]: Taking taylor expansion of 1.0 in k 2.947 * [backup-simplify]: Simplify 1.0 into 1.0 2.947 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.947 * [taylor]: Taking taylor expansion of k in k 2.947 * [backup-simplify]: Simplify 0 into 0 2.947 * [backup-simplify]: Simplify 1 into 1 2.948 * [backup-simplify]: Simplify (sqrt 0) into 0 2.948 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.949 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.949 * [backup-simplify]: Simplify 0 into 0 2.949 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.950 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.951 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.952 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.952 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.954 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.955 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.956 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.957 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 2.957 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 2.957 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.957 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.957 * [taylor]: Taking taylor expansion of 1.0 in k 2.957 * [backup-simplify]: Simplify 1.0 into 1.0 2.957 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.957 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.957 * [taylor]: Taking taylor expansion of -1 in k 2.957 * [backup-simplify]: Simplify -1 into -1 2.957 * [taylor]: Taking taylor expansion of k in k 2.957 * [backup-simplify]: Simplify 0 into 0 2.957 * [backup-simplify]: Simplify 1 into 1 2.957 * [backup-simplify]: Simplify (/ -1 1) into -1 2.957 * [backup-simplify]: Simplify (sqrt 0) into 0 2.958 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.958 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.958 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.958 * [taylor]: Taking taylor expansion of 1.0 in k 2.958 * [backup-simplify]: Simplify 1.0 into 1.0 2.958 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.958 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.958 * [taylor]: Taking taylor expansion of -1 in k 2.958 * [backup-simplify]: Simplify -1 into -1 2.958 * [taylor]: Taking taylor expansion of k in k 2.958 * [backup-simplify]: Simplify 0 into 0 2.958 * [backup-simplify]: Simplify 1 into 1 2.959 * [backup-simplify]: Simplify (/ -1 1) into -1 2.959 * [backup-simplify]: Simplify (sqrt 0) into 0 2.960 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.960 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.960 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.960 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.962 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.963 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 2.964 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.964 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.970 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.972 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 2.973 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.973 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 2.973 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 2.974 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.974 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.974 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.974 * [taylor]: Taking taylor expansion of 2.0 in n 2.974 * [backup-simplify]: Simplify 2.0 into 2.0 2.974 * [taylor]: Taking taylor expansion of (* n PI) in n 2.974 * [taylor]: Taking taylor expansion of n in n 2.974 * [backup-simplify]: Simplify 0 into 0 2.974 * [backup-simplify]: Simplify 1 into 1 2.974 * [taylor]: Taking taylor expansion of PI in n 2.974 * [backup-simplify]: Simplify PI into PI 2.974 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.974 * [taylor]: Taking taylor expansion of 2.0 in n 2.974 * [backup-simplify]: Simplify 2.0 into 2.0 2.974 * [taylor]: Taking taylor expansion of (* n PI) in n 2.974 * [taylor]: Taking taylor expansion of n in n 2.974 * [backup-simplify]: Simplify 0 into 0 2.974 * [backup-simplify]: Simplify 1 into 1 2.974 * [taylor]: Taking taylor expansion of PI in n 2.974 * [backup-simplify]: Simplify PI into PI 2.974 * [backup-simplify]: Simplify (* 0 PI) into 0 2.975 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.975 * [backup-simplify]: Simplify 0 into 0 2.976 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.977 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.977 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.978 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.978 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.978 * [backup-simplify]: Simplify 0 into 0 2.979 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.979 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.979 * [backup-simplify]: Simplify 0 into 0 2.980 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.981 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.981 * [backup-simplify]: Simplify 0 into 0 2.982 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.982 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.982 * [backup-simplify]: Simplify 0 into 0 2.983 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.984 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.984 * [backup-simplify]: Simplify 0 into 0 2.985 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.986 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.986 * [backup-simplify]: Simplify 0 into 0 2.986 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.986 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.987 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.987 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.987 * [taylor]: Taking taylor expansion of 2.0 in n 2.987 * [backup-simplify]: Simplify 2.0 into 2.0 2.987 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.987 * [taylor]: Taking taylor expansion of PI in n 2.987 * [backup-simplify]: Simplify PI into PI 2.987 * [taylor]: Taking taylor expansion of n in n 2.987 * [backup-simplify]: Simplify 0 into 0 2.987 * [backup-simplify]: Simplify 1 into 1 2.987 * [backup-simplify]: Simplify (/ PI 1) into PI 2.987 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.987 * [taylor]: Taking taylor expansion of 2.0 in n 2.987 * [backup-simplify]: Simplify 2.0 into 2.0 2.987 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.987 * [taylor]: Taking taylor expansion of PI in n 2.987 * [backup-simplify]: Simplify PI into PI 2.987 * [taylor]: Taking taylor expansion of n in n 2.987 * [backup-simplify]: Simplify 0 into 0 2.987 * [backup-simplify]: Simplify 1 into 1 2.987 * [backup-simplify]: Simplify (/ PI 1) into PI 2.988 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.988 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.988 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.989 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.989 * [backup-simplify]: Simplify 0 into 0 2.989 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.990 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.990 * [backup-simplify]: Simplify 0 into 0 2.991 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.991 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.991 * [backup-simplify]: Simplify 0 into 0 2.992 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.992 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.992 * [backup-simplify]: Simplify 0 into 0 2.993 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.994 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.994 * [backup-simplify]: Simplify 0 into 0 2.994 * [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 2.995 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.995 * [backup-simplify]: Simplify 0 into 0 2.995 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.996 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.996 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.996 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.996 * [taylor]: Taking taylor expansion of -2.0 in n 2.996 * [backup-simplify]: Simplify -2.0 into -2.0 2.996 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.996 * [taylor]: Taking taylor expansion of PI in n 2.996 * [backup-simplify]: Simplify PI into PI 2.996 * [taylor]: Taking taylor expansion of n in n 2.996 * [backup-simplify]: Simplify 0 into 0 2.996 * [backup-simplify]: Simplify 1 into 1 2.996 * [backup-simplify]: Simplify (/ PI 1) into PI 2.996 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.996 * [taylor]: Taking taylor expansion of -2.0 in n 2.996 * [backup-simplify]: Simplify -2.0 into -2.0 2.996 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.996 * [taylor]: Taking taylor expansion of PI in n 2.996 * [backup-simplify]: Simplify PI into PI 2.996 * [taylor]: Taking taylor expansion of n in n 2.996 * [backup-simplify]: Simplify 0 into 0 2.996 * [backup-simplify]: Simplify 1 into 1 2.997 * [backup-simplify]: Simplify (/ PI 1) into PI 2.997 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.997 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.998 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.998 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.998 * [backup-simplify]: Simplify 0 into 0 2.999 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.999 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.999 * [backup-simplify]: Simplify 0 into 0 3.000 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.000 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.000 * [backup-simplify]: Simplify 0 into 0 3.001 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.002 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.002 * [backup-simplify]: Simplify 0 into 0 3.002 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.003 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.003 * [backup-simplify]: Simplify 0 into 0 3.004 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.004 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.004 * [backup-simplify]: Simplify 0 into 0 3.005 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 3.005 * * * [progress]: simplifying candidates 3.008 * [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) 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(* 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 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2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 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 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(* (* (* (* 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 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h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 1) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) 1) (sqrt 2))) (pow (* (* h0 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(exp (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)))) (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (* (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (expm1 (/ h3 (sqrt h4))) (log1p (/ h3 (sqrt h4))) (- (log h3) (log (sqrt h4))) (log (/ h3 (sqrt h4))) (exp (/ h3 (sqrt h4))) (/ (* (* h3 h3) h3) (* (* (sqrt h4) (sqrt h4)) (sqrt h4))) (* (cbrt (/ h3 (sqrt h4))) (cbrt (/ h3 (sqrt h4)))) (cbrt (/ h3 (sqrt h4))) (* (* (/ h3 (sqrt h4)) (/ h3 (sqrt h4))) (/ h3 (sqrt h4))) (sqrt (/ h3 (sqrt h4))) (sqrt (/ h3 (sqrt h4))) (- h3) (- (sqrt h4)) (/ (* (cbrt h3) (cbrt h3)) (* (cbrt (sqrt 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(sqrt h4))) (/ h3 (sqrt (sqrt h4))) (/ 1 1) (/ h3 (sqrt h4)) (/ 1 (sqrt h4)) (/ (sqrt h4) h3) (/ h3 (* (cbrt (sqrt h4)) (cbrt (sqrt h4)))) (/ h3 (sqrt (* (cbrt h4) (cbrt h4)))) (/ h3 (sqrt (sqrt h4))) (/ h3 (sqrt 1)) (/ h3 (sqrt (sqrt h4))) (/ h3 1) (/ (sqrt h4) (cbrt h3)) (/ (sqrt h4) (sqrt h3)) (/ (sqrt h4) h3) (expm1 (* (* h0 h1) h2)) (log1p (* (* h0 h1) h2)) (* (* h0 h1) h2) (* (* h0 h1) h2) (+ (+ (log h0) (log h1)) (log h2)) (+ (log (* h0 h1)) (log h2)) (log (* (* h0 h1) h2)) (exp (* (* h0 h1) h2)) (* (* (* (* h0 h0) h0) (* (* h1 h1) h1)) (* (* h2 h2) h2)) (* (* (* (* h0 h1) (* h0 h1)) (* h0 h1)) (* (* h2 h2) h2)) (* (cbrt (* (* h0 h1) h2)) (cbrt (* (* h0 h1) h2))) (cbrt (* (* h0 h1) h2)) (* (* (* (* h0 h1) h2) (* (* h0 h1) h2)) (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (* (* h0 h1) (* (cbrt h2) (cbrt h2))) (* (* h0 h1) (sqrt h2)) (* (* h0 h1) 1) (* h1 h2) (- (+ (* h5 (* (pow h4 2) (* (pow (log (* h0 h1)) 2) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (+ (* h7 (* (pow h4 2) (* (log (* h0 h1)) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2))))) (* h5 (* (pow h4 2) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2))))))) (+ (* h6 (* h4 (* (log (* h0 h1)) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (* h6 (* h4 (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2)))))) (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (- (+ (* h5 (* (pow h4 2) (* (pow (log (* h0 h1)) 2) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (+ (* h7 (* (pow h4 2) (* (log (* h0 h1)) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2))))) (* h5 (* (pow h4 2) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2))))))) (+ (* h6 (* h4 (* (log (* h0 h1)) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (* h6 (* h4 (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2)))))) (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (- (+ (* h9 h4) (- (+ (* h9 (pow h4 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- (* h9 (/ 1 (pow h4 3)))))))) (- (+ (* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- h9))))) (* h0 (* h2 h1)) (* h0 (* h2 h1)) (* h0 (* h2 h1)) 3.018 * * [simplify]: iteration 0 : 874 enodes (cost 1888 ) 3.032 * * [simplify]: iteration 1 : 3432 enodes (cost 1810 ) 3.080 * * [simplify]: iteration 2 : 5001 enodes (cost 1792 ) 3.088 * * * [progress]: adding candidates to table 3.815 * * [progress]: iteration 4 / 4 3.815 * * * [progress]: picking best candidate 3.833 * * * * [pick]: Picked # 3.833 * * * [progress]: localizing error 3.849 * * * [progress]: generating rewritten candidates 3.850 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 3.876 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 3.901 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 3.945 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1) 3.971 * * * [progress]: generating series expansions 3.971 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 3.971 * [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))) 3.972 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 3.972 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 3.972 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.972 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.972 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 3.972 * [taylor]: Taking taylor expansion of 0.25 in k 3.972 * [backup-simplify]: Simplify 0.25 into 0.25 3.972 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.972 * [taylor]: Taking taylor expansion of 1.0 in k 3.972 * [backup-simplify]: Simplify 1.0 into 1.0 3.972 * [taylor]: Taking taylor expansion of k in k 3.972 * [backup-simplify]: Simplify 0 into 0 3.972 * [backup-simplify]: Simplify 1 into 1 3.972 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.972 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.972 * [taylor]: Taking taylor expansion of 2.0 in k 3.972 * [backup-simplify]: Simplify 2.0 into 2.0 3.972 * [taylor]: Taking taylor expansion of (* n PI) in k 3.972 * [taylor]: Taking taylor expansion of n in k 3.972 * [backup-simplify]: Simplify n into n 3.972 * [taylor]: Taking taylor expansion of PI in k 3.972 * [backup-simplify]: Simplify PI into PI 3.972 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.972 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.972 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.972 * [backup-simplify]: Simplify (- 0) into 0 3.973 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.973 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 3.973 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 3.973 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 3.973 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 3.973 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.973 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.973 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 3.973 * [taylor]: Taking taylor expansion of 0.25 in n 3.973 * [backup-simplify]: Simplify 0.25 into 0.25 3.973 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.973 * [taylor]: Taking taylor expansion of 1.0 in n 3.973 * [backup-simplify]: Simplify 1.0 into 1.0 3.973 * [taylor]: Taking taylor expansion of k in n 3.973 * [backup-simplify]: Simplify k into k 3.973 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.973 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.973 * [taylor]: Taking taylor expansion of 2.0 in n 3.973 * [backup-simplify]: Simplify 2.0 into 2.0 3.973 * [taylor]: Taking taylor expansion of (* n PI) in n 3.973 * [taylor]: Taking taylor expansion of n in n 3.973 * [backup-simplify]: Simplify 0 into 0 3.973 * [backup-simplify]: Simplify 1 into 1 3.973 * [taylor]: Taking taylor expansion of PI in n 3.973 * [backup-simplify]: Simplify PI into PI 3.974 * [backup-simplify]: Simplify (* 0 PI) into 0 3.974 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.975 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.976 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.976 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.976 * [backup-simplify]: Simplify (- k) into (- k) 3.976 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.976 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 3.977 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.978 * [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)))) 3.979 * [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))))) 3.979 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 3.979 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.979 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.979 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 3.979 * [taylor]: Taking taylor expansion of 0.25 in n 3.979 * [backup-simplify]: Simplify 0.25 into 0.25 3.979 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.979 * [taylor]: Taking taylor expansion of 1.0 in n 3.979 * [backup-simplify]: Simplify 1.0 into 1.0 3.979 * [taylor]: Taking taylor expansion of k in n 3.979 * [backup-simplify]: Simplify k into k 3.979 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.979 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.979 * [taylor]: Taking taylor expansion of 2.0 in n 3.979 * [backup-simplify]: Simplify 2.0 into 2.0 3.979 * [taylor]: Taking taylor expansion of (* n PI) in n 3.979 * [taylor]: Taking taylor expansion of n in n 3.979 * [backup-simplify]: Simplify 0 into 0 3.979 * [backup-simplify]: Simplify 1 into 1 3.979 * [taylor]: Taking taylor expansion of PI in n 3.979 * [backup-simplify]: Simplify PI into PI 3.979 * [backup-simplify]: Simplify (* 0 PI) into 0 3.979 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.980 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.981 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.982 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.982 * [backup-simplify]: Simplify (- k) into (- k) 3.982 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.982 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 3.983 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.983 * [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)))) 3.989 * [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))))) 3.989 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.989 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.989 * [taylor]: Taking taylor expansion of 0.25 in k 3.989 * [backup-simplify]: Simplify 0.25 into 0.25 3.989 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.990 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.990 * [taylor]: Taking taylor expansion of 1.0 in k 3.990 * [backup-simplify]: Simplify 1.0 into 1.0 3.990 * [taylor]: Taking taylor expansion of k in k 3.990 * [backup-simplify]: Simplify 0 into 0 3.990 * [backup-simplify]: Simplify 1 into 1 3.990 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.990 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.990 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.990 * [taylor]: Taking taylor expansion of 2.0 in k 3.990 * [backup-simplify]: Simplify 2.0 into 2.0 3.990 * [taylor]: Taking taylor expansion of PI in k 3.990 * [backup-simplify]: Simplify PI into PI 3.990 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.991 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.991 * [taylor]: Taking taylor expansion of (log n) in k 3.991 * [taylor]: Taking taylor expansion of n in k 3.991 * [backup-simplify]: Simplify n into n 3.991 * [backup-simplify]: Simplify (log n) into (log n) 3.991 * [backup-simplify]: Simplify (- 0) into 0 3.991 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.992 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.992 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.993 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 3.994 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 3.994 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 3.995 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.995 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.996 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.996 * [backup-simplify]: Simplify (- 0) into 0 3.997 * [backup-simplify]: Simplify (+ 0 0) into 0 3.997 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 3.998 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.998 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.000 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.000 * [taylor]: Taking taylor expansion of 0 in k 4.000 * [backup-simplify]: Simplify 0 into 0 4.000 * [backup-simplify]: Simplify 0 into 0 4.000 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.001 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.001 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.002 * [backup-simplify]: Simplify (+ 0 0) into 0 4.002 * [backup-simplify]: Simplify (- 1) into -1 4.002 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.003 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.004 * [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)))) 4.006 * [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)))))) 4.008 * [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)))))) 4.008 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.009 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.010 * [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 4.011 * [backup-simplify]: Simplify (- 0) into 0 4.011 * [backup-simplify]: Simplify (+ 0 0) into 0 4.011 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.012 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.013 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.015 * [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 4.015 * [taylor]: Taking taylor expansion of 0 in k 4.015 * [backup-simplify]: Simplify 0 into 0 4.015 * [backup-simplify]: Simplify 0 into 0 4.015 * [backup-simplify]: Simplify 0 into 0 4.015 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.017 * [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 4.018 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.018 * [backup-simplify]: Simplify (+ 0 0) into 0 4.018 * [backup-simplify]: Simplify (- 0) into 0 4.019 * [backup-simplify]: Simplify (+ 0 0) into 0 4.020 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.021 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.023 * [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))))) 4.026 * [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))))) 4.032 * [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)))))) 4.033 * [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)))) 4.033 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 4.033 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 4.033 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.033 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.033 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 4.033 * [taylor]: Taking taylor expansion of 0.25 in k 4.033 * [backup-simplify]: Simplify 0.25 into 0.25 4.033 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.033 * [taylor]: Taking taylor expansion of 1.0 in k 4.033 * [backup-simplify]: Simplify 1.0 into 1.0 4.033 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.033 * [taylor]: Taking taylor expansion of k in k 4.033 * [backup-simplify]: Simplify 0 into 0 4.033 * [backup-simplify]: Simplify 1 into 1 4.033 * [backup-simplify]: Simplify (/ 1 1) into 1 4.033 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.033 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.033 * [taylor]: Taking taylor expansion of 2.0 in k 4.033 * [backup-simplify]: Simplify 2.0 into 2.0 4.033 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.033 * [taylor]: Taking taylor expansion of PI in k 4.033 * [backup-simplify]: Simplify PI into PI 4.033 * [taylor]: Taking taylor expansion of n in k 4.033 * [backup-simplify]: Simplify n into n 4.033 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.033 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.033 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.034 * [backup-simplify]: Simplify (- 1) into -1 4.034 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.034 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 4.034 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 4.034 * [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))))) 4.034 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.034 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.034 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.034 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.034 * [taylor]: Taking taylor expansion of 0.25 in n 4.034 * [backup-simplify]: Simplify 0.25 into 0.25 4.034 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.034 * [taylor]: Taking taylor expansion of 1.0 in n 4.034 * [backup-simplify]: Simplify 1.0 into 1.0 4.034 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.034 * [taylor]: Taking taylor expansion of k in n 4.034 * [backup-simplify]: Simplify k into k 4.035 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.035 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.035 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.035 * [taylor]: Taking taylor expansion of 2.0 in n 4.035 * [backup-simplify]: Simplify 2.0 into 2.0 4.035 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.035 * [taylor]: Taking taylor expansion of PI in n 4.035 * [backup-simplify]: Simplify PI into PI 4.035 * [taylor]: Taking taylor expansion of n in n 4.035 * [backup-simplify]: Simplify 0 into 0 4.035 * [backup-simplify]: Simplify 1 into 1 4.035 * [backup-simplify]: Simplify (/ PI 1) into PI 4.035 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.036 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.036 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.036 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.036 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.037 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.037 * [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)))) 4.038 * [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))))) 4.038 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.038 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.038 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.038 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.038 * [taylor]: Taking taylor expansion of 0.25 in n 4.038 * [backup-simplify]: Simplify 0.25 into 0.25 4.038 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.038 * [taylor]: Taking taylor expansion of 1.0 in n 4.038 * [backup-simplify]: Simplify 1.0 into 1.0 4.038 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.038 * [taylor]: Taking taylor expansion of k in n 4.038 * [backup-simplify]: Simplify k into k 4.038 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.038 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.038 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.038 * [taylor]: Taking taylor expansion of 2.0 in n 4.038 * [backup-simplify]: Simplify 2.0 into 2.0 4.038 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.038 * [taylor]: Taking taylor expansion of PI in n 4.039 * [backup-simplify]: Simplify PI into PI 4.039 * [taylor]: Taking taylor expansion of n in n 4.039 * [backup-simplify]: Simplify 0 into 0 4.039 * [backup-simplify]: Simplify 1 into 1 4.039 * [backup-simplify]: Simplify (/ PI 1) into PI 4.039 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.040 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.040 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.040 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.040 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.041 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.041 * [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)))) 4.042 * [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))))) 4.042 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.042 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.042 * [taylor]: Taking taylor expansion of 0.25 in k 4.042 * [backup-simplify]: Simplify 0.25 into 0.25 4.042 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.042 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.042 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.042 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.042 * [taylor]: Taking taylor expansion of 2.0 in k 4.042 * [backup-simplify]: Simplify 2.0 into 2.0 4.042 * [taylor]: Taking taylor expansion of PI in k 4.042 * [backup-simplify]: Simplify PI into PI 4.043 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.043 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.043 * [taylor]: Taking taylor expansion of (log n) in k 4.043 * [taylor]: Taking taylor expansion of n in k 4.043 * [backup-simplify]: Simplify n into n 4.043 * [backup-simplify]: Simplify (log n) into (log n) 4.043 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.043 * [taylor]: Taking taylor expansion of 1.0 in k 4.043 * [backup-simplify]: Simplify 1.0 into 1.0 4.043 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.043 * [taylor]: Taking taylor expansion of k in k 4.043 * [backup-simplify]: Simplify 0 into 0 4.043 * [backup-simplify]: Simplify 1 into 1 4.044 * [backup-simplify]: Simplify (/ 1 1) into 1 4.044 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.044 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.044 * [backup-simplify]: Simplify (- 1) into -1 4.045 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.045 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.046 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 4.047 * [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))))) 4.047 * [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))))) 4.048 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.048 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.049 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.049 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.049 * [backup-simplify]: Simplify (- 0) into 0 4.050 * [backup-simplify]: Simplify (+ 0 0) into 0 4.050 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.051 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.051 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.052 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.052 * [taylor]: Taking taylor expansion of 0 in k 4.053 * [backup-simplify]: Simplify 0 into 0 4.053 * [backup-simplify]: Simplify 0 into 0 4.053 * [backup-simplify]: Simplify 0 into 0 4.053 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.054 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.055 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.055 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.056 * [backup-simplify]: Simplify (- 0) into 0 4.056 * [backup-simplify]: Simplify (+ 0 0) into 0 4.056 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.057 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.058 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.059 * [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 4.059 * [taylor]: Taking taylor expansion of 0 in k 4.059 * [backup-simplify]: Simplify 0 into 0 4.059 * [backup-simplify]: Simplify 0 into 0 4.060 * [backup-simplify]: Simplify 0 into 0 4.060 * [backup-simplify]: Simplify 0 into 0 4.060 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.061 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.063 * [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 4.064 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.064 * [backup-simplify]: Simplify (- 0) into 0 4.064 * [backup-simplify]: Simplify (+ 0 0) into 0 4.065 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.066 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.067 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.069 * [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 4.069 * [taylor]: Taking taylor expansion of 0 in k 4.069 * [backup-simplify]: Simplify 0 into 0 4.069 * [backup-simplify]: Simplify 0 into 0 4.069 * [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)))) 4.070 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 4.070 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 4.070 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 4.070 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.070 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.070 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 4.070 * [taylor]: Taking taylor expansion of 0.25 in k 4.070 * [backup-simplify]: Simplify 0.25 into 0.25 4.070 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.070 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.070 * [taylor]: Taking taylor expansion of k in k 4.070 * [backup-simplify]: Simplify 0 into 0 4.070 * [backup-simplify]: Simplify 1 into 1 4.070 * [backup-simplify]: Simplify (/ 1 1) into 1 4.070 * [taylor]: Taking taylor expansion of 1.0 in k 4.070 * [backup-simplify]: Simplify 1.0 into 1.0 4.070 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.070 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.070 * [taylor]: Taking taylor expansion of -2.0 in k 4.070 * [backup-simplify]: Simplify -2.0 into -2.0 4.070 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.070 * [taylor]: Taking taylor expansion of PI in k 4.070 * [backup-simplify]: Simplify PI into PI 4.070 * [taylor]: Taking taylor expansion of n in k 4.070 * [backup-simplify]: Simplify n into n 4.071 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.071 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.071 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.071 * [backup-simplify]: Simplify (+ 1 0) into 1 4.071 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 4.071 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 4.071 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.071 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.071 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.071 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.071 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.071 * [taylor]: Taking taylor expansion of 0.25 in n 4.071 * [backup-simplify]: Simplify 0.25 into 0.25 4.071 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.071 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.071 * [taylor]: Taking taylor expansion of k in n 4.072 * [backup-simplify]: Simplify k into k 4.072 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.072 * [taylor]: Taking taylor expansion of 1.0 in n 4.072 * [backup-simplify]: Simplify 1.0 into 1.0 4.072 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.072 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.072 * [taylor]: Taking taylor expansion of -2.0 in n 4.072 * [backup-simplify]: Simplify -2.0 into -2.0 4.072 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.072 * [taylor]: Taking taylor expansion of PI in n 4.072 * [backup-simplify]: Simplify PI into PI 4.072 * [taylor]: Taking taylor expansion of n in n 4.072 * [backup-simplify]: Simplify 0 into 0 4.072 * [backup-simplify]: Simplify 1 into 1 4.072 * [backup-simplify]: Simplify (/ PI 1) into PI 4.072 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.073 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.073 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.073 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.074 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.074 * [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)))) 4.075 * [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))))) 4.075 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.075 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.075 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.075 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.075 * [taylor]: Taking taylor expansion of 0.25 in n 4.075 * [backup-simplify]: Simplify 0.25 into 0.25 4.075 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.075 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.075 * [taylor]: Taking taylor expansion of k in n 4.081 * [backup-simplify]: Simplify k into k 4.081 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.081 * [taylor]: Taking taylor expansion of 1.0 in n 4.081 * [backup-simplify]: Simplify 1.0 into 1.0 4.081 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.081 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.081 * [taylor]: Taking taylor expansion of -2.0 in n 4.081 * [backup-simplify]: Simplify -2.0 into -2.0 4.081 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.081 * [taylor]: Taking taylor expansion of PI in n 4.081 * [backup-simplify]: Simplify PI into PI 4.081 * [taylor]: Taking taylor expansion of n in n 4.081 * [backup-simplify]: Simplify 0 into 0 4.081 * [backup-simplify]: Simplify 1 into 1 4.081 * [backup-simplify]: Simplify (/ PI 1) into PI 4.082 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.082 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.082 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.082 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.083 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.084 * [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)))) 4.085 * [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))))) 4.085 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.085 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.085 * [taylor]: Taking taylor expansion of 0.25 in k 4.085 * [backup-simplify]: Simplify 0.25 into 0.25 4.085 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.085 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.085 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.085 * [taylor]: Taking taylor expansion of k in k 4.085 * [backup-simplify]: Simplify 0 into 0 4.085 * [backup-simplify]: Simplify 1 into 1 4.085 * [backup-simplify]: Simplify (/ 1 1) into 1 4.085 * [taylor]: Taking taylor expansion of 1.0 in k 4.085 * [backup-simplify]: Simplify 1.0 into 1.0 4.085 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.085 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.085 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.085 * [taylor]: Taking taylor expansion of -2.0 in k 4.085 * [backup-simplify]: Simplify -2.0 into -2.0 4.085 * [taylor]: Taking taylor expansion of PI in k 4.085 * [backup-simplify]: Simplify PI into PI 4.085 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.086 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.086 * [taylor]: Taking taylor expansion of (log n) in k 4.086 * [taylor]: Taking taylor expansion of n in k 4.086 * [backup-simplify]: Simplify n into n 4.086 * [backup-simplify]: Simplify (log n) into (log n) 4.086 * [backup-simplify]: Simplify (+ 1 0) into 1 4.086 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.087 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.088 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.088 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 4.089 * [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))))) 4.090 * [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))))) 4.090 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.091 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.092 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.092 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.092 * [backup-simplify]: Simplify (+ 0 0) into 0 4.092 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.093 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.094 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.095 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.095 * [taylor]: Taking taylor expansion of 0 in k 4.095 * [backup-simplify]: Simplify 0 into 0 4.095 * [backup-simplify]: Simplify 0 into 0 4.095 * [backup-simplify]: Simplify 0 into 0 4.095 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.096 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.097 * [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 4.098 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.098 * [backup-simplify]: Simplify (+ 0 0) into 0 4.098 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.099 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.100 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.101 * [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 4.101 * [taylor]: Taking taylor expansion of 0 in k 4.101 * [backup-simplify]: Simplify 0 into 0 4.101 * [backup-simplify]: Simplify 0 into 0 4.101 * [backup-simplify]: Simplify 0 into 0 4.101 * [backup-simplify]: Simplify 0 into 0 4.102 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.103 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.105 * [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 4.105 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.106 * [backup-simplify]: Simplify (+ 0 0) into 0 4.106 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.107 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.108 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.110 * [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 4.110 * [taylor]: Taking taylor expansion of 0 in k 4.110 * [backup-simplify]: Simplify 0 into 0 4.110 * [backup-simplify]: Simplify 0 into 0 4.110 * [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)))))) 4.111 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 4.111 * [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))) 4.111 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 4.111 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 4.111 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.112 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.112 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 4.112 * [taylor]: Taking taylor expansion of 0.25 in k 4.112 * [backup-simplify]: Simplify 0.25 into 0.25 4.112 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.112 * [taylor]: Taking taylor expansion of 1.0 in k 4.112 * [backup-simplify]: Simplify 1.0 into 1.0 4.112 * [taylor]: Taking taylor expansion of k in k 4.112 * [backup-simplify]: Simplify 0 into 0 4.112 * [backup-simplify]: Simplify 1 into 1 4.112 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.112 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.112 * [taylor]: Taking taylor expansion of 2.0 in k 4.112 * [backup-simplify]: Simplify 2.0 into 2.0 4.112 * [taylor]: Taking taylor expansion of (* n PI) in k 4.112 * [taylor]: Taking taylor expansion of n in k 4.112 * [backup-simplify]: Simplify n into n 4.112 * [taylor]: Taking taylor expansion of PI in k 4.112 * [backup-simplify]: Simplify PI into PI 4.112 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.112 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.112 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.112 * [backup-simplify]: Simplify (- 0) into 0 4.112 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.113 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 4.113 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 4.113 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 4.113 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.113 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.113 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.113 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.113 * [taylor]: Taking taylor expansion of 0.25 in n 4.113 * [backup-simplify]: Simplify 0.25 into 0.25 4.113 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.113 * [taylor]: Taking taylor expansion of 1.0 in n 4.113 * [backup-simplify]: Simplify 1.0 into 1.0 4.113 * [taylor]: Taking taylor expansion of k in n 4.113 * [backup-simplify]: Simplify k into k 4.113 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.113 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.113 * [taylor]: Taking taylor expansion of 2.0 in n 4.113 * [backup-simplify]: Simplify 2.0 into 2.0 4.113 * [taylor]: Taking taylor expansion of (* n PI) in n 4.113 * [taylor]: Taking taylor expansion of n in n 4.113 * [backup-simplify]: Simplify 0 into 0 4.113 * [backup-simplify]: Simplify 1 into 1 4.113 * [taylor]: Taking taylor expansion of PI in n 4.113 * [backup-simplify]: Simplify PI into PI 4.113 * [backup-simplify]: Simplify (* 0 PI) into 0 4.114 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.114 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.115 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.116 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.116 * [backup-simplify]: Simplify (- k) into (- k) 4.116 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.116 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.117 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.117 * [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)))) 4.118 * [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))))) 4.118 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.118 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.118 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.118 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.118 * [taylor]: Taking taylor expansion of 0.25 in n 4.118 * [backup-simplify]: Simplify 0.25 into 0.25 4.118 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.118 * [taylor]: Taking taylor expansion of 1.0 in n 4.118 * [backup-simplify]: Simplify 1.0 into 1.0 4.118 * [taylor]: Taking taylor expansion of k in n 4.118 * [backup-simplify]: Simplify k into k 4.118 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.118 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.118 * [taylor]: Taking taylor expansion of 2.0 in n 4.118 * [backup-simplify]: Simplify 2.0 into 2.0 4.118 * [taylor]: Taking taylor expansion of (* n PI) in n 4.118 * [taylor]: Taking taylor expansion of n in n 4.118 * [backup-simplify]: Simplify 0 into 0 4.118 * [backup-simplify]: Simplify 1 into 1 4.118 * [taylor]: Taking taylor expansion of PI in n 4.118 * [backup-simplify]: Simplify PI into PI 4.119 * [backup-simplify]: Simplify (* 0 PI) into 0 4.119 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.120 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.121 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.121 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.121 * [backup-simplify]: Simplify (- k) into (- k) 4.121 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.121 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.122 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.123 * [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)))) 4.123 * [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))))) 4.124 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.124 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.124 * [taylor]: Taking taylor expansion of 0.25 in k 4.124 * [backup-simplify]: Simplify 0.25 into 0.25 4.124 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.124 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.124 * [taylor]: Taking taylor expansion of 1.0 in k 4.124 * [backup-simplify]: Simplify 1.0 into 1.0 4.124 * [taylor]: Taking taylor expansion of k in k 4.124 * [backup-simplify]: Simplify 0 into 0 4.124 * [backup-simplify]: Simplify 1 into 1 4.124 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.124 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.124 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.124 * [taylor]: Taking taylor expansion of 2.0 in k 4.124 * [backup-simplify]: Simplify 2.0 into 2.0 4.124 * [taylor]: Taking taylor expansion of PI in k 4.124 * [backup-simplify]: Simplify PI into PI 4.124 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.125 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.125 * [taylor]: Taking taylor expansion of (log n) in k 4.125 * [taylor]: Taking taylor expansion of n in k 4.125 * [backup-simplify]: Simplify n into n 4.125 * [backup-simplify]: Simplify (log n) into (log n) 4.125 * [backup-simplify]: Simplify (- 0) into 0 4.125 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.126 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.126 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.127 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 4.128 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.128 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.129 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.129 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.130 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.131 * [backup-simplify]: Simplify (- 0) into 0 4.131 * [backup-simplify]: Simplify (+ 0 0) into 0 4.131 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 4.132 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.132 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.134 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.134 * [taylor]: Taking taylor expansion of 0 in k 4.134 * [backup-simplify]: Simplify 0 into 0 4.134 * [backup-simplify]: Simplify 0 into 0 4.134 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.135 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.135 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.136 * [backup-simplify]: Simplify (+ 0 0) into 0 4.136 * [backup-simplify]: Simplify (- 1) into -1 4.136 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.137 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.138 * [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)))) 4.140 * [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)))))) 4.142 * [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)))))) 4.142 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.143 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.145 * [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 4.145 * [backup-simplify]: Simplify (- 0) into 0 4.145 * [backup-simplify]: Simplify (+ 0 0) into 0 4.146 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.146 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.147 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.148 * [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 4.148 * [taylor]: Taking taylor expansion of 0 in k 4.149 * [backup-simplify]: Simplify 0 into 0 4.149 * [backup-simplify]: Simplify 0 into 0 4.149 * [backup-simplify]: Simplify 0 into 0 4.149 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.151 * [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 4.152 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.152 * [backup-simplify]: Simplify (+ 0 0) into 0 4.152 * [backup-simplify]: Simplify (- 0) into 0 4.152 * [backup-simplify]: Simplify (+ 0 0) into 0 4.153 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.155 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.157 * [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))))) 4.160 * [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))))) 4.165 * [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)))))) 4.171 * [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)))) 4.171 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 4.171 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 4.171 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.171 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.171 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 4.171 * [taylor]: Taking taylor expansion of 0.25 in k 4.171 * [backup-simplify]: Simplify 0.25 into 0.25 4.171 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.171 * [taylor]: Taking taylor expansion of 1.0 in k 4.171 * [backup-simplify]: Simplify 1.0 into 1.0 4.171 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.171 * [taylor]: Taking taylor expansion of k in k 4.171 * [backup-simplify]: Simplify 0 into 0 4.171 * [backup-simplify]: Simplify 1 into 1 4.172 * [backup-simplify]: Simplify (/ 1 1) into 1 4.172 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.172 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.172 * [taylor]: Taking taylor expansion of 2.0 in k 4.172 * [backup-simplify]: Simplify 2.0 into 2.0 4.172 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.172 * [taylor]: Taking taylor expansion of PI in k 4.172 * [backup-simplify]: Simplify PI into PI 4.172 * [taylor]: Taking taylor expansion of n in k 4.172 * [backup-simplify]: Simplify n into n 4.172 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.172 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.172 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.172 * [backup-simplify]: Simplify (- 1) into -1 4.172 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.173 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 4.173 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 4.173 * [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))))) 4.173 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.173 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.173 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.173 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.173 * [taylor]: Taking taylor expansion of 0.25 in n 4.173 * [backup-simplify]: Simplify 0.25 into 0.25 4.173 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.173 * [taylor]: Taking taylor expansion of 1.0 in n 4.173 * [backup-simplify]: Simplify 1.0 into 1.0 4.173 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.173 * [taylor]: Taking taylor expansion of k in n 4.173 * [backup-simplify]: Simplify k into k 4.173 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.173 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.173 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.173 * [taylor]: Taking taylor expansion of 2.0 in n 4.173 * [backup-simplify]: Simplify 2.0 into 2.0 4.173 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.173 * [taylor]: Taking taylor expansion of PI in n 4.173 * [backup-simplify]: Simplify PI into PI 4.173 * [taylor]: Taking taylor expansion of n in n 4.173 * [backup-simplify]: Simplify 0 into 0 4.173 * [backup-simplify]: Simplify 1 into 1 4.173 * [backup-simplify]: Simplify (/ PI 1) into PI 4.174 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.174 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.174 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.174 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.174 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.175 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.176 * [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)))) 4.177 * [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))))) 4.177 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.177 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.177 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.177 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.177 * [taylor]: Taking taylor expansion of 0.25 in n 4.177 * [backup-simplify]: Simplify 0.25 into 0.25 4.177 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.177 * [taylor]: Taking taylor expansion of 1.0 in n 4.177 * [backup-simplify]: Simplify 1.0 into 1.0 4.177 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.177 * [taylor]: Taking taylor expansion of k in n 4.177 * [backup-simplify]: Simplify k into k 4.177 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.177 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.177 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.177 * [taylor]: Taking taylor expansion of 2.0 in n 4.177 * [backup-simplify]: Simplify 2.0 into 2.0 4.177 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.177 * [taylor]: Taking taylor expansion of PI in n 4.177 * [backup-simplify]: Simplify PI into PI 4.177 * [taylor]: Taking taylor expansion of n in n 4.177 * [backup-simplify]: Simplify 0 into 0 4.177 * [backup-simplify]: Simplify 1 into 1 4.177 * [backup-simplify]: Simplify (/ PI 1) into PI 4.178 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.178 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.179 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.179 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.179 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.180 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.180 * [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)))) 4.181 * [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))))) 4.181 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.181 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.181 * [taylor]: Taking taylor expansion of 0.25 in k 4.181 * [backup-simplify]: Simplify 0.25 into 0.25 4.181 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.181 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.181 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.181 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.181 * [taylor]: Taking taylor expansion of 2.0 in k 4.181 * [backup-simplify]: Simplify 2.0 into 2.0 4.181 * [taylor]: Taking taylor expansion of PI in k 4.181 * [backup-simplify]: Simplify PI into PI 4.181 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.182 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.182 * [taylor]: Taking taylor expansion of (log n) in k 4.182 * [taylor]: Taking taylor expansion of n in k 4.182 * [backup-simplify]: Simplify n into n 4.182 * [backup-simplify]: Simplify (log n) into (log n) 4.182 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.182 * [taylor]: Taking taylor expansion of 1.0 in k 4.182 * [backup-simplify]: Simplify 1.0 into 1.0 4.182 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.182 * [taylor]: Taking taylor expansion of k in k 4.182 * [backup-simplify]: Simplify 0 into 0 4.182 * [backup-simplify]: Simplify 1 into 1 4.182 * [backup-simplify]: Simplify (/ 1 1) into 1 4.183 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.183 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.183 * [backup-simplify]: Simplify (- 1) into -1 4.184 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.184 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.185 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 4.185 * [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))))) 4.186 * [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))))) 4.187 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.187 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.188 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.188 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.188 * [backup-simplify]: Simplify (- 0) into 0 4.189 * [backup-simplify]: Simplify (+ 0 0) into 0 4.189 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.190 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.190 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.192 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.192 * [taylor]: Taking taylor expansion of 0 in k 4.192 * [backup-simplify]: Simplify 0 into 0 4.192 * [backup-simplify]: Simplify 0 into 0 4.192 * [backup-simplify]: Simplify 0 into 0 4.192 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.193 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.194 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.194 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.195 * [backup-simplify]: Simplify (- 0) into 0 4.195 * [backup-simplify]: Simplify (+ 0 0) into 0 4.195 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.196 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.197 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.198 * [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 4.198 * [taylor]: Taking taylor expansion of 0 in k 4.198 * [backup-simplify]: Simplify 0 into 0 4.198 * [backup-simplify]: Simplify 0 into 0 4.198 * [backup-simplify]: Simplify 0 into 0 4.198 * [backup-simplify]: Simplify 0 into 0 4.199 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.200 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.202 * [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 4.202 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.203 * [backup-simplify]: Simplify (- 0) into 0 4.203 * [backup-simplify]: Simplify (+ 0 0) into 0 4.204 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.204 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.205 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.207 * [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 4.207 * [taylor]: Taking taylor expansion of 0 in k 4.207 * [backup-simplify]: Simplify 0 into 0 4.207 * [backup-simplify]: Simplify 0 into 0 4.208 * [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)))) 4.208 * [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))) 4.209 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 4.209 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 4.209 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.209 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.209 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 4.209 * [taylor]: Taking taylor expansion of 0.25 in k 4.209 * [backup-simplify]: Simplify 0.25 into 0.25 4.209 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.209 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.209 * [taylor]: Taking taylor expansion of k in k 4.209 * [backup-simplify]: Simplify 0 into 0 4.209 * [backup-simplify]: Simplify 1 into 1 4.209 * [backup-simplify]: Simplify (/ 1 1) into 1 4.209 * [taylor]: Taking taylor expansion of 1.0 in k 4.209 * [backup-simplify]: Simplify 1.0 into 1.0 4.209 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.209 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.209 * [taylor]: Taking taylor expansion of -2.0 in k 4.209 * [backup-simplify]: Simplify -2.0 into -2.0 4.209 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.209 * [taylor]: Taking taylor expansion of PI in k 4.209 * [backup-simplify]: Simplify PI into PI 4.209 * [taylor]: Taking taylor expansion of n in k 4.209 * [backup-simplify]: Simplify n into n 4.209 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.209 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.209 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.209 * [backup-simplify]: Simplify (+ 1 0) into 1 4.210 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 4.210 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 4.210 * [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)))))) 4.210 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.210 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.210 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.210 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.210 * [taylor]: Taking taylor expansion of 0.25 in n 4.210 * [backup-simplify]: Simplify 0.25 into 0.25 4.210 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.210 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.210 * [taylor]: Taking taylor expansion of k in n 4.210 * [backup-simplify]: Simplify k into k 4.210 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.210 * [taylor]: Taking taylor expansion of 1.0 in n 4.210 * [backup-simplify]: Simplify 1.0 into 1.0 4.210 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.210 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.210 * [taylor]: Taking taylor expansion of -2.0 in n 4.210 * [backup-simplify]: Simplify -2.0 into -2.0 4.210 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.210 * [taylor]: Taking taylor expansion of PI in n 4.210 * [backup-simplify]: Simplify PI into PI 4.210 * [taylor]: Taking taylor expansion of n in n 4.210 * [backup-simplify]: Simplify 0 into 0 4.210 * [backup-simplify]: Simplify 1 into 1 4.211 * [backup-simplify]: Simplify (/ PI 1) into PI 4.211 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.211 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.212 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.212 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.212 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.213 * [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)))) 4.214 * [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))))) 4.214 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.214 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.214 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.214 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.214 * [taylor]: Taking taylor expansion of 0.25 in n 4.214 * [backup-simplify]: Simplify 0.25 into 0.25 4.214 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.214 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.214 * [taylor]: Taking taylor expansion of k in n 4.214 * [backup-simplify]: Simplify k into k 4.214 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.214 * [taylor]: Taking taylor expansion of 1.0 in n 4.214 * [backup-simplify]: Simplify 1.0 into 1.0 4.214 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.214 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.214 * [taylor]: Taking taylor expansion of -2.0 in n 4.214 * [backup-simplify]: Simplify -2.0 into -2.0 4.214 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.214 * [taylor]: Taking taylor expansion of PI in n 4.214 * [backup-simplify]: Simplify PI into PI 4.214 * [taylor]: Taking taylor expansion of n in n 4.214 * [backup-simplify]: Simplify 0 into 0 4.214 * [backup-simplify]: Simplify 1 into 1 4.214 * [backup-simplify]: Simplify (/ PI 1) into PI 4.215 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.215 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.215 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.215 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.216 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.217 * [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)))) 4.218 * [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))))) 4.218 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.218 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.218 * [taylor]: Taking taylor expansion of 0.25 in k 4.218 * [backup-simplify]: Simplify 0.25 into 0.25 4.218 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.218 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.218 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.218 * [taylor]: Taking taylor expansion of k in k 4.218 * [backup-simplify]: Simplify 0 into 0 4.218 * [backup-simplify]: Simplify 1 into 1 4.218 * [backup-simplify]: Simplify (/ 1 1) into 1 4.218 * [taylor]: Taking taylor expansion of 1.0 in k 4.218 * [backup-simplify]: Simplify 1.0 into 1.0 4.218 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.218 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.218 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.218 * [taylor]: Taking taylor expansion of -2.0 in k 4.218 * [backup-simplify]: Simplify -2.0 into -2.0 4.218 * [taylor]: Taking taylor expansion of PI in k 4.218 * [backup-simplify]: Simplify PI into PI 4.219 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.219 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.219 * [taylor]: Taking taylor expansion of (log n) in k 4.219 * [taylor]: Taking taylor expansion of n in k 4.219 * [backup-simplify]: Simplify n into n 4.219 * [backup-simplify]: Simplify (log n) into (log n) 4.219 * [backup-simplify]: Simplify (+ 1 0) into 1 4.219 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.220 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.221 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.221 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 4.222 * [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))))) 4.223 * [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))))) 4.223 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.224 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.224 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.225 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.225 * [backup-simplify]: Simplify (+ 0 0) into 0 4.225 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.226 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.227 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.228 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.228 * [taylor]: Taking taylor expansion of 0 in k 4.228 * [backup-simplify]: Simplify 0 into 0 4.228 * [backup-simplify]: Simplify 0 into 0 4.228 * [backup-simplify]: Simplify 0 into 0 4.228 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.229 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.230 * [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 4.231 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.231 * [backup-simplify]: Simplify (+ 0 0) into 0 4.231 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.232 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.233 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.234 * [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 4.234 * [taylor]: Taking taylor expansion of 0 in k 4.234 * [backup-simplify]: Simplify 0 into 0 4.234 * [backup-simplify]: Simplify 0 into 0 4.234 * [backup-simplify]: Simplify 0 into 0 4.234 * [backup-simplify]: Simplify 0 into 0 4.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.236 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.238 * [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 4.239 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.239 * [backup-simplify]: Simplify (+ 0 0) into 0 4.240 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.240 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.241 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.243 * [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 4.243 * [taylor]: Taking taylor expansion of 0 in k 4.243 * [backup-simplify]: Simplify 0 into 0 4.243 * [backup-simplify]: Simplify 0 into 0 4.244 * [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)))))) 4.244 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 4.244 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) into (* (sqrt (/ 1 k)) (pow (sqrt 1.0) 2)) 4.244 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (sqrt 1.0) 2)) in (k) around 0 4.244 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (sqrt 1.0) 2)) in k 4.244 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.244 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.244 * [taylor]: Taking taylor expansion of k in k 4.244 * [backup-simplify]: Simplify 0 into 0 4.244 * [backup-simplify]: Simplify 1 into 1 4.244 * [backup-simplify]: Simplify (/ 1 1) into 1 4.244 * [backup-simplify]: Simplify (sqrt 0) into 0 4.245 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.245 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 4.245 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 4.245 * [taylor]: Taking taylor expansion of 1.0 in k 4.245 * [backup-simplify]: Simplify 1.0 into 1.0 4.246 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 4.246 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 4.246 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (sqrt 1.0) 2)) in k 4.246 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.246 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.246 * [taylor]: Taking taylor expansion of k in k 4.246 * [backup-simplify]: Simplify 0 into 0 4.246 * [backup-simplify]: Simplify 1 into 1 4.246 * [backup-simplify]: Simplify (/ 1 1) into 1 4.246 * [backup-simplify]: Simplify (sqrt 0) into 0 4.247 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.247 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 4.247 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 4.247 * [taylor]: Taking taylor expansion of 1.0 in k 4.247 * [backup-simplify]: Simplify 1.0 into 1.0 4.247 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 4.248 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 4.249 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 4.249 * [backup-simplify]: Simplify (* 0 (pow (sqrt 1.0) 2)) into 0 4.249 * [backup-simplify]: Simplify 0 into 0 4.249 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 4.251 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.252 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.253 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 4.254 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 4.254 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.256 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.263 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.265 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.266 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0 4.266 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0 4.267 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.269 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.272 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (sqrt 1.0) 2))))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.273 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.278 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow k 2)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) k) (- (* +nan.0 (pow (sqrt 1.0) 2))))) into (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (+ (* +nan.0 (* k (pow (sqrt 1.0) 2))) (- (* +nan.0 (* (pow k 2) (pow (sqrt 1.0) 2)))))))) 4.278 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt (/ 1 k)))) (sqrt (/ 1.0 (sqrt (/ 1 k))))) into (* (sqrt k) (pow (sqrt 1.0) 2)) 4.278 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (sqrt 1.0) 2)) in (k) around 0 4.278 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (sqrt 1.0) 2)) in k 4.278 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.278 * [taylor]: Taking taylor expansion of k in k 4.278 * [backup-simplify]: Simplify 0 into 0 4.278 * [backup-simplify]: Simplify 1 into 1 4.278 * [backup-simplify]: Simplify (sqrt 0) into 0 4.279 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.279 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 4.279 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 4.279 * [taylor]: Taking taylor expansion of 1.0 in k 4.279 * [backup-simplify]: Simplify 1.0 into 1.0 4.279 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 4.280 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 4.280 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (sqrt 1.0) 2)) in k 4.280 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.280 * [taylor]: Taking taylor expansion of k in k 4.280 * [backup-simplify]: Simplify 0 into 0 4.280 * [backup-simplify]: Simplify 1 into 1 4.280 * [backup-simplify]: Simplify (sqrt 0) into 0 4.281 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.281 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 4.281 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 4.281 * [taylor]: Taking taylor expansion of 1.0 in k 4.281 * [backup-simplify]: Simplify 1.0 into 1.0 4.281 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 4.281 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 4.282 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 4.282 * [backup-simplify]: Simplify (* 0 (pow (sqrt 1.0) 2)) into 0 4.283 * [backup-simplify]: Simplify 0 into 0 4.283 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 4.285 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.286 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.287 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 4.287 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 4.289 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.292 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.293 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.294 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0 4.294 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0 4.296 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.300 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (sqrt 1.0) 2))))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.301 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.306 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 3))) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k))))))) 4.306 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt (/ 1 (- k))))) (sqrt (/ 1.0 (sqrt (/ 1 (- k)))))) into (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) 4.306 * [approximate]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in (k) around 0 4.306 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in k 4.306 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 4.306 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 4.306 * [taylor]: Taking taylor expansion of 1.0 in k 4.306 * [backup-simplify]: Simplify 1.0 into 1.0 4.306 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 4.307 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 4.307 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.307 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.307 * [taylor]: Taking taylor expansion of -1 in k 4.307 * [backup-simplify]: Simplify -1 into -1 4.307 * [taylor]: Taking taylor expansion of k in k 4.307 * [backup-simplify]: Simplify 0 into 0 4.307 * [backup-simplify]: Simplify 1 into 1 4.307 * [backup-simplify]: Simplify (/ -1 1) into -1 4.307 * [backup-simplify]: Simplify (sqrt 0) into 0 4.308 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.308 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 4.309 * [backup-simplify]: Simplify (/ (pow (sqrt 1.0) 2) +nan.0) into (* +nan.0 (pow (sqrt 1.0) 2)) 4.309 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in k 4.309 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 4.309 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 4.310 * [taylor]: Taking taylor expansion of 1.0 in k 4.310 * [backup-simplify]: Simplify 1.0 into 1.0 4.310 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 4.310 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 4.310 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.310 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.310 * [taylor]: Taking taylor expansion of -1 in k 4.310 * [backup-simplify]: Simplify -1 into -1 4.310 * [taylor]: Taking taylor expansion of k in k 4.310 * [backup-simplify]: Simplify 0 into 0 4.310 * [backup-simplify]: Simplify 1 into 1 4.310 * [backup-simplify]: Simplify (/ -1 1) into -1 4.311 * [backup-simplify]: Simplify (sqrt 0) into 0 4.311 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.312 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 4.313 * [backup-simplify]: Simplify (/ (pow (sqrt 1.0) 2) +nan.0) into (* +nan.0 (pow (sqrt 1.0) 2)) 4.314 * [backup-simplify]: Simplify (* +nan.0 (pow (sqrt 1.0) 2)) into (* +nan.0 (pow (sqrt 1.0) 2)) 4.314 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 4.315 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.316 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.319 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (sqrt 1.0) 2)) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.321 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.322 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 4.322 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 4.323 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.325 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.330 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (sqrt 1.0) 2)) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.332 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 4.336 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ 1 (- k))) (* +nan.0 (pow (sqrt 1.0) 2)))) into (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k))))))) 4.336 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1) 4.336 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.336 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.336 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.336 * [taylor]: Taking taylor expansion of 1.0 in k 4.336 * [backup-simplify]: Simplify 1.0 into 1.0 4.336 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.336 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.336 * [taylor]: Taking taylor expansion of k in k 4.336 * [backup-simplify]: Simplify 0 into 0 4.336 * [backup-simplify]: Simplify 1 into 1 4.336 * [backup-simplify]: Simplify (/ 1 1) into 1 4.337 * [backup-simplify]: Simplify (sqrt 0) into 0 4.337 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.337 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.337 * [taylor]: Taking taylor expansion of 1.0 in k 4.337 * [backup-simplify]: Simplify 1.0 into 1.0 4.337 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.337 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.337 * [taylor]: Taking taylor expansion of k in k 4.337 * [backup-simplify]: Simplify 0 into 0 4.337 * [backup-simplify]: Simplify 1 into 1 4.338 * [backup-simplify]: Simplify (/ 1 1) into 1 4.338 * [backup-simplify]: Simplify (sqrt 0) into 0 4.339 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.339 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.339 * [backup-simplify]: Simplify 0 into 0 4.340 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.340 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.340 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.342 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.343 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.343 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.344 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.352 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.353 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.354 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.355 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.355 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.355 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.355 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.355 * [taylor]: Taking taylor expansion of 1.0 in k 4.355 * [backup-simplify]: Simplify 1.0 into 1.0 4.355 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.355 * [taylor]: Taking taylor expansion of k in k 4.355 * [backup-simplify]: Simplify 0 into 0 4.355 * [backup-simplify]: Simplify 1 into 1 4.355 * [backup-simplify]: Simplify (sqrt 0) into 0 4.356 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.356 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.356 * [taylor]: Taking taylor expansion of 1.0 in k 4.356 * [backup-simplify]: Simplify 1.0 into 1.0 4.356 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.356 * [taylor]: Taking taylor expansion of k in k 4.356 * [backup-simplify]: Simplify 0 into 0 4.356 * [backup-simplify]: Simplify 1 into 1 4.356 * [backup-simplify]: Simplify (sqrt 0) into 0 4.357 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.357 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.357 * [backup-simplify]: Simplify 0 into 0 4.358 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.358 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.360 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.361 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.361 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.363 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.364 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.364 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.365 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 4.365 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.365 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.365 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.365 * [taylor]: Taking taylor expansion of 1.0 in k 4.365 * [backup-simplify]: Simplify 1.0 into 1.0 4.365 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.365 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.365 * [taylor]: Taking taylor expansion of -1 in k 4.365 * [backup-simplify]: Simplify -1 into -1 4.365 * [taylor]: Taking taylor expansion of k in k 4.366 * [backup-simplify]: Simplify 0 into 0 4.366 * [backup-simplify]: Simplify 1 into 1 4.366 * [backup-simplify]: Simplify (/ -1 1) into -1 4.366 * [backup-simplify]: Simplify (sqrt 0) into 0 4.367 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.367 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.367 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.367 * [taylor]: Taking taylor expansion of 1.0 in k 4.367 * [backup-simplify]: Simplify 1.0 into 1.0 4.367 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.367 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.367 * [taylor]: Taking taylor expansion of -1 in k 4.367 * [backup-simplify]: Simplify -1 into -1 4.367 * [taylor]: Taking taylor expansion of k in k 4.367 * [backup-simplify]: Simplify 0 into 0 4.367 * [backup-simplify]: Simplify 1 into 1 4.367 * [backup-simplify]: Simplify (/ -1 1) into -1 4.368 * [backup-simplify]: Simplify (sqrt 0) into 0 4.368 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.368 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.369 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.369 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.371 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.372 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.372 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.373 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.375 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.377 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.377 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.378 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 4.378 * * * [progress]: simplifying candidates 4.383 * [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 (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (log1p (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (+ 1/2 1/2) (+ 1/2 (/ 1 2)) (+ 1 1) (+ (/ 1 2) 1/2) (+ (/ 1 2) (/ 1 2)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (* (sqrt (/ 1.0 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(* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- (* h9 (/ 1 (pow h4 3)))))))) (- (+ (* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- h9))))) 4.397 * * [simplify]: iteration 0 : 1060 enodes (cost 2815 ) 4.416 * * [simplify]: iteration 1 : 4951 enodes (cost 2660 ) 4.497 * * [simplify]: iteration 2 : 5001 enodes (cost 2660 ) 4.509 * * * [progress]: adding candidates to table 5.566 * [progress]: [Phase 3 of 3] Extracting. 5.566 * * [regime]: Finding splitpoints for: (# # # # # # # #) 5.568 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 5.568 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 5.603 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 5.639 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 5.673 * * * [regime]: Found split indices: #