11.418 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.077 * * * [progress]: [2/2] Setting up program. 0.080 * [progress]: [Phase 2 of 3] Improving. 0.080 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.080 * [simplify]: Sending expressions to egg_math: (* (/ h0 (sqrt h1)) (pow (* (* h2 PI) h3) (/ (- h0 h1) h2))) 0.082 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.084 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.086 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.088 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.094 * * [simplify]: iteration 4 : 1034 enodes (cost 8 ) 0.118 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.119 * * [progress]: iteration 1 / 4 0.119 * * * [progress]: picking best candidate 0.121 * * * * [pick]: Picked # 0.121 * * * [progress]: localizing error 0.134 * * * [progress]: generating rewritten candidates 0.134 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.156 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.173 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.179 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.223 * * * [progress]: generating series expansions 0.223 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.224 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 0.224 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.224 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.224 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.224 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.224 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.224 * [taylor]: Taking taylor expansion of 0.5 in k 0.224 * [backup-simplify]: Simplify 0.5 into 0.5 0.224 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.224 * [taylor]: Taking taylor expansion of 1.0 in k 0.224 * [backup-simplify]: Simplify 1.0 into 1.0 0.224 * [taylor]: Taking taylor expansion of k in k 0.224 * [backup-simplify]: Simplify 0 into 0 0.225 * [backup-simplify]: Simplify 1 into 1 0.225 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.225 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.225 * [taylor]: Taking taylor expansion of 2.0 in k 0.225 * [backup-simplify]: Simplify 2.0 into 2.0 0.225 * [taylor]: Taking taylor expansion of (* n PI) in k 0.225 * [taylor]: Taking taylor expansion of n in k 0.225 * [backup-simplify]: Simplify n into n 0.225 * [taylor]: Taking taylor expansion of PI in k 0.225 * [backup-simplify]: Simplify PI into PI 0.225 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.225 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.225 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.225 * [backup-simplify]: Simplify (- 0) into 0 0.225 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.226 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.226 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.226 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.226 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.226 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.226 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.226 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.226 * [taylor]: Taking taylor expansion of 0.5 in n 0.226 * [backup-simplify]: Simplify 0.5 into 0.5 0.226 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.226 * [taylor]: Taking taylor expansion of 1.0 in n 0.226 * [backup-simplify]: Simplify 1.0 into 1.0 0.226 * [taylor]: Taking taylor expansion of k in n 0.226 * [backup-simplify]: Simplify k into k 0.226 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.226 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.226 * [taylor]: Taking taylor expansion of 2.0 in n 0.226 * [backup-simplify]: Simplify 2.0 into 2.0 0.226 * [taylor]: Taking taylor expansion of (* n PI) in n 0.226 * [taylor]: Taking taylor expansion of n in n 0.226 * [backup-simplify]: Simplify 0 into 0 0.226 * [backup-simplify]: Simplify 1 into 1 0.226 * [taylor]: Taking taylor expansion of PI in n 0.226 * [backup-simplify]: Simplify PI into PI 0.226 * [backup-simplify]: Simplify (* 0 PI) into 0 0.227 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.228 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.229 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.229 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.229 * [backup-simplify]: Simplify (- k) into (- k) 0.229 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.229 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.230 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.231 * [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)))) 0.231 * [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))))) 0.232 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.232 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.232 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.232 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.232 * [taylor]: Taking taylor expansion of 0.5 in n 0.232 * [backup-simplify]: Simplify 0.5 into 0.5 0.232 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.232 * [taylor]: Taking taylor expansion of 1.0 in n 0.232 * [backup-simplify]: Simplify 1.0 into 1.0 0.232 * [taylor]: Taking taylor expansion of k in n 0.232 * [backup-simplify]: Simplify k into k 0.232 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.232 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.232 * [taylor]: Taking taylor expansion of 2.0 in n 0.232 * [backup-simplify]: Simplify 2.0 into 2.0 0.232 * [taylor]: Taking taylor expansion of (* n PI) in n 0.232 * [taylor]: Taking taylor expansion of n in n 0.232 * [backup-simplify]: Simplify 0 into 0 0.232 * [backup-simplify]: Simplify 1 into 1 0.232 * [taylor]: Taking taylor expansion of PI in n 0.232 * [backup-simplify]: Simplify PI into PI 0.232 * [backup-simplify]: Simplify (* 0 PI) into 0 0.232 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.233 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.234 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.235 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.235 * [backup-simplify]: Simplify (- k) into (- k) 0.235 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.235 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.236 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.236 * [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)))) 0.237 * [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))))) 0.237 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.237 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.237 * [taylor]: Taking taylor expansion of 0.5 in k 0.237 * [backup-simplify]: Simplify 0.5 into 0.5 0.237 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.237 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.237 * [taylor]: Taking taylor expansion of 1.0 in k 0.237 * [backup-simplify]: Simplify 1.0 into 1.0 0.237 * [taylor]: Taking taylor expansion of k in k 0.237 * [backup-simplify]: Simplify 0 into 0 0.237 * [backup-simplify]: Simplify 1 into 1 0.237 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.237 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.237 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.237 * [taylor]: Taking taylor expansion of 2.0 in k 0.237 * [backup-simplify]: Simplify 2.0 into 2.0 0.237 * [taylor]: Taking taylor expansion of PI in k 0.237 * [backup-simplify]: Simplify PI into PI 0.238 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.238 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.238 * [taylor]: Taking taylor expansion of (log n) in k 0.238 * [taylor]: Taking taylor expansion of n in k 0.238 * [backup-simplify]: Simplify n into n 0.238 * [backup-simplify]: Simplify (log n) into (log n) 0.239 * [backup-simplify]: Simplify (- 0) into 0 0.239 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.239 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.240 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.241 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.241 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.242 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.243 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.243 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.244 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.244 * [backup-simplify]: Simplify (- 0) into 0 0.245 * [backup-simplify]: Simplify (+ 0 0) into 0 0.245 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 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)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.248 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.248 * [taylor]: Taking taylor expansion of 0 in k 0.248 * [backup-simplify]: Simplify 0 into 0 0.248 * [backup-simplify]: Simplify 0 into 0 0.248 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.249 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.250 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.250 * [backup-simplify]: Simplify (+ 0 0) into 0 0.250 * [backup-simplify]: Simplify (- 1) into -1 0.250 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.251 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.252 * [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)))) 0.254 * [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)))))) 0.256 * [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)))))) 0.257 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.257 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.259 * [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 0.259 * [backup-simplify]: Simplify (- 0) into 0 0.260 * [backup-simplify]: Simplify (+ 0 0) into 0 0.260 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 0.261 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.262 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.263 * [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 0.263 * [taylor]: Taking taylor expansion of 0 in k 0.263 * [backup-simplify]: Simplify 0 into 0 0.263 * [backup-simplify]: Simplify 0 into 0 0.263 * [backup-simplify]: Simplify 0 into 0 0.264 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.266 * [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 0.267 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 0.267 * [backup-simplify]: Simplify (+ 0 0) into 0 0.267 * [backup-simplify]: Simplify (- 0) into 0 0.267 * [backup-simplify]: Simplify (+ 0 0) into 0 0.268 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.270 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 0.272 * [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)))))) 0.275 * [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)))))) 0.281 * [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)))))) 0.281 * [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)))) 0.282 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.282 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.282 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.282 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.282 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.282 * [taylor]: Taking taylor expansion of 0.5 in k 0.282 * [backup-simplify]: Simplify 0.5 into 0.5 0.282 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.282 * [taylor]: Taking taylor expansion of 1.0 in k 0.282 * [backup-simplify]: Simplify 1.0 into 1.0 0.282 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.282 * [taylor]: Taking taylor expansion of k in k 0.282 * [backup-simplify]: Simplify 0 into 0 0.282 * [backup-simplify]: Simplify 1 into 1 0.282 * [backup-simplify]: Simplify (/ 1 1) into 1 0.282 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.282 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.282 * [taylor]: Taking taylor expansion of 2.0 in k 0.282 * [backup-simplify]: Simplify 2.0 into 2.0 0.282 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.282 * [taylor]: Taking taylor expansion of PI in k 0.282 * [backup-simplify]: Simplify PI into PI 0.282 * [taylor]: Taking taylor expansion of n in k 0.282 * [backup-simplify]: Simplify n into n 0.282 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.282 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.282 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.283 * [backup-simplify]: Simplify (- 1) into -1 0.283 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.283 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.283 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.283 * [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))))) 0.283 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.283 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.283 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.283 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.283 * [taylor]: Taking taylor expansion of 0.5 in n 0.283 * [backup-simplify]: Simplify 0.5 into 0.5 0.283 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.283 * [taylor]: Taking taylor expansion of 1.0 in n 0.283 * [backup-simplify]: Simplify 1.0 into 1.0 0.284 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.284 * [taylor]: Taking taylor expansion of k in n 0.284 * [backup-simplify]: Simplify k into k 0.284 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.284 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.284 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.284 * [taylor]: Taking taylor expansion of 2.0 in n 0.284 * [backup-simplify]: Simplify 2.0 into 2.0 0.284 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.284 * [taylor]: Taking taylor expansion of PI in n 0.284 * [backup-simplify]: Simplify PI into PI 0.284 * [taylor]: Taking taylor expansion of n in n 0.284 * [backup-simplify]: Simplify 0 into 0 0.284 * [backup-simplify]: Simplify 1 into 1 0.284 * [backup-simplify]: Simplify (/ PI 1) into PI 0.284 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.285 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.285 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.285 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.285 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.286 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.287 * [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)))) 0.287 * [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))))) 0.287 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.287 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.287 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.287 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.287 * [taylor]: Taking taylor expansion of 0.5 in n 0.287 * [backup-simplify]: Simplify 0.5 into 0.5 0.287 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.287 * [taylor]: Taking taylor expansion of 1.0 in n 0.288 * [backup-simplify]: Simplify 1.0 into 1.0 0.288 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.288 * [taylor]: Taking taylor expansion of k in n 0.288 * [backup-simplify]: Simplify k into k 0.288 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.288 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.288 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.288 * [taylor]: Taking taylor expansion of 2.0 in n 0.288 * [backup-simplify]: Simplify 2.0 into 2.0 0.288 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.288 * [taylor]: Taking taylor expansion of PI in n 0.288 * [backup-simplify]: Simplify PI into PI 0.288 * [taylor]: Taking taylor expansion of n in n 0.288 * [backup-simplify]: Simplify 0 into 0 0.288 * [backup-simplify]: Simplify 1 into 1 0.288 * [backup-simplify]: Simplify (/ PI 1) into PI 0.288 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.289 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.289 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.289 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.289 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.290 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.291 * [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)))) 0.291 * [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))))) 0.291 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.291 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.291 * [taylor]: Taking taylor expansion of 0.5 in k 0.291 * [backup-simplify]: Simplify 0.5 into 0.5 0.291 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.291 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.291 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.292 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.292 * [taylor]: Taking taylor expansion of 2.0 in k 0.292 * [backup-simplify]: Simplify 2.0 into 2.0 0.292 * [taylor]: Taking taylor expansion of PI in k 0.292 * [backup-simplify]: Simplify PI into PI 0.292 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.292 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.292 * [taylor]: Taking taylor expansion of (log n) in k 0.293 * [taylor]: Taking taylor expansion of n in k 0.293 * [backup-simplify]: Simplify n into n 0.293 * [backup-simplify]: Simplify (log n) into (log n) 0.293 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.293 * [taylor]: Taking taylor expansion of 1.0 in k 0.293 * [backup-simplify]: Simplify 1.0 into 1.0 0.293 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.293 * [taylor]: Taking taylor expansion of k in k 0.293 * [backup-simplify]: Simplify 0 into 0 0.293 * [backup-simplify]: Simplify 1 into 1 0.293 * [backup-simplify]: Simplify (/ 1 1) into 1 0.293 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.294 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.294 * [backup-simplify]: Simplify (- 1) into -1 0.294 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.295 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.295 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 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))))) 0.297 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.297 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.298 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.303 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.303 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.303 * [backup-simplify]: Simplify (- 0) into 0 0.303 * [backup-simplify]: Simplify (+ 0 0) into 0 0.304 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.305 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.306 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.307 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.307 * [taylor]: Taking taylor expansion of 0 in k 0.307 * [backup-simplify]: Simplify 0 into 0 0.307 * [backup-simplify]: Simplify 0 into 0 0.307 * [backup-simplify]: Simplify 0 into 0 0.307 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.308 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.310 * [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 0.310 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.310 * [backup-simplify]: Simplify (- 0) into 0 0.310 * [backup-simplify]: Simplify (+ 0 0) into 0 0.311 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 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)) 0.312 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 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 2) 2)) (* (/ (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 0.314 * [backup-simplify]: Simplify 0 into 0 0.315 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.315 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.318 * [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 0.318 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.318 * [backup-simplify]: Simplify (- 0) into 0 0.319 * [backup-simplify]: Simplify (+ 0 0) into 0 0.320 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 0.320 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.321 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 0.323 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 0.323 * [taylor]: Taking taylor expansion of 0 in k 0.323 * [backup-simplify]: Simplify 0 into 0 0.323 * [backup-simplify]: Simplify 0 into 0 0.324 * [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)))) 0.324 * [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))) 0.324 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.324 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.324 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.324 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.324 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.324 * [taylor]: Taking taylor expansion of 0.5 in k 0.324 * [backup-simplify]: Simplify 0.5 into 0.5 0.325 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.325 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.325 * [taylor]: Taking taylor expansion of k in k 0.325 * [backup-simplify]: Simplify 0 into 0 0.325 * [backup-simplify]: Simplify 1 into 1 0.325 * [backup-simplify]: Simplify (/ 1 1) into 1 0.325 * [taylor]: Taking taylor expansion of 1.0 in k 0.325 * [backup-simplify]: Simplify 1.0 into 1.0 0.325 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.325 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.325 * [taylor]: Taking taylor expansion of -2.0 in k 0.325 * [backup-simplify]: Simplify -2.0 into -2.0 0.325 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.325 * [taylor]: Taking taylor expansion of PI in k 0.325 * [backup-simplify]: Simplify PI into PI 0.325 * [taylor]: Taking taylor expansion of n in k 0.325 * [backup-simplify]: Simplify n into n 0.325 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.325 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.325 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.325 * [backup-simplify]: Simplify (+ 1 0) into 1 0.326 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.326 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.326 * [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)))))) 0.326 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.326 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.326 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.326 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.326 * [taylor]: Taking taylor expansion of 0.5 in n 0.326 * [backup-simplify]: Simplify 0.5 into 0.5 0.326 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.326 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.326 * [taylor]: Taking taylor expansion of k in n 0.326 * [backup-simplify]: Simplify k into k 0.326 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.326 * [taylor]: Taking taylor expansion of 1.0 in n 0.326 * [backup-simplify]: Simplify 1.0 into 1.0 0.326 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.326 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.326 * [taylor]: Taking taylor expansion of -2.0 in n 0.326 * [backup-simplify]: Simplify -2.0 into -2.0 0.326 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.326 * [taylor]: Taking taylor expansion of PI in n 0.326 * [backup-simplify]: Simplify PI into PI 0.326 * [taylor]: Taking taylor expansion of n in n 0.326 * [backup-simplify]: Simplify 0 into 0 0.326 * [backup-simplify]: Simplify 1 into 1 0.327 * [backup-simplify]: Simplify (/ PI 1) into PI 0.327 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.327 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.327 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.328 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.328 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.329 * [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)))) 0.330 * [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))))) 0.330 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.330 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.330 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.330 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.330 * [taylor]: Taking taylor expansion of 0.5 in n 0.330 * [backup-simplify]: Simplify 0.5 into 0.5 0.330 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.330 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.330 * [taylor]: Taking taylor expansion of k in n 0.330 * [backup-simplify]: Simplify k into k 0.330 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.330 * [taylor]: Taking taylor expansion of 1.0 in n 0.330 * [backup-simplify]: Simplify 1.0 into 1.0 0.330 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.330 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.330 * [taylor]: Taking taylor expansion of -2.0 in n 0.330 * [backup-simplify]: Simplify -2.0 into -2.0 0.330 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.330 * [taylor]: Taking taylor expansion of PI in n 0.330 * [backup-simplify]: Simplify PI into PI 0.330 * [taylor]: Taking taylor expansion of n in n 0.330 * [backup-simplify]: Simplify 0 into 0 0.330 * [backup-simplify]: Simplify 1 into 1 0.330 * [backup-simplify]: Simplify (/ PI 1) into PI 0.331 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.331 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.331 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.331 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.332 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.333 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.334 * [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))))) 0.334 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.334 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.334 * [taylor]: Taking taylor expansion of 0.5 in k 0.334 * [backup-simplify]: Simplify 0.5 into 0.5 0.334 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.334 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.334 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.334 * [taylor]: Taking taylor expansion of k in k 0.334 * [backup-simplify]: Simplify 0 into 0 0.334 * [backup-simplify]: Simplify 1 into 1 0.334 * [backup-simplify]: Simplify (/ 1 1) into 1 0.334 * [taylor]: Taking taylor expansion of 1.0 in k 0.334 * [backup-simplify]: Simplify 1.0 into 1.0 0.334 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.334 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.334 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.334 * [taylor]: Taking taylor expansion of -2.0 in k 0.334 * [backup-simplify]: Simplify -2.0 into -2.0 0.334 * [taylor]: Taking taylor expansion of PI in k 0.334 * [backup-simplify]: Simplify PI into PI 0.335 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.335 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.335 * [taylor]: Taking taylor expansion of (log n) in k 0.335 * [taylor]: Taking taylor expansion of n in k 0.335 * [backup-simplify]: Simplify n into n 0.335 * [backup-simplify]: Simplify (log n) into (log n) 0.336 * [backup-simplify]: Simplify (+ 1 0) into 1 0.336 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.336 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 0.337 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 0.337 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 0.338 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.339 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.339 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.340 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.341 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.341 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.341 * [backup-simplify]: Simplify (+ 0 0) into 0 0.341 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 0.342 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.343 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.344 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.344 * [taylor]: Taking taylor expansion of 0 in k 0.344 * [backup-simplify]: Simplify 0 into 0 0.344 * [backup-simplify]: Simplify 0 into 0 0.344 * [backup-simplify]: Simplify 0 into 0 0.345 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.345 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.347 * [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 0.347 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.347 * [backup-simplify]: Simplify (+ 0 0) into 0 0.348 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 0.349 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.350 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 0.351 * [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 0.351 * [taylor]: Taking taylor expansion of 0 in k 0.351 * [backup-simplify]: Simplify 0 into 0 0.351 * [backup-simplify]: Simplify 0 into 0 0.351 * [backup-simplify]: Simplify 0 into 0 0.351 * [backup-simplify]: Simplify 0 into 0 0.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.352 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.355 * [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 0.355 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.355 * [backup-simplify]: Simplify (+ 0 0) into 0 0.356 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.357 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.358 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 0.360 * [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 0.360 * [taylor]: Taking taylor expansion of 0 in k 0.360 * [backup-simplify]: Simplify 0 into 0 0.360 * [backup-simplify]: Simplify 0 into 0 0.361 * [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)))))) 0.361 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.361 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.361 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.361 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.361 * [taylor]: Taking taylor expansion of 2.0 in n 0.361 * [backup-simplify]: Simplify 2.0 into 2.0 0.361 * [taylor]: Taking taylor expansion of (* n PI) in n 0.361 * [taylor]: Taking taylor expansion of n in n 0.361 * [backup-simplify]: Simplify 0 into 0 0.361 * [backup-simplify]: Simplify 1 into 1 0.361 * [taylor]: Taking taylor expansion of PI in n 0.361 * [backup-simplify]: Simplify PI into PI 0.361 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.361 * [taylor]: Taking taylor expansion of 2.0 in n 0.361 * [backup-simplify]: Simplify 2.0 into 2.0 0.361 * [taylor]: Taking taylor expansion of (* n PI) in n 0.361 * [taylor]: Taking taylor expansion of n in n 0.361 * [backup-simplify]: Simplify 0 into 0 0.361 * [backup-simplify]: Simplify 1 into 1 0.361 * [taylor]: Taking taylor expansion of PI in n 0.361 * [backup-simplify]: Simplify PI into PI 0.362 * [backup-simplify]: Simplify (* 0 PI) into 0 0.362 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.362 * [backup-simplify]: Simplify 0 into 0 0.363 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.364 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.364 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.364 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.365 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.365 * [backup-simplify]: Simplify 0 into 0 0.366 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.366 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.366 * [backup-simplify]: Simplify 0 into 0 0.367 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.368 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.368 * [backup-simplify]: Simplify 0 into 0 0.368 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.369 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 0.369 * [backup-simplify]: Simplify 0 into 0 0.370 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.371 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.371 * [backup-simplify]: Simplify 0 into 0 0.372 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.373 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.373 * [backup-simplify]: Simplify 0 into 0 0.374 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.374 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 0.374 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.374 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.374 * [taylor]: Taking taylor expansion of 2.0 in n 0.374 * [backup-simplify]: Simplify 2.0 into 2.0 0.374 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.374 * [taylor]: Taking taylor expansion of PI in n 0.374 * [backup-simplify]: Simplify PI into PI 0.374 * [taylor]: Taking taylor expansion of n in n 0.374 * [backup-simplify]: Simplify 0 into 0 0.374 * [backup-simplify]: Simplify 1 into 1 0.374 * [backup-simplify]: Simplify (/ PI 1) into PI 0.374 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.374 * [taylor]: Taking taylor expansion of 2.0 in n 0.374 * [backup-simplify]: Simplify 2.0 into 2.0 0.374 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.374 * [taylor]: Taking taylor expansion of PI in n 0.375 * [backup-simplify]: Simplify PI into PI 0.375 * [taylor]: Taking taylor expansion of n in n 0.375 * [backup-simplify]: Simplify 0 into 0 0.375 * [backup-simplify]: Simplify 1 into 1 0.375 * [backup-simplify]: Simplify (/ PI 1) into PI 0.375 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.375 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.376 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.376 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.376 * [backup-simplify]: Simplify 0 into 0 0.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.378 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.378 * [backup-simplify]: Simplify 0 into 0 0.378 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.379 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.379 * [backup-simplify]: Simplify 0 into 0 0.379 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.380 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.380 * [backup-simplify]: Simplify 0 into 0 0.381 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.381 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.381 * [backup-simplify]: Simplify 0 into 0 0.382 * [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 0.383 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.383 * [backup-simplify]: Simplify 0 into 0 0.383 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.384 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.384 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.384 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.384 * [taylor]: Taking taylor expansion of -2.0 in n 0.384 * [backup-simplify]: Simplify -2.0 into -2.0 0.384 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.384 * [taylor]: Taking taylor expansion of PI in n 0.384 * [backup-simplify]: Simplify PI into PI 0.384 * [taylor]: Taking taylor expansion of n in n 0.384 * [backup-simplify]: Simplify 0 into 0 0.384 * [backup-simplify]: Simplify 1 into 1 0.384 * [backup-simplify]: Simplify (/ PI 1) into PI 0.384 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.384 * [taylor]: Taking taylor expansion of -2.0 in n 0.384 * [backup-simplify]: Simplify -2.0 into -2.0 0.384 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.384 * [taylor]: Taking taylor expansion of PI in n 0.384 * [backup-simplify]: Simplify PI into PI 0.384 * [taylor]: Taking taylor expansion of n in n 0.384 * [backup-simplify]: Simplify 0 into 0 0.384 * [backup-simplify]: Simplify 1 into 1 0.385 * [backup-simplify]: Simplify (/ PI 1) into PI 0.385 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.385 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.386 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.386 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.386 * [backup-simplify]: Simplify 0 into 0 0.387 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.387 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.387 * [backup-simplify]: Simplify 0 into 0 0.388 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.388 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.388 * [backup-simplify]: Simplify 0 into 0 0.395 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.395 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.395 * [backup-simplify]: Simplify 0 into 0 0.396 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.397 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.397 * [backup-simplify]: Simplify 0 into 0 0.397 * [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 0.398 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.398 * [backup-simplify]: Simplify 0 into 0 0.399 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.399 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.399 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.399 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.399 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.399 * [taylor]: Taking taylor expansion of 1.0 in k 0.399 * [backup-simplify]: Simplify 1.0 into 1.0 0.399 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.399 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.399 * [taylor]: Taking taylor expansion of k in k 0.399 * [backup-simplify]: Simplify 0 into 0 0.399 * [backup-simplify]: Simplify 1 into 1 0.399 * [backup-simplify]: Simplify (/ 1 1) into 1 0.400 * [backup-simplify]: Simplify (sqrt 0) into 0 0.400 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.400 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.400 * [taylor]: Taking taylor expansion of 1.0 in k 0.400 * [backup-simplify]: Simplify 1.0 into 1.0 0.400 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.400 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.400 * [taylor]: Taking taylor expansion of k in k 0.400 * [backup-simplify]: Simplify 0 into 0 0.400 * [backup-simplify]: Simplify 1 into 1 0.401 * [backup-simplify]: Simplify (/ 1 1) into 1 0.401 * [backup-simplify]: Simplify (sqrt 0) into 0 0.402 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.402 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.402 * [backup-simplify]: Simplify 0 into 0 0.403 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.403 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.404 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.405 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.406 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.407 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.407 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.409 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.410 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.411 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.412 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 0.412 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 0.412 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.412 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.412 * [taylor]: Taking taylor expansion of 1.0 in k 0.412 * [backup-simplify]: Simplify 1.0 into 1.0 0.412 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.412 * [taylor]: Taking taylor expansion of k in k 0.412 * [backup-simplify]: Simplify 0 into 0 0.412 * [backup-simplify]: Simplify 1 into 1 0.412 * [backup-simplify]: Simplify (sqrt 0) into 0 0.413 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.413 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.413 * [taylor]: Taking taylor expansion of 1.0 in k 0.413 * [backup-simplify]: Simplify 1.0 into 1.0 0.413 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.413 * [taylor]: Taking taylor expansion of k in k 0.413 * [backup-simplify]: Simplify 0 into 0 0.413 * [backup-simplify]: Simplify 1 into 1 0.413 * [backup-simplify]: Simplify (sqrt 0) into 0 0.414 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.414 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.414 * [backup-simplify]: Simplify 0 into 0 0.415 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.415 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.417 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.418 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.418 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.421 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.422 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.422 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.423 * [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)))))))) 0.424 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.424 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.424 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.424 * [taylor]: Taking taylor expansion of 1.0 in k 0.424 * [backup-simplify]: Simplify 1.0 into 1.0 0.424 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.424 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.424 * [taylor]: Taking taylor expansion of -1 in k 0.424 * [backup-simplify]: Simplify -1 into -1 0.424 * [taylor]: Taking taylor expansion of k in k 0.424 * [backup-simplify]: Simplify 0 into 0 0.424 * [backup-simplify]: Simplify 1 into 1 0.424 * [backup-simplify]: Simplify (/ -1 1) into -1 0.424 * [backup-simplify]: Simplify (sqrt 0) into 0 0.425 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.425 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.425 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.425 * [taylor]: Taking taylor expansion of 1.0 in k 0.425 * [backup-simplify]: Simplify 1.0 into 1.0 0.425 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.426 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.426 * [taylor]: Taking taylor expansion of -1 in k 0.426 * [backup-simplify]: Simplify -1 into -1 0.426 * [taylor]: Taking taylor expansion of k in k 0.426 * [backup-simplify]: Simplify 0 into 0 0.426 * [backup-simplify]: Simplify 1 into 1 0.426 * [backup-simplify]: Simplify (/ -1 1) into -1 0.426 * [backup-simplify]: Simplify (sqrt 0) into 0 0.427 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.427 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.427 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.428 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.429 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.431 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 0.431 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.434 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.436 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 0.436 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.437 * [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))))) 0.437 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.437 * [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 0.438 * [taylor]: Taking taylor expansion of 1.0 in n 0.438 * [backup-simplify]: Simplify 1.0 into 1.0 0.438 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.438 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.438 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.438 * [taylor]: Taking taylor expansion of k in n 0.438 * [backup-simplify]: Simplify k into k 0.438 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.438 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 0.438 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.438 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 0.438 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.438 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.438 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.438 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.438 * [taylor]: Taking taylor expansion of 0.5 in n 0.438 * [backup-simplify]: Simplify 0.5 into 0.5 0.438 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.438 * [taylor]: Taking taylor expansion of 1.0 in n 0.438 * [backup-simplify]: Simplify 1.0 into 1.0 0.438 * [taylor]: Taking taylor expansion of k in n 0.438 * [backup-simplify]: Simplify k into k 0.438 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.438 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.438 * [taylor]: Taking taylor expansion of 2.0 in n 0.438 * [backup-simplify]: Simplify 2.0 into 2.0 0.438 * [taylor]: Taking taylor expansion of (* n PI) in n 0.438 * [taylor]: Taking taylor expansion of n in n 0.438 * [backup-simplify]: Simplify 0 into 0 0.438 * [backup-simplify]: Simplify 1 into 1 0.438 * [taylor]: Taking taylor expansion of PI in n 0.438 * [backup-simplify]: Simplify PI into PI 0.439 * [backup-simplify]: Simplify (* 0 PI) into 0 0.439 * [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) 0.441 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.441 * [backup-simplify]: Simplify (- k) into (- k) 0.441 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.441 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.442 * [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)))) 0.443 * [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))))) 0.443 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.443 * [taylor]: Taking taylor expansion of 1.0 in k 0.443 * [backup-simplify]: Simplify 1.0 into 1.0 0.443 * [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 0.444 * [backup-simplify]: Simplify (/ 1 1) into 1 0.444 * [backup-simplify]: Simplify (sqrt 0) into 0 0.445 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.445 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.445 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.445 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.445 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.445 * [taylor]: Taking taylor expansion of 0.5 in k 0.445 * [backup-simplify]: Simplify 0.5 into 0.5 0.445 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.445 * [taylor]: Taking taylor expansion of 1.0 in k 0.445 * [backup-simplify]: Simplify 1.0 into 1.0 0.445 * [taylor]: Taking taylor expansion of k in k 0.445 * [backup-simplify]: Simplify 0 into 0 0.445 * [backup-simplify]: Simplify 1 into 1 0.445 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.445 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.445 * [taylor]: Taking taylor expansion of 2.0 in k 0.445 * [backup-simplify]: Simplify 2.0 into 2.0 0.445 * [taylor]: Taking taylor expansion of (* n PI) in k 0.445 * [taylor]: Taking taylor expansion of n in k 0.445 * [backup-simplify]: Simplify n into n 0.445 * [taylor]: Taking taylor expansion of PI in k 0.445 * [backup-simplify]: Simplify PI into PI 0.445 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.445 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.445 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.445 * [backup-simplify]: Simplify (- 0) into 0 0.446 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.446 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.446 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.446 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.446 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 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 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.446 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.446 * [taylor]: Taking taylor expansion of (/ 1 k) in k 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 * [backup-simplify]: Simplify (/ 1 1) into 1 0.447 * [backup-simplify]: Simplify (sqrt 0) into 0 0.447 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.447 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.447 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.447 * [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 0.448 * [taylor]: Taking taylor expansion of n in k 0.448 * [backup-simplify]: Simplify n into n 0.448 * [taylor]: Taking taylor expansion of PI in k 0.448 * [backup-simplify]: Simplify PI into PI 0.448 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.448 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.448 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.448 * [backup-simplify]: Simplify (- 0) into 0 0.448 * [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)))) 0.449 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.449 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 0.449 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.449 * [taylor]: Taking taylor expansion of 0 in n 0.449 * [backup-simplify]: Simplify 0 into 0 0.449 * [backup-simplify]: Simplify 0 into 0 0.450 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 0.450 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 0.450 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 0.451 * [backup-simplify]: Simplify (- 1) into -1 0.451 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.452 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 0.452 * [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))) 0.455 * [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))) 0.455 * [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 0.455 * [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 0.455 * [taylor]: Taking taylor expansion of +nan.0 in n 0.455 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.455 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.455 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.455 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.455 * [taylor]: Taking taylor expansion of 0.5 in n 0.455 * [backup-simplify]: Simplify 0.5 into 0.5 0.455 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.455 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.455 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.455 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.455 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.455 * [taylor]: Taking taylor expansion of 1.0 in n 0.455 * [backup-simplify]: Simplify 1.0 into 1.0 0.455 * [taylor]: Taking taylor expansion of (log PI) in n 0.455 * [taylor]: Taking taylor expansion of PI in n 0.455 * [backup-simplify]: Simplify PI into PI 0.455 * [backup-simplify]: Simplify (log PI) into (log PI) 0.456 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.457 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.457 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.457 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.457 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.457 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.457 * [taylor]: Taking taylor expansion of 1.0 in n 0.457 * [backup-simplify]: Simplify 1.0 into 1.0 0.457 * [taylor]: Taking taylor expansion of (log n) in n 0.457 * [taylor]: Taking taylor expansion of n in n 0.457 * [backup-simplify]: Simplify 0 into 0 0.457 * [backup-simplify]: Simplify 1 into 1 0.457 * [backup-simplify]: Simplify (log 1) into 0 0.457 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.458 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.458 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.458 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.458 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.458 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) 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 2.0) in n 0.458 * [taylor]: Taking taylor expansion of 2.0 in n 0.458 * [backup-simplify]: Simplify 2.0 into 2.0 0.458 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.458 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.459 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.460 * [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) 0.461 * [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) 0.461 * [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)) 0.462 * [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))) 0.463 * [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) 0.464 * [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)) 0.465 * [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))) 0.465 * [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))) 0.465 * [backup-simplify]: Simplify 0 into 0 0.466 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 0.466 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 0.467 * [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 0.468 * [backup-simplify]: Simplify (- 0) into 0 0.468 * [backup-simplify]: Simplify (+ 0 0) into 0 0.468 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.469 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 0.470 * [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))) 0.470 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.472 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.474 * [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)))))))) 0.477 * [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)))))))) 0.477 * [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 0.477 * [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 0.477 * [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 0.477 * [taylor]: Taking taylor expansion of +nan.0 in n 0.477 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.477 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.477 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.477 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.477 * [taylor]: Taking taylor expansion of 0.5 in n 0.477 * [backup-simplify]: Simplify 0.5 into 0.5 0.477 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.477 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.477 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.477 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.477 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.477 * [taylor]: Taking taylor expansion of 1.0 in n 0.477 * [backup-simplify]: Simplify 1.0 into 1.0 0.477 * [taylor]: Taking taylor expansion of (log PI) in n 0.477 * [taylor]: Taking taylor expansion of PI in n 0.477 * [backup-simplify]: Simplify PI into PI 0.478 * [backup-simplify]: Simplify (log PI) into (log PI) 0.478 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.479 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.479 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.479 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.479 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.479 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.479 * [taylor]: Taking taylor expansion of 1.0 in n 0.479 * [backup-simplify]: Simplify 1.0 into 1.0 0.479 * [taylor]: Taking taylor expansion of (log n) in n 0.479 * [taylor]: Taking taylor expansion of n in n 0.479 * [backup-simplify]: Simplify 0 into 0 0.479 * [backup-simplify]: Simplify 1 into 1 0.480 * [backup-simplify]: Simplify (log 1) into 0 0.480 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.480 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.480 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.480 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.480 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.480 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) 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 2.0) in n 0.480 * [taylor]: Taking taylor expansion of 2.0 in n 0.480 * [backup-simplify]: Simplify 2.0 into 2.0 0.480 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.481 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.482 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.482 * [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) 0.483 * [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) 0.483 * [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)) 0.484 * [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))) 0.485 * [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) 0.485 * [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 0.485 * [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 0.485 * [taylor]: Taking taylor expansion of +nan.0 in n 0.485 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.485 * [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 0.485 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.485 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.485 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.485 * [taylor]: Taking taylor expansion of 0.5 in n 0.485 * [backup-simplify]: Simplify 0.5 into 0.5 0.485 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.485 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.485 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.485 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.485 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.485 * [taylor]: Taking taylor expansion of 1.0 in n 0.485 * [backup-simplify]: Simplify 1.0 into 1.0 0.485 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.485 * [taylor]: Taking taylor expansion of 2.0 in n 0.485 * [backup-simplify]: Simplify 2.0 into 2.0 0.486 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.486 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.493 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.493 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.493 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.493 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.493 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.493 * [taylor]: Taking taylor expansion of 1.0 in n 0.493 * [backup-simplify]: Simplify 1.0 into 1.0 0.493 * [taylor]: Taking taylor expansion of (log PI) in n 0.493 * [taylor]: Taking taylor expansion of PI in n 0.493 * [backup-simplify]: Simplify PI into PI 0.493 * [backup-simplify]: Simplify (log PI) into (log PI) 0.494 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.495 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.495 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.495 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.495 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.495 * [taylor]: Taking taylor expansion of 1.0 in n 0.495 * [backup-simplify]: Simplify 1.0 into 1.0 0.495 * [taylor]: Taking taylor expansion of (log n) in n 0.495 * [taylor]: Taking taylor expansion of n in n 0.495 * [backup-simplify]: Simplify 0 into 0 0.495 * [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) 0.496 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.496 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.496 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.497 * [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))) 0.499 * [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) 0.499 * [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 0.500 * [backup-simplify]: Simplify (* 0 PI) into 0 0.500 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.501 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.501 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.502 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.503 * [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)) 0.504 * [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)) 0.507 * [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)))))))) 0.515 * [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 0.520 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 0.521 * [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 0.522 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.522 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.523 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 0.523 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 0.524 * [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 0.525 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 0.526 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 0.527 * [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 0.530 * [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 0.531 * [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 0.531 * [backup-simplify]: Simplify (- 0) into 0 0.531 * [backup-simplify]: Simplify 0 into 0 0.531 * [backup-simplify]: Simplify 0 into 0 0.532 * [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 0.535 * [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))) 0.538 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.540 * [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 0.550 * [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 0.552 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.552 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.552 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.552 * [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) 0.553 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.554 * [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) 0.556 * [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 0.558 * [taylor]: Taking taylor expansion of 1.0 in n 0.558 * [backup-simplify]: Simplify 1.0 into 1.0 0.558 * [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)) 0.564 * [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))) 0.565 * [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) 0.565 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.565 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.565 * [taylor]: Taking taylor expansion of 2.0 in n 0.565 * [backup-simplify]: Simplify 2.0 into 2.0 0.565 * [taylor]: Taking taylor expansion of (* n PI) in n 0.565 * [taylor]: Taking taylor expansion of n in n 0.565 * [backup-simplify]: Simplify 0 into 0 0.565 * [backup-simplify]: Simplify 1 into 1 0.565 * [taylor]: Taking taylor expansion of PI in n 0.565 * [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) 0.568 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.568 * [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 0.568 * [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 0.568 * [taylor]: Taking taylor expansion of +nan.0 in n 0.568 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.568 * [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 0.568 * [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)) 0.570 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.570 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.570 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.570 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.570 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.570 * [taylor]: Taking taylor expansion of 1.0 in n 0.570 * [backup-simplify]: Simplify 1.0 into 1.0 0.570 * [taylor]: Taking taylor expansion of (log PI) in n 0.570 * [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) 0.572 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.572 * [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)) 0.582 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.584 * [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)) 0.596 * [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)))))))) 0.604 * [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)))))))))))) 0.612 * [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)))))))))))) 0.621 * [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)))))))))))))) 0.630 * [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)))))))))))))) 0.639 * [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)))))))))))))) 0.653 * [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)))))))))))))))))))))) 0.654 * [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)))))) 0.654 * [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 0.654 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.654 * [taylor]: Taking taylor expansion of 1.0 in n 0.654 * [backup-simplify]: Simplify 1.0 into 1.0 0.654 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.654 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.654 * [taylor]: Taking taylor expansion of k in n 0.654 * [backup-simplify]: Simplify k into k 0.654 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 0.654 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 0.654 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.654 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.654 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.654 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.654 * [taylor]: Taking taylor expansion of 0.5 in n 0.654 * [backup-simplify]: Simplify 0.5 into 0.5 0.654 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.654 * [taylor]: Taking taylor expansion of 1.0 in n 0.654 * [backup-simplify]: Simplify 1.0 into 1.0 0.655 * [taylor]: Taking taylor expansion of (/ 1 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 (/ 1 k) into (/ 1 k) 0.655 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.655 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.655 * [taylor]: Taking taylor expansion of 2.0 in n 0.655 * [backup-simplify]: Simplify 2.0 into 2.0 0.655 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.655 * [taylor]: Taking taylor expansion of PI in n 0.655 * [backup-simplify]: Simplify PI into PI 0.655 * [taylor]: Taking taylor expansion of n in n 0.655 * [backup-simplify]: Simplify 0 into 0 0.655 * [backup-simplify]: Simplify 1 into 1 0.655 * [backup-simplify]: Simplify (/ PI 1) into PI 0.655 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.656 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.656 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.656 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.656 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.657 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.658 * [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)))) 0.658 * [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))))) 0.658 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.658 * [taylor]: Taking taylor expansion of 1.0 in k 0.658 * [backup-simplify]: Simplify 1.0 into 1.0 0.658 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.658 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.658 * [taylor]: Taking taylor expansion of k in k 0.658 * [backup-simplify]: Simplify 0 into 0 0.658 * [backup-simplify]: Simplify 1 into 1 0.659 * [backup-simplify]: Simplify (sqrt 0) into 0 0.659 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.659 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.659 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.660 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.660 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.660 * [taylor]: Taking taylor expansion of 0.5 in k 0.660 * [backup-simplify]: Simplify 0.5 into 0.5 0.660 * [taylor]: Taking taylor expansion of (- 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 (/ 1 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 (/ 1 1) into 1 0.660 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.660 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.660 * [taylor]: Taking taylor expansion of 2.0 in k 0.660 * [backup-simplify]: Simplify 2.0 into 2.0 0.660 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.660 * [taylor]: Taking taylor expansion of PI in k 0.660 * [backup-simplify]: Simplify PI into PI 0.660 * [taylor]: Taking taylor expansion of n in k 0.660 * [backup-simplify]: Simplify n into n 0.660 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.660 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.660 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.660 * [backup-simplify]: Simplify (- 1) into -1 0.661 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.661 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.661 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.661 * [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))))) 0.661 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 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 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.661 * [taylor]: Taking taylor expansion of (sqrt 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 0.662 * [backup-simplify]: Simplify (sqrt 0) into 0 0.662 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.662 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.662 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.662 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.662 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.662 * [taylor]: Taking taylor expansion of 0.5 in k 0.662 * [backup-simplify]: Simplify 0.5 into 0.5 0.662 * [taylor]: Taking taylor expansion of (- 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 (/ 1 k) in k 0.663 * [taylor]: Taking taylor expansion of k in k 0.663 * [backup-simplify]: Simplify 0 into 0 0.663 * [backup-simplify]: Simplify 1 into 1 0.663 * [backup-simplify]: Simplify (/ 1 1) into 1 0.663 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.663 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.663 * [taylor]: Taking taylor expansion of 2.0 in k 0.663 * [backup-simplify]: Simplify 2.0 into 2.0 0.663 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.663 * [taylor]: Taking taylor expansion of PI in k 0.663 * [backup-simplify]: Simplify PI into PI 0.663 * [taylor]: Taking taylor expansion of n in k 0.663 * [backup-simplify]: Simplify n into n 0.663 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.663 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.663 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.663 * [backup-simplify]: Simplify (- 1) into -1 0.664 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.664 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.664 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.664 * [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 0.665 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.665 * [taylor]: Taking taylor expansion of 0 in n 0.665 * [backup-simplify]: Simplify 0 into 0 0.665 * [backup-simplify]: Simplify 0 into 0 0.665 * [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 0.666 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.666 * [taylor]: Taking taylor expansion of +nan.0 in n 0.666 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.666 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.666 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.666 * [taylor]: Taking taylor expansion of 0.5 in n 0.666 * [backup-simplify]: Simplify 0.5 into 0.5 0.666 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.666 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.666 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.666 * [taylor]: Taking taylor expansion of 2.0 in n 0.666 * [backup-simplify]: Simplify 2.0 into 2.0 0.666 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.666 * [taylor]: Taking taylor expansion of PI in n 0.666 * [backup-simplify]: Simplify PI into PI 0.666 * [taylor]: Taking taylor expansion of n in n 0.666 * [backup-simplify]: Simplify 0 into 0 0.666 * [backup-simplify]: Simplify 1 into 1 0.666 * [backup-simplify]: Simplify (/ PI 1) into PI 0.667 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.667 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.667 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.667 * [taylor]: Taking taylor expansion of 1.0 in n 0.667 * [backup-simplify]: Simplify 1.0 into 1.0 0.667 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.667 * [taylor]: Taking taylor expansion of k in n 0.667 * [backup-simplify]: Simplify k into k 0.667 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.668 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.668 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.668 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.669 * [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)))) 0.670 * [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))))) 0.671 * [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)))))) 0.672 * [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 0 into 0 0.675 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.679 * [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 0.681 * [taylor]: Taking taylor expansion of PI in n 0.681 * [backup-simplify]: Simplify PI into PI 0.681 * [taylor]: Taking taylor expansion of n in n 0.681 * [backup-simplify]: Simplify 0 into 0 0.681 * [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)))))) 0.686 * [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))))))) 0.688 * [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 0.688 * [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 0.689 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.690 * [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 0.696 * [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 0.698 * [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) 0.699 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.699 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.699 * [taylor]: Taking taylor expansion of 1.0 in n 0.699 * [backup-simplify]: Simplify 1.0 into 1.0 0.699 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.700 * [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) 0.700 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.700 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.701 * [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))))))) 0.707 * [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 0.708 * [backup-simplify]: Simplify 1.0 into 1.0 0.708 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.708 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.708 * [taylor]: Taking taylor expansion of -2.0 in n 0.708 * [backup-simplify]: Simplify -2.0 into -2.0 0.708 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.708 * [taylor]: Taking taylor expansion of PI in n 0.708 * [backup-simplify]: Simplify PI into PI 0.708 * [taylor]: Taking taylor expansion of n in n 0.708 * [backup-simplify]: Simplify 0 into 0 0.708 * [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) 0.713 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 0.713 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 0.713 * [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 0.714 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.714 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.714 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.714 * [taylor]: Taking taylor expansion of 0.5 in k 0.714 * [backup-simplify]: Simplify 0.5 into 0.5 0.714 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.714 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.714 * [taylor]: Taking taylor expansion of k in k 0.714 * [backup-simplify]: Simplify 0 into 0 0.714 * [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 0.716 * [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 0.717 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.717 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.717 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.717 * [taylor]: Taking taylor expansion of 0.5 in k 0.717 * [backup-simplify]: Simplify 0.5 into 0.5 0.717 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.717 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.717 * [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 0.719 * [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))))))) 0.720 * [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))))))) 0.720 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.720 * [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 0.721 * [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))) 0.724 * [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)))))) 0.726 * [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 0.729 * [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)))))))) 0.729 * [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 0.730 * [backup-simplify]: Simplify 0.5 into 0.5 0.730 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.730 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.730 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.730 * [taylor]: Taking taylor expansion of k in n 0.730 * [backup-simplify]: Simplify k into k 0.730 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.730 * [taylor]: Taking taylor expansion of 1.0 in n 0.730 * [backup-simplify]: Simplify 1.0 into 1.0 0.730 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.730 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.730 * [taylor]: Taking taylor expansion of -2.0 in n 0.730 * [backup-simplify]: Simplify -2.0 into -2.0 0.730 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.730 * [taylor]: Taking taylor expansion of PI in n 0.730 * [backup-simplify]: Simplify PI into PI 0.730 * [taylor]: Taking taylor expansion of n in n 0.730 * [backup-simplify]: Simplify 0 into 0 0.730 * [backup-simplify]: Simplify 1 into 1 0.730 * [backup-simplify]: Simplify (/ PI 1) into PI 0.730 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.731 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.731 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.732 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.733 * [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)))) 0.734 * [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))))) 0.735 * [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 (- (* +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))))))) 0.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.737 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.738 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.738 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.738 * [backup-simplify]: Simplify (+ 0 0) into 0 0.739 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.740 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.741 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 0.742 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.743 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 0.743 * [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 0.748 * [backup-simplify]: Simplify (/ PI 1) into PI 0.748 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.749 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.749 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.750 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.750 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.751 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.752 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.752 * [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: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 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(- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 0.760 * [simplify]: Sending expressions to egg_math: (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 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(* (* h1 h1) h1)) (* (cbrt (* (* h0 PI) h1)) (cbrt (* (* h0 PI) h1))) (cbrt (* (* h0 PI) h1)) (* (* (* (* h0 PI) h1) (* (* h0 PI) h1)) (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (* (* h0 PI) (sqrt h1)) (* (* h0 PI) 1) (* PI h1) (- (log h2) (log (sqrt h3))) (log (/ h2 (sqrt h3))) (exp (/ h2 (sqrt h3))) (/ (* (* h2 h2) h2) (* (* (sqrt h3) (sqrt h3)) (sqrt h3))) (* (cbrt (/ h2 (sqrt h3))) (cbrt (/ h2 (sqrt h3)))) (cbrt (/ h2 (sqrt h3))) (* (* (/ h2 (sqrt h3)) (/ h2 (sqrt h3))) (/ h2 (sqrt h3))) (sqrt (/ h2 (sqrt h3))) (sqrt (/ h2 (sqrt h3))) (- h2) (- (sqrt h3)) (/ (* (cbrt h2) (cbrt h2)) (* (cbrt (sqrt h3)) (cbrt (sqrt h3)))) (/ (cbrt h2) (cbrt (sqrt h3))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (* (cbrt h3) (cbrt h3)))) (/ (cbrt h2) (sqrt (cbrt h3))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h3))) (/ (cbrt h2) (sqrt (sqrt h3))) (/ (* (cbrt h2) (cbrt h2)) (sqrt 1)) (/ (cbrt h2) (sqrt h3)) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt h3))) (/ 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(log (sqrt h3))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0))) (+ (- (log h2) (log (sqrt h3))) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0))) (+ (- (log h2) (log (sqrt h3))) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0))) (+ (- (log h2) (log (sqrt h3))) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0))) (+ (- (log h2) (log (sqrt h3))) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (+ (log (/ h2 (sqrt h3))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0))) (+ (log (/ h2 (sqrt h3))) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0))) (+ (log (/ h2 (sqrt h3))) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0))) (+ (log (/ h2 (sqrt h3))) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0))) (+ (log (/ h2 (sqrt h3))) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (log (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (exp (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ (* (* h2 h2) h2) (* (* (sqrt h3) (sqrt h3)) (sqrt h3))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (* (* (/ h2 (sqrt h3)) (/ h2 (sqrt h3))) (/ h2 (sqrt h3))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (cbrt (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))))) (cbrt (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (* (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (sqrt (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (sqrt (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* h2 (pow (* (* h0 PI) h1) (/ h2 h0))) (* (sqrt h3) (pow (* (* h0 PI) h1) (/ h3 h0))) (* (sqrt (/ h2 (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (sqrt (/ h2 (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (sqrt (/ h2 (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (sqrt (/ h2 (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (/ h2 (sqrt h3)) (pow (* h0 PI) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))))) (* (/ h2 (sqrt h3)) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (* (/ h2 (sqrt h3)) 1) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2))) (* (cbrt (/ h2 (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (sqrt (/ h2 (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (cbrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (sqrt (cbrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (cbrt h2) (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (cbrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (sqrt (cbrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ (sqrt h2) (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (cbrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt (cbrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt (sqrt h3))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ 1 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ h2 h0))) (* h2 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (- (+ (* h8 h3) (- (+ (* h8 (pow h3 2)) (- h8))))) (- (+ (* h8 (/ 1 (pow h3 2))) (- (+ (* h8 (/ 1 h3)) (- (* h8 (/ 1 (pow h3 3)))))))) (- (+ (* h8 (/ 1 (pow h3 2))) (- (+ (* h8 (/ 1 h3)) (- h8))))) (- (+ (* h8 (* (* (pow h3 2) (pow (log (* h0 PI)) 2)) (pow (* (pow h0 h2) (* (pow h1 h2) (pow PI h2))) h5))) (- (+ (* h8 (* (* (pow h3 2) (log (* h0 PI))) (pow (* (pow PI h2) (* (pow h1 h2) (pow h0 h2))) h5))) (- (+ (* h8 (* (* (pow h3 2) (* (log (* h0 PI)) (log h1))) (pow (* (pow PI h2) (* (pow h0 h2) (pow h1 h2))) h5))) (- (+ (* h8 (* (* (pow h3 2) (log h1)) (pow (* (pow h0 h2) (* (pow PI h2) (pow h1 h2))) h5))) (- (+ (* h8 (* (* h3 (log (* h0 PI))) (pow (* (pow h0 h2) (* (pow h1 h2) (pow PI h2))) h5))) (- (+ (* h8 (* (* (pow h3 2) (pow (log h1) 2)) (pow (* (pow h0 h2) (* (pow PI h2) (pow h1 h2))) h5))) (- (+ (* h8 (* (* h3 (log h1)) (pow (* (pow h0 h2) (* (pow PI h2) (pow h1 h2))) h5))) (- (+ (* h8 (pow (* (pow h0 h2) (* (pow h1 h2) (pow PI h2))) h5)) (- (+ (* h8 (* (pow h3 2) (pow (* (pow PI h2) (* (pow h1 h2) (pow h0 h2))) h5))) (- (* h8 (* h3 (pow (* (pow h0 h2) (* (pow h1 h2) (pow PI h2))) h5)))))))))))))))))))))) (- (+ (* h8 (/ (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (pow h3 3))) (- (+ (* h8 (/ (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) h3)) (- (* h8 (/ (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (pow h3 2)))))))) (- (+ (* h8 (/ (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) h3)) (- (+ (* h8 (/ (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (pow h3 2))) (- (* h8 (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))))))))) 0.769 * * [simplify]: iteration 0 : 950 enodes (cost 1461 ) 0.786 * * [simplify]: iteration 1 : 3924 enodes (cost 1358 ) 0.850 * * [simplify]: iteration 2 : 5002 enodes (cost 1344 ) 0.861 * * * [progress]: adding candidates to table 1.245 * * [progress]: iteration 2 / 4 1.245 * * * [progress]: picking best candidate 1.262 * * * * [pick]: Picked # 1.262 * * * [progress]: localizing error 1.277 * * * [progress]: generating rewritten candidates 1.277 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 1.297 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 1.320 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 1) 1.337 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1) 1.357 * * * [progress]: generating series expansions 1.357 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 1.358 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.358 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.358 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.358 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.358 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.358 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.358 * [taylor]: Taking taylor expansion of 0.5 in k 1.358 * [backup-simplify]: Simplify 0.5 into 0.5 1.359 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.359 * [taylor]: Taking taylor expansion of 1.0 in k 1.359 * [backup-simplify]: Simplify 1.0 into 1.0 1.359 * [taylor]: Taking taylor expansion of k in k 1.359 * [backup-simplify]: Simplify 0 into 0 1.359 * [backup-simplify]: Simplify 1 into 1 1.359 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.359 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.359 * [taylor]: Taking taylor expansion of 2.0 in k 1.359 * [backup-simplify]: Simplify 2.0 into 2.0 1.359 * [taylor]: Taking taylor expansion of (* n PI) in k 1.359 * [taylor]: Taking taylor expansion of n in k 1.359 * [backup-simplify]: Simplify n into n 1.359 * [taylor]: Taking taylor expansion of PI in k 1.359 * [backup-simplify]: Simplify PI into PI 1.359 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.359 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.359 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.359 * [backup-simplify]: Simplify (- 0) into 0 1.359 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.360 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.360 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.360 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.360 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.360 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.360 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.360 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.360 * [taylor]: Taking taylor expansion of 0.5 in n 1.360 * [backup-simplify]: Simplify 0.5 into 0.5 1.360 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.360 * [taylor]: Taking taylor expansion of 1.0 in n 1.360 * [backup-simplify]: Simplify 1.0 into 1.0 1.360 * [taylor]: Taking taylor expansion of k in n 1.360 * [backup-simplify]: Simplify k into k 1.360 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.360 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.360 * [taylor]: Taking taylor expansion of 2.0 in n 1.360 * [backup-simplify]: Simplify 2.0 into 2.0 1.360 * [taylor]: Taking taylor expansion of (* n PI) in n 1.360 * [taylor]: Taking taylor expansion of n in n 1.360 * [backup-simplify]: Simplify 0 into 0 1.360 * [backup-simplify]: Simplify 1 into 1 1.360 * [taylor]: Taking taylor expansion of PI in n 1.360 * [backup-simplify]: Simplify PI into PI 1.360 * [backup-simplify]: Simplify (* 0 PI) into 0 1.361 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.362 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.362 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.363 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.363 * [backup-simplify]: Simplify (- k) into (- k) 1.363 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.363 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.364 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.365 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.365 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.365 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.365 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.365 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.365 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.366 * [taylor]: Taking taylor expansion of 0.5 in n 1.366 * [backup-simplify]: Simplify 0.5 into 0.5 1.366 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.366 * [taylor]: Taking taylor expansion of 1.0 in n 1.366 * [backup-simplify]: Simplify 1.0 into 1.0 1.366 * [taylor]: Taking taylor expansion of k in n 1.366 * [backup-simplify]: Simplify k into k 1.366 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.366 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.366 * [taylor]: Taking taylor expansion of 2.0 in n 1.366 * [backup-simplify]: Simplify 2.0 into 2.0 1.366 * [taylor]: Taking taylor expansion of (* n PI) in n 1.366 * [taylor]: Taking taylor expansion of n in n 1.366 * [backup-simplify]: Simplify 0 into 0 1.366 * [backup-simplify]: Simplify 1 into 1 1.366 * [taylor]: Taking taylor expansion of PI in n 1.366 * [backup-simplify]: Simplify PI into PI 1.366 * [backup-simplify]: Simplify (* 0 PI) into 0 1.366 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.367 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.368 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.369 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.369 * [backup-simplify]: Simplify (- k) into (- k) 1.369 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.369 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.373 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.373 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.374 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.374 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.374 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.374 * [taylor]: Taking taylor expansion of 0.5 in k 1.374 * [backup-simplify]: Simplify 0.5 into 0.5 1.374 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.374 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.374 * [taylor]: Taking taylor expansion of 1.0 in k 1.374 * [backup-simplify]: Simplify 1.0 into 1.0 1.374 * [taylor]: Taking taylor expansion of k in k 1.374 * [backup-simplify]: Simplify 0 into 0 1.374 * [backup-simplify]: Simplify 1 into 1 1.374 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.374 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.374 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.375 * [taylor]: Taking taylor expansion of 2.0 in k 1.375 * [backup-simplify]: Simplify 2.0 into 2.0 1.375 * [taylor]: Taking taylor expansion of PI in k 1.375 * [backup-simplify]: Simplify PI into PI 1.375 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.375 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.376 * [taylor]: Taking taylor expansion of (log n) in k 1.376 * [taylor]: Taking taylor expansion of n in k 1.376 * [backup-simplify]: Simplify n into n 1.376 * [backup-simplify]: Simplify (log n) into (log n) 1.376 * [backup-simplify]: Simplify (- 0) into 0 1.376 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.377 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.377 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.378 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.379 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.379 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.380 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.380 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.381 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.382 * [backup-simplify]: Simplify (- 0) into 0 1.382 * [backup-simplify]: Simplify (+ 0 0) into 0 1.382 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.383 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.384 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.385 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.385 * [taylor]: Taking taylor expansion of 0 in k 1.385 * [backup-simplify]: Simplify 0 into 0 1.385 * [backup-simplify]: Simplify 0 into 0 1.385 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.386 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.387 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.387 * [backup-simplify]: Simplify (+ 0 0) into 0 1.387 * [backup-simplify]: Simplify (- 1) into -1 1.387 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.388 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.390 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1.392 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.393 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.394 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.395 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.396 * [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 1.397 * [backup-simplify]: Simplify (- 0) into 0 1.397 * [backup-simplify]: Simplify (+ 0 0) into 0 1.397 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.398 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.399 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.400 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.401 * [taylor]: Taking taylor expansion of 0 in k 1.401 * [backup-simplify]: Simplify 0 into 0 1.401 * [backup-simplify]: Simplify 0 into 0 1.401 * [backup-simplify]: Simplify 0 into 0 1.401 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.403 * [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 1.404 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.404 * [backup-simplify]: Simplify (+ 0 0) into 0 1.405 * [backup-simplify]: Simplify (- 0) into 0 1.405 * [backup-simplify]: Simplify (+ 0 0) into 0 1.406 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.407 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.410 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 1.413 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 1.418 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 1.419 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 1.419 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.419 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.419 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.419 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.419 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.419 * [taylor]: Taking taylor expansion of 0.5 in k 1.419 * [backup-simplify]: Simplify 0.5 into 0.5 1.419 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.419 * [taylor]: Taking taylor expansion of 1.0 in k 1.419 * [backup-simplify]: Simplify 1.0 into 1.0 1.419 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.419 * [taylor]: Taking taylor expansion of k in k 1.419 * [backup-simplify]: Simplify 0 into 0 1.419 * [backup-simplify]: Simplify 1 into 1 1.420 * [backup-simplify]: Simplify (/ 1 1) into 1 1.420 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.420 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.420 * [taylor]: Taking taylor expansion of 2.0 in k 1.420 * [backup-simplify]: Simplify 2.0 into 2.0 1.420 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.420 * [taylor]: Taking taylor expansion of PI in k 1.420 * [backup-simplify]: Simplify PI into PI 1.420 * [taylor]: Taking taylor expansion of n in k 1.420 * [backup-simplify]: Simplify n into n 1.420 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.420 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.420 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.420 * [backup-simplify]: Simplify (- 1) into -1 1.420 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.421 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.421 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.421 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.421 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.421 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.421 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.421 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.421 * [taylor]: Taking taylor expansion of 0.5 in n 1.421 * [backup-simplify]: Simplify 0.5 into 0.5 1.421 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.421 * [taylor]: Taking taylor expansion of 1.0 in n 1.421 * [backup-simplify]: Simplify 1.0 into 1.0 1.421 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.421 * [taylor]: Taking taylor expansion of k in n 1.421 * [backup-simplify]: Simplify k into k 1.421 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.421 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.421 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.421 * [taylor]: Taking taylor expansion of 2.0 in n 1.421 * [backup-simplify]: Simplify 2.0 into 2.0 1.421 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.421 * [taylor]: Taking taylor expansion of PI in n 1.421 * [backup-simplify]: Simplify PI into PI 1.421 * [taylor]: Taking taylor expansion of n in n 1.421 * [backup-simplify]: Simplify 0 into 0 1.421 * [backup-simplify]: Simplify 1 into 1 1.421 * [backup-simplify]: Simplify (/ PI 1) 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 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.422 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.423 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.423 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.424 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.425 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.425 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.425 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.425 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.425 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.425 * [taylor]: Taking taylor expansion of 0.5 in n 1.425 * [backup-simplify]: Simplify 0.5 into 0.5 1.425 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.425 * [taylor]: Taking taylor expansion of 1.0 in n 1.425 * [backup-simplify]: Simplify 1.0 into 1.0 1.425 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.425 * [taylor]: Taking taylor expansion of k in n 1.425 * [backup-simplify]: Simplify k into k 1.425 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.425 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.425 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.425 * [taylor]: Taking taylor expansion of 2.0 in n 1.425 * [backup-simplify]: Simplify 2.0 into 2.0 1.425 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.425 * [taylor]: Taking taylor expansion of PI in n 1.425 * [backup-simplify]: Simplify PI into PI 1.425 * [taylor]: Taking taylor expansion of n in n 1.425 * [backup-simplify]: Simplify 0 into 0 1.425 * [backup-simplify]: Simplify 1 into 1 1.425 * [backup-simplify]: Simplify (/ PI 1) into PI 1.426 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.426 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.426 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.426 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.427 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.427 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.428 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.429 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.429 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.429 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.429 * [taylor]: Taking taylor expansion of 0.5 in k 1.429 * [backup-simplify]: Simplify 0.5 into 0.5 1.429 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.429 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.429 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.429 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.429 * [taylor]: Taking taylor expansion of 2.0 in k 1.429 * [backup-simplify]: Simplify 2.0 into 2.0 1.429 * [taylor]: Taking taylor expansion of PI in k 1.429 * [backup-simplify]: Simplify PI into PI 1.429 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.430 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.430 * [taylor]: Taking taylor expansion of (log n) in k 1.430 * [taylor]: Taking taylor expansion of n in k 1.430 * [backup-simplify]: Simplify n into n 1.430 * [backup-simplify]: Simplify (log n) into (log n) 1.430 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.430 * [taylor]: Taking taylor expansion of 1.0 in k 1.430 * [backup-simplify]: Simplify 1.0 into 1.0 1.430 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.430 * [taylor]: Taking taylor expansion of k in k 1.430 * [backup-simplify]: Simplify 0 into 0 1.430 * [backup-simplify]: Simplify 1 into 1 1.430 * [backup-simplify]: Simplify (/ 1 1) into 1 1.430 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.431 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.431 * [backup-simplify]: Simplify (- 1) into -1 1.432 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.432 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.433 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.433 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.434 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.435 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.436 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.436 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.436 * [backup-simplify]: Simplify (- 0) into 0 1.437 * [backup-simplify]: Simplify (+ 0 0) into 0 1.437 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.438 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.438 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.440 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.440 * [taylor]: Taking taylor expansion of 0 in k 1.440 * [backup-simplify]: Simplify 0 into 0 1.440 * [backup-simplify]: Simplify 0 into 0 1.440 * [backup-simplify]: Simplify 0 into 0 1.440 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.441 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) 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 (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.443 * [backup-simplify]: Simplify (- 0) into 0 1.443 * [backup-simplify]: Simplify (+ 0 0) into 0 1.444 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 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 (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.447 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.447 * [taylor]: Taking taylor expansion of 0 in k 1.447 * [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 0 into 0 1.448 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.448 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.451 * [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 1.451 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.451 * [backup-simplify]: Simplify (- 0) into 0 1.452 * [backup-simplify]: Simplify (+ 0 0) into 0 1.452 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.453 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.455 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.456 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.457 * [taylor]: Taking taylor expansion of 0 in k 1.457 * [backup-simplify]: Simplify 0 into 0 1.457 * [backup-simplify]: Simplify 0 into 0 1.458 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 1.458 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 1.458 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.458 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.458 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.458 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.458 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.458 * [taylor]: Taking taylor expansion of 0.5 in k 1.458 * [backup-simplify]: Simplify 0.5 into 0.5 1.458 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.458 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.458 * [taylor]: Taking taylor expansion of k in k 1.458 * [backup-simplify]: Simplify 0 into 0 1.458 * [backup-simplify]: Simplify 1 into 1 1.459 * [backup-simplify]: Simplify (/ 1 1) into 1 1.459 * [taylor]: Taking taylor expansion of 1.0 in k 1.459 * [backup-simplify]: Simplify 1.0 into 1.0 1.459 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.459 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.459 * [taylor]: Taking taylor expansion of -2.0 in k 1.459 * [backup-simplify]: Simplify -2.0 into -2.0 1.459 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.459 * [taylor]: Taking taylor expansion of PI in k 1.459 * [backup-simplify]: Simplify PI into PI 1.459 * [taylor]: Taking taylor expansion of n in k 1.459 * [backup-simplify]: Simplify n into n 1.459 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.459 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.459 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.459 * [backup-simplify]: Simplify (+ 1 0) into 1 1.460 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.460 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.460 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.460 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.460 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.460 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.460 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.460 * [taylor]: Taking taylor expansion of 0.5 in n 1.460 * [backup-simplify]: Simplify 0.5 into 0.5 1.460 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.460 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.460 * [taylor]: Taking taylor expansion of k in n 1.460 * [backup-simplify]: Simplify k into k 1.460 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.460 * [taylor]: Taking taylor expansion of 1.0 in n 1.460 * [backup-simplify]: Simplify 1.0 into 1.0 1.460 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.460 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.460 * [taylor]: Taking taylor expansion of -2.0 in n 1.460 * [backup-simplify]: Simplify -2.0 into -2.0 1.460 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.460 * [taylor]: Taking taylor expansion of PI in n 1.460 * [backup-simplify]: Simplify PI into PI 1.460 * [taylor]: Taking taylor expansion of n in n 1.460 * [backup-simplify]: Simplify 0 into 0 1.460 * [backup-simplify]: Simplify 1 into 1 1.460 * [backup-simplify]: Simplify (/ PI 1) into PI 1.461 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.461 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.461 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.461 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.462 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.468 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.469 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.469 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.469 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.469 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.469 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.469 * [taylor]: Taking taylor expansion of 0.5 in n 1.469 * [backup-simplify]: Simplify 0.5 into 0.5 1.469 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.469 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.469 * [taylor]: Taking taylor expansion of k in n 1.469 * [backup-simplify]: Simplify k into k 1.469 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.469 * [taylor]: Taking taylor expansion of 1.0 in n 1.469 * [backup-simplify]: Simplify 1.0 into 1.0 1.469 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.469 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.469 * [taylor]: Taking taylor expansion of -2.0 in n 1.469 * [backup-simplify]: Simplify -2.0 into -2.0 1.469 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.469 * [taylor]: Taking taylor expansion of PI in n 1.469 * [backup-simplify]: Simplify PI into PI 1.469 * [taylor]: Taking taylor expansion of n in n 1.469 * [backup-simplify]: Simplify 0 into 0 1.469 * [backup-simplify]: Simplify 1 into 1 1.470 * [backup-simplify]: Simplify (/ PI 1) into PI 1.470 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.470 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.471 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.471 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.471 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.472 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.473 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.473 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.473 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.473 * [taylor]: Taking taylor expansion of 0.5 in k 1.473 * [backup-simplify]: Simplify 0.5 into 0.5 1.473 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.473 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.473 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.473 * [taylor]: Taking taylor expansion of k in k 1.473 * [backup-simplify]: Simplify 0 into 0 1.473 * [backup-simplify]: Simplify 1 into 1 1.473 * [backup-simplify]: Simplify (/ 1 1) into 1 1.473 * [taylor]: Taking taylor expansion of 1.0 in k 1.473 * [backup-simplify]: Simplify 1.0 into 1.0 1.473 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.473 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.473 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.474 * [taylor]: Taking taylor expansion of -2.0 in k 1.474 * [backup-simplify]: Simplify -2.0 into -2.0 1.474 * [taylor]: Taking taylor expansion of PI in k 1.474 * [backup-simplify]: Simplify PI into PI 1.474 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.474 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.474 * [taylor]: Taking taylor expansion of (log n) in k 1.474 * [taylor]: Taking taylor expansion of n in k 1.474 * [backup-simplify]: Simplify n into n 1.475 * [backup-simplify]: Simplify (log n) into (log n) 1.475 * [backup-simplify]: Simplify (+ 1 0) into 1 1.475 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.475 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.476 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.477 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.477 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.478 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.479 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.479 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.480 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.480 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.480 * [backup-simplify]: Simplify (+ 0 0) into 0 1.481 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.481 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.482 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.483 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.483 * [taylor]: Taking taylor expansion of 0 in k 1.483 * [backup-simplify]: Simplify 0 into 0 1.483 * [backup-simplify]: Simplify 0 into 0 1.483 * [backup-simplify]: Simplify 0 into 0 1.484 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.485 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.486 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 1.486 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.487 * [backup-simplify]: Simplify (+ 0 0) into 0 1.487 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.488 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.489 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.490 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.490 * [taylor]: Taking taylor expansion of 0 in k 1.490 * [backup-simplify]: Simplify 0 into 0 1.490 * [backup-simplify]: Simplify 0 into 0 1.490 * [backup-simplify]: Simplify 0 into 0 1.491 * [backup-simplify]: Simplify 0 into 0 1.491 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.492 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.495 * [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 1.495 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.495 * [backup-simplify]: Simplify (+ 0 0) into 0 1.496 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.497 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.498 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.499 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.499 * [taylor]: Taking taylor expansion of 0 in k 1.499 * [backup-simplify]: Simplify 0 into 0 1.499 * [backup-simplify]: Simplify 0 into 0 1.500 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 1.500 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 1.501 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.501 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.501 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.501 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.501 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.501 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.501 * [taylor]: Taking taylor expansion of 0.5 in k 1.501 * [backup-simplify]: Simplify 0.5 into 0.5 1.501 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.501 * [taylor]: Taking taylor expansion of 1.0 in k 1.501 * [backup-simplify]: Simplify 1.0 into 1.0 1.501 * [taylor]: Taking taylor expansion of k in k 1.501 * [backup-simplify]: Simplify 0 into 0 1.501 * [backup-simplify]: Simplify 1 into 1 1.501 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.501 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.501 * [taylor]: Taking taylor expansion of 2.0 in k 1.501 * [backup-simplify]: Simplify 2.0 into 2.0 1.501 * [taylor]: Taking taylor expansion of (* n PI) in k 1.501 * [taylor]: Taking taylor expansion of n in k 1.501 * [backup-simplify]: Simplify n into n 1.501 * [taylor]: Taking taylor expansion of PI in k 1.501 * [backup-simplify]: Simplify PI into PI 1.501 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.501 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.501 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.501 * [backup-simplify]: Simplify (- 0) into 0 1.502 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.502 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.502 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.502 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.502 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.502 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.502 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.502 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.502 * [taylor]: Taking taylor expansion of 0.5 in n 1.502 * [backup-simplify]: Simplify 0.5 into 0.5 1.502 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.502 * [taylor]: Taking taylor expansion of 1.0 in n 1.502 * [backup-simplify]: Simplify 1.0 into 1.0 1.502 * [taylor]: Taking taylor expansion of k in n 1.502 * [backup-simplify]: Simplify k into k 1.502 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.502 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.502 * [taylor]: Taking taylor expansion of 2.0 in n 1.502 * [backup-simplify]: Simplify 2.0 into 2.0 1.502 * [taylor]: Taking taylor expansion of (* n PI) in n 1.502 * [taylor]: Taking taylor expansion of n in n 1.502 * [backup-simplify]: Simplify 0 into 0 1.502 * [backup-simplify]: Simplify 1 into 1 1.502 * [taylor]: Taking taylor expansion of PI in n 1.502 * [backup-simplify]: Simplify PI into PI 1.503 * [backup-simplify]: Simplify (* 0 PI) into 0 1.503 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.504 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.505 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.506 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.506 * [backup-simplify]: Simplify (- k) into (- k) 1.506 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.506 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.506 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.507 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.508 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.508 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.508 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.508 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.508 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.508 * [taylor]: Taking taylor expansion of 0.5 in n 1.508 * [backup-simplify]: Simplify 0.5 into 0.5 1.508 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.508 * [taylor]: Taking taylor expansion of 1.0 in n 1.508 * [backup-simplify]: Simplify 1.0 into 1.0 1.508 * [taylor]: Taking taylor expansion of k in n 1.508 * [backup-simplify]: Simplify k into k 1.508 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.508 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.508 * [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 (* n PI) in n 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 * [taylor]: Taking taylor expansion of PI in n 1.508 * [backup-simplify]: Simplify PI into PI 1.508 * [backup-simplify]: Simplify (* 0 PI) into 0 1.509 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.510 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.510 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.511 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.511 * [backup-simplify]: Simplify (- k) into (- k) 1.511 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.511 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.512 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.513 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.513 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.513 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.513 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.513 * [taylor]: Taking taylor expansion of 0.5 in k 1.513 * [backup-simplify]: Simplify 0.5 into 0.5 1.513 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.513 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.513 * [taylor]: Taking taylor expansion of 1.0 in k 1.514 * [backup-simplify]: Simplify 1.0 into 1.0 1.514 * [taylor]: Taking taylor expansion of k in k 1.514 * [backup-simplify]: Simplify 0 into 0 1.514 * [backup-simplify]: Simplify 1 into 1 1.514 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.514 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.514 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.514 * [taylor]: Taking taylor expansion of 2.0 in k 1.514 * [backup-simplify]: Simplify 2.0 into 2.0 1.514 * [taylor]: Taking taylor expansion of PI in k 1.514 * [backup-simplify]: Simplify PI into PI 1.514 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.515 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.515 * [taylor]: Taking taylor expansion of (log n) in k 1.515 * [taylor]: Taking taylor expansion of n in k 1.515 * [backup-simplify]: Simplify n into n 1.515 * [backup-simplify]: Simplify (log n) into (log n) 1.515 * [backup-simplify]: Simplify (- 0) into 0 1.515 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.516 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.516 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.517 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.518 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.518 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.519 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.519 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.520 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.521 * [backup-simplify]: Simplify (- 0) into 0 1.521 * [backup-simplify]: Simplify (+ 0 0) into 0 1.521 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.522 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.523 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.524 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.524 * [taylor]: Taking taylor expansion of 0 in k 1.524 * [backup-simplify]: Simplify 0 into 0 1.524 * [backup-simplify]: Simplify 0 into 0 1.524 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.525 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.526 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.526 * [backup-simplify]: Simplify (+ 0 0) into 0 1.526 * [backup-simplify]: Simplify (- 1) into -1 1.526 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.527 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.529 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1.530 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.532 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.533 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.533 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.535 * [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 1.535 * [backup-simplify]: Simplify (- 0) into 0 1.536 * [backup-simplify]: Simplify (+ 0 0) into 0 1.536 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.537 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.538 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.539 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.539 * [taylor]: Taking taylor expansion of 0 in k 1.539 * [backup-simplify]: Simplify 0 into 0 1.539 * [backup-simplify]: Simplify 0 into 0 1.539 * [backup-simplify]: Simplify 0 into 0 1.540 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.541 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.543 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.543 * [backup-simplify]: Simplify (+ 0 0) into 0 1.543 * [backup-simplify]: Simplify (- 0) into 0 1.543 * [backup-simplify]: Simplify (+ 0 0) into 0 1.544 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.546 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.548 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 1.551 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 1.562 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 1.563 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 1.563 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.563 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.563 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.563 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.563 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.563 * [taylor]: Taking taylor expansion of 0.5 in k 1.563 * [backup-simplify]: Simplify 0.5 into 0.5 1.563 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.563 * [taylor]: Taking taylor expansion of 1.0 in k 1.563 * [backup-simplify]: Simplify 1.0 into 1.0 1.563 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.563 * [taylor]: Taking taylor expansion of k in k 1.563 * [backup-simplify]: Simplify 0 into 0 1.563 * [backup-simplify]: Simplify 1 into 1 1.563 * [backup-simplify]: Simplify (/ 1 1) into 1 1.563 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.563 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.563 * [taylor]: Taking taylor expansion of 2.0 in k 1.564 * [backup-simplify]: Simplify 2.0 into 2.0 1.564 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.564 * [taylor]: Taking taylor expansion of PI in k 1.564 * [backup-simplify]: Simplify PI into PI 1.564 * [taylor]: Taking taylor expansion of n in k 1.564 * [backup-simplify]: Simplify n into n 1.564 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.564 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.564 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.564 * [backup-simplify]: Simplify (- 1) into -1 1.564 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.564 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.565 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.565 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.565 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.565 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.565 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.565 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.565 * [taylor]: Taking taylor expansion of 0.5 in n 1.565 * [backup-simplify]: Simplify 0.5 into 0.5 1.565 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.565 * [taylor]: Taking taylor expansion of 1.0 in n 1.565 * [backup-simplify]: Simplify 1.0 into 1.0 1.565 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.565 * [taylor]: Taking taylor expansion of k in n 1.565 * [backup-simplify]: Simplify k into k 1.565 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.565 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.565 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.565 * [taylor]: Taking taylor expansion of 2.0 in n 1.565 * [backup-simplify]: Simplify 2.0 into 2.0 1.565 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.565 * [taylor]: Taking taylor expansion of PI in n 1.565 * [backup-simplify]: Simplify PI into PI 1.565 * [taylor]: Taking taylor expansion of n in n 1.565 * [backup-simplify]: Simplify 0 into 0 1.565 * [backup-simplify]: Simplify 1 into 1 1.565 * [backup-simplify]: Simplify (/ PI 1) into PI 1.566 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.566 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.566 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.566 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.566 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.567 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.568 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.569 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.569 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.569 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.569 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.569 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.569 * [taylor]: Taking taylor expansion of 0.5 in n 1.569 * [backup-simplify]: Simplify 0.5 into 0.5 1.569 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.569 * [taylor]: Taking taylor expansion of 1.0 in n 1.569 * [backup-simplify]: Simplify 1.0 into 1.0 1.569 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.569 * [taylor]: Taking taylor expansion of k in n 1.569 * [backup-simplify]: Simplify k into k 1.569 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.569 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.569 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.569 * [taylor]: Taking taylor expansion of 2.0 in n 1.569 * [backup-simplify]: Simplify 2.0 into 2.0 1.569 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.569 * [taylor]: Taking taylor expansion of PI in n 1.569 * [backup-simplify]: Simplify PI into PI 1.569 * [taylor]: Taking taylor expansion of n in n 1.569 * [backup-simplify]: Simplify 0 into 0 1.569 * [backup-simplify]: Simplify 1 into 1 1.569 * [backup-simplify]: Simplify (/ PI 1) into PI 1.570 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.570 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.570 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.570 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.570 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.571 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.572 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.573 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.573 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.573 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.573 * [taylor]: Taking taylor expansion of 0.5 in k 1.573 * [backup-simplify]: Simplify 0.5 into 0.5 1.573 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.573 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.573 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.573 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.573 * [taylor]: Taking taylor expansion of 2.0 in k 1.573 * [backup-simplify]: Simplify 2.0 into 2.0 1.573 * [taylor]: Taking taylor expansion of PI in k 1.573 * [backup-simplify]: Simplify PI into PI 1.573 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.574 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.574 * [taylor]: Taking taylor expansion of (log n) in k 1.574 * [taylor]: Taking taylor expansion of n in k 1.574 * [backup-simplify]: Simplify n into n 1.574 * [backup-simplify]: Simplify (log n) into (log n) 1.574 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.574 * [taylor]: Taking taylor expansion of 1.0 in k 1.574 * [backup-simplify]: Simplify 1.0 into 1.0 1.574 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.574 * [taylor]: Taking taylor expansion of k in k 1.574 * [backup-simplify]: Simplify 0 into 0 1.574 * [backup-simplify]: Simplify 1 into 1 1.574 * [backup-simplify]: Simplify (/ 1 1) into 1 1.574 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.575 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.575 * [backup-simplify]: Simplify (- 1) into -1 1.575 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.576 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.577 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.577 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.578 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.579 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.579 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.580 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.580 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.580 * [backup-simplify]: Simplify (- 0) into 0 1.581 * [backup-simplify]: Simplify (+ 0 0) into 0 1.581 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.582 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.582 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.584 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.584 * [taylor]: Taking taylor expansion of 0 in k 1.584 * [backup-simplify]: Simplify 0 into 0 1.584 * [backup-simplify]: Simplify 0 into 0 1.584 * [backup-simplify]: Simplify 0 into 0 1.584 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.585 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.586 * [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 1.587 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.587 * [backup-simplify]: Simplify (- 0) into 0 1.587 * [backup-simplify]: Simplify (+ 0 0) into 0 1.588 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.589 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.590 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.591 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.591 * [taylor]: Taking taylor expansion of 0 in k 1.591 * [backup-simplify]: Simplify 0 into 0 1.591 * [backup-simplify]: Simplify 0 into 0 1.591 * [backup-simplify]: Simplify 0 into 0 1.591 * [backup-simplify]: Simplify 0 into 0 1.592 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.592 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.595 * [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 1.595 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.596 * [backup-simplify]: Simplify (- 0) into 0 1.596 * [backup-simplify]: Simplify (+ 0 0) into 0 1.597 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.597 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.598 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.600 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.600 * [taylor]: Taking taylor expansion of 0 in k 1.600 * [backup-simplify]: Simplify 0 into 0 1.600 * [backup-simplify]: Simplify 0 into 0 1.601 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 1.601 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 1.601 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.601 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.601 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.601 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.601 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.601 * [taylor]: Taking taylor expansion of 0.5 in k 1.601 * [backup-simplify]: Simplify 0.5 into 0.5 1.601 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.601 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.601 * [taylor]: Taking taylor expansion of k in k 1.601 * [backup-simplify]: Simplify 0 into 0 1.601 * [backup-simplify]: Simplify 1 into 1 1.602 * [backup-simplify]: Simplify (/ 1 1) into 1 1.602 * [taylor]: Taking taylor expansion of 1.0 in k 1.602 * [backup-simplify]: Simplify 1.0 into 1.0 1.602 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.602 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.602 * [taylor]: Taking taylor expansion of -2.0 in k 1.602 * [backup-simplify]: Simplify -2.0 into -2.0 1.602 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.602 * [taylor]: Taking taylor expansion of PI in k 1.602 * [backup-simplify]: Simplify PI into PI 1.602 * [taylor]: Taking taylor expansion of n in k 1.602 * [backup-simplify]: Simplify n into n 1.602 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.602 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.602 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.602 * [backup-simplify]: Simplify (+ 1 0) into 1 1.603 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.603 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.603 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.603 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.603 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.603 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.603 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.603 * [taylor]: Taking taylor expansion of 0.5 in n 1.603 * [backup-simplify]: Simplify 0.5 into 0.5 1.603 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.603 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.603 * [taylor]: Taking taylor expansion of k in n 1.603 * [backup-simplify]: Simplify k into k 1.603 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.603 * [taylor]: Taking taylor expansion of 1.0 in n 1.603 * [backup-simplify]: Simplify 1.0 into 1.0 1.603 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.603 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.603 * [taylor]: Taking taylor expansion of -2.0 in n 1.603 * [backup-simplify]: Simplify -2.0 into -2.0 1.603 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.603 * [taylor]: Taking taylor expansion of PI in n 1.603 * [backup-simplify]: Simplify PI into PI 1.603 * [taylor]: Taking taylor expansion of n in n 1.603 * [backup-simplify]: Simplify 0 into 0 1.603 * [backup-simplify]: Simplify 1 into 1 1.603 * [backup-simplify]: Simplify (/ PI 1) into PI 1.604 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.605 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.605 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.605 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.606 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.606 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.607 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.607 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.607 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.607 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.607 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.607 * [taylor]: Taking taylor expansion of 0.5 in n 1.607 * [backup-simplify]: Simplify 0.5 into 0.5 1.607 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.607 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.607 * [taylor]: Taking taylor expansion of k in n 1.607 * [backup-simplify]: Simplify k into k 1.607 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.607 * [taylor]: Taking taylor expansion of 1.0 in n 1.607 * [backup-simplify]: Simplify 1.0 into 1.0 1.607 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.607 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.607 * [taylor]: Taking taylor expansion of -2.0 in n 1.607 * [backup-simplify]: Simplify -2.0 into -2.0 1.607 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.607 * [taylor]: Taking taylor expansion of PI in n 1.607 * [backup-simplify]: Simplify PI into PI 1.607 * [taylor]: Taking taylor expansion of n in n 1.607 * [backup-simplify]: Simplify 0 into 0 1.607 * [backup-simplify]: Simplify 1 into 1 1.608 * [backup-simplify]: Simplify (/ PI 1) into PI 1.608 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.609 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.609 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.609 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.609 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.610 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.611 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.611 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.611 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.611 * [taylor]: Taking taylor expansion of 0.5 in k 1.611 * [backup-simplify]: Simplify 0.5 into 0.5 1.611 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.611 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 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 * [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 (- (log (* -2.0 PI)) (log n)) in k 1.611 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.611 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.611 * [taylor]: Taking taylor expansion of -2.0 in k 1.612 * [backup-simplify]: Simplify -2.0 into -2.0 1.612 * [taylor]: Taking taylor expansion of PI in k 1.612 * [backup-simplify]: Simplify PI into PI 1.612 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.612 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.612 * [taylor]: Taking taylor expansion of (log n) in k 1.612 * [taylor]: Taking taylor expansion of n in k 1.612 * [backup-simplify]: Simplify n into n 1.613 * [backup-simplify]: Simplify (log n) into (log n) 1.613 * [backup-simplify]: Simplify (+ 1 0) into 1 1.613 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.613 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.614 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.615 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.615 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.616 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.617 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.617 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.618 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.618 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.618 * [backup-simplify]: Simplify (+ 0 0) into 0 1.619 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.619 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.620 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.621 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.621 * [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 1.622 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.623 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.624 * [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 1.624 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.625 * [backup-simplify]: Simplify (+ 0 0) into 0 1.625 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.626 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.627 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.628 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.628 * [taylor]: Taking taylor expansion of 0 in k 1.628 * [backup-simplify]: Simplify 0 into 0 1.628 * [backup-simplify]: Simplify 0 into 0 1.628 * [backup-simplify]: Simplify 0 into 0 1.628 * [backup-simplify]: Simplify 0 into 0 1.629 * [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 1.632 * [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 1.633 * [backup-simplify]: Simplify (+ 0 0) into 0 1.633 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) 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 (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.637 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.637 * [taylor]: Taking taylor expansion of 0 in k 1.637 * [backup-simplify]: Simplify 0 into 0 1.637 * [backup-simplify]: Simplify 0 into 0 1.638 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 1.638 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 1) 1.638 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.638 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.638 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.638 * [taylor]: Taking taylor expansion of 2.0 in n 1.638 * [backup-simplify]: Simplify 2.0 into 2.0 1.638 * [taylor]: Taking taylor expansion of (* n PI) in n 1.638 * [taylor]: Taking taylor expansion of n in n 1.638 * [backup-simplify]: Simplify 0 into 0 1.638 * [backup-simplify]: Simplify 1 into 1 1.638 * [taylor]: Taking taylor expansion of PI in n 1.638 * [backup-simplify]: Simplify PI into PI 1.638 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.638 * [taylor]: Taking taylor expansion of 2.0 in n 1.638 * [backup-simplify]: Simplify 2.0 into 2.0 1.638 * [taylor]: Taking taylor expansion of (* n PI) in n 1.638 * [taylor]: Taking taylor expansion of n in n 1.638 * [backup-simplify]: Simplify 0 into 0 1.638 * [backup-simplify]: Simplify 1 into 1 1.638 * [taylor]: Taking taylor expansion of PI in n 1.638 * [backup-simplify]: Simplify PI into PI 1.639 * [backup-simplify]: Simplify (* 0 PI) into 0 1.639 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.639 * [backup-simplify]: Simplify 0 into 0 1.640 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.641 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.641 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.642 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.642 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.642 * [backup-simplify]: Simplify 0 into 0 1.643 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.644 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.644 * [backup-simplify]: Simplify 0 into 0 1.644 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.645 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.645 * [backup-simplify]: Simplify 0 into 0 1.646 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.647 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.647 * [backup-simplify]: Simplify 0 into 0 1.647 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.648 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.648 * [backup-simplify]: Simplify 0 into 0 1.654 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.656 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.656 * [backup-simplify]: Simplify 0 into 0 1.656 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.656 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.656 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.656 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.656 * [taylor]: Taking taylor expansion of 2.0 in n 1.657 * [backup-simplify]: Simplify 2.0 into 2.0 1.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.657 * [taylor]: Taking taylor expansion of PI in n 1.657 * [backup-simplify]: Simplify PI into PI 1.657 * [taylor]: Taking taylor expansion of n in n 1.657 * [backup-simplify]: Simplify 0 into 0 1.657 * [backup-simplify]: Simplify 1 into 1 1.657 * [backup-simplify]: Simplify (/ PI 1) into PI 1.657 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.657 * [taylor]: Taking taylor expansion of 2.0 in n 1.657 * [backup-simplify]: Simplify 2.0 into 2.0 1.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.657 * [taylor]: Taking taylor expansion of PI in n 1.657 * [backup-simplify]: Simplify PI into PI 1.657 * [taylor]: Taking taylor expansion of n in n 1.657 * [backup-simplify]: Simplify 0 into 0 1.657 * [backup-simplify]: Simplify 1 into 1 1.657 * [backup-simplify]: Simplify (/ PI 1) into PI 1.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.658 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.659 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.659 * [backup-simplify]: Simplify 0 into 0 1.659 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.660 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.660 * [backup-simplify]: Simplify 0 into 0 1.661 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.661 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.661 * [backup-simplify]: Simplify 0 into 0 1.662 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.662 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.662 * [backup-simplify]: Simplify 0 into 0 1.663 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.664 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) 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)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.665 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.665 * [backup-simplify]: Simplify 0 into 0 1.666 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.666 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.666 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.666 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.666 * [taylor]: Taking taylor expansion of -2.0 in n 1.666 * [backup-simplify]: Simplify -2.0 into -2.0 1.666 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.666 * [taylor]: Taking taylor expansion of PI in n 1.666 * [backup-simplify]: Simplify PI into PI 1.666 * [taylor]: Taking taylor expansion of n in n 1.666 * [backup-simplify]: Simplify 0 into 0 1.666 * [backup-simplify]: Simplify 1 into 1 1.667 * [backup-simplify]: Simplify (/ PI 1) into PI 1.667 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.667 * [taylor]: Taking taylor expansion of -2.0 in n 1.667 * [backup-simplify]: Simplify -2.0 into -2.0 1.667 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.667 * [taylor]: Taking taylor expansion of PI in n 1.667 * [backup-simplify]: Simplify PI into PI 1.667 * [taylor]: Taking taylor expansion of n in n 1.667 * [backup-simplify]: Simplify 0 into 0 1.667 * [backup-simplify]: Simplify 1 into 1 1.667 * [backup-simplify]: Simplify (/ PI 1) into PI 1.667 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.668 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.668 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.668 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.669 * [backup-simplify]: Simplify 0 into 0 1.669 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.670 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.670 * [backup-simplify]: Simplify 0 into 0 1.670 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.671 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.671 * [backup-simplify]: Simplify 0 into 0 1.671 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.672 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.672 * [backup-simplify]: Simplify 0 into 0 1.673 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.673 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.674 * [backup-simplify]: Simplify 0 into 0 1.674 * [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 1.675 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.675 * [backup-simplify]: Simplify 0 into 0 1.675 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.675 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1) 1.676 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.676 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.676 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.676 * [taylor]: Taking taylor expansion of 2.0 in n 1.676 * [backup-simplify]: Simplify 2.0 into 2.0 1.676 * [taylor]: Taking taylor expansion of (* n PI) in n 1.676 * [taylor]: Taking taylor expansion of n in n 1.676 * [backup-simplify]: Simplify 0 into 0 1.676 * [backup-simplify]: Simplify 1 into 1 1.676 * [taylor]: Taking taylor expansion of PI in n 1.676 * [backup-simplify]: Simplify PI into PI 1.676 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.676 * [taylor]: Taking taylor expansion of 2.0 in n 1.676 * [backup-simplify]: Simplify 2.0 into 2.0 1.676 * [taylor]: Taking taylor expansion of (* n PI) in n 1.676 * [taylor]: Taking taylor expansion of n in n 1.676 * [backup-simplify]: Simplify 0 into 0 1.676 * [backup-simplify]: Simplify 1 into 1 1.676 * [taylor]: Taking taylor expansion of PI in n 1.676 * [backup-simplify]: Simplify PI into PI 1.676 * [backup-simplify]: Simplify (* 0 PI) into 0 1.677 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.677 * [backup-simplify]: Simplify 0 into 0 1.677 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.678 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.679 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.679 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.680 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.680 * [backup-simplify]: Simplify 0 into 0 1.680 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.681 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.681 * [backup-simplify]: Simplify 0 into 0 1.682 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.682 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.682 * [backup-simplify]: Simplify 0 into 0 1.683 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.684 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.684 * [backup-simplify]: Simplify 0 into 0 1.685 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.686 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.686 * [backup-simplify]: Simplify 0 into 0 1.687 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.688 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.688 * [backup-simplify]: Simplify 0 into 0 1.689 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.689 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.689 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.689 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.689 * [taylor]: Taking taylor expansion of 2.0 in n 1.689 * [backup-simplify]: Simplify 2.0 into 2.0 1.689 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.689 * [taylor]: Taking taylor expansion of PI in n 1.689 * [backup-simplify]: Simplify PI into PI 1.689 * [taylor]: Taking taylor expansion of n in n 1.689 * [backup-simplify]: Simplify 0 into 0 1.689 * [backup-simplify]: Simplify 1 into 1 1.689 * [backup-simplify]: Simplify (/ PI 1) into PI 1.689 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.689 * [taylor]: Taking taylor expansion of 2.0 in n 1.689 * [backup-simplify]: Simplify 2.0 into 2.0 1.689 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.689 * [taylor]: Taking taylor expansion of PI in n 1.689 * [backup-simplify]: Simplify PI into PI 1.689 * [taylor]: Taking taylor expansion of n in n 1.689 * [backup-simplify]: Simplify 0 into 0 1.689 * [backup-simplify]: Simplify 1 into 1 1.690 * [backup-simplify]: Simplify (/ PI 1) into PI 1.690 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.690 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.691 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.691 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.691 * [backup-simplify]: Simplify 0 into 0 1.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.692 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.692 * [backup-simplify]: Simplify 0 into 0 1.693 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.694 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.694 * [backup-simplify]: Simplify 0 into 0 1.694 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.695 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.695 * [backup-simplify]: Simplify 0 into 0 1.696 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.696 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.696 * [backup-simplify]: Simplify 0 into 0 1.697 * [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 1.698 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.698 * [backup-simplify]: Simplify 0 into 0 1.698 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.699 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.699 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.699 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.699 * [taylor]: Taking taylor expansion of -2.0 in n 1.699 * [backup-simplify]: Simplify -2.0 into -2.0 1.699 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.699 * [taylor]: Taking taylor expansion of PI in n 1.699 * [backup-simplify]: Simplify PI into PI 1.699 * [taylor]: Taking taylor expansion of n in n 1.699 * [backup-simplify]: Simplify 0 into 0 1.699 * [backup-simplify]: Simplify 1 into 1 1.699 * [backup-simplify]: Simplify (/ PI 1) into PI 1.699 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.699 * [taylor]: Taking taylor expansion of -2.0 in n 1.699 * [backup-simplify]: Simplify -2.0 into -2.0 1.699 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.699 * [taylor]: Taking taylor expansion of PI in n 1.699 * [backup-simplify]: Simplify PI into PI 1.699 * [taylor]: Taking taylor expansion of n in n 1.699 * [backup-simplify]: Simplify 0 into 0 1.699 * [backup-simplify]: Simplify 1 into 1 1.699 * [backup-simplify]: Simplify (/ PI 1) into PI 1.700 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.700 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.701 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.701 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.701 * [backup-simplify]: Simplify 0 into 0 1.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.702 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.702 * [backup-simplify]: Simplify 0 into 0 1.703 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.703 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.703 * [backup-simplify]: Simplify 0 into 0 1.704 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.705 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.705 * [backup-simplify]: Simplify 0 into 0 1.706 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.707 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.707 * [backup-simplify]: Simplify 0 into 0 1.708 * [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 1.708 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.708 * [backup-simplify]: Simplify 0 into 0 1.709 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.709 * * * [progress]: simplifying candidates 1.711 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.125 (* (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)))))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 1.711 * [simplify]: Sending expressions to egg_math: (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ h2 h0)) (pow (* (* h0 PI) h1) (/ h3 h0)) (pow (* (* h0 PI) h1) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* h0 PI) h1) (sqrt (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) 1) (pow (* (* h0 PI) h1) (- h2 h3)) (pow (* h0 PI) (/ (- h2 h3) h0)) (pow h1 (/ (- h2 h3) h0)) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (exp (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ h2 h0)) (pow (* (* h0 PI) h1) (/ h3 h0)) (pow (* (* h0 PI) h1) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* h0 PI) h1) (sqrt (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) 1) (pow (* (* h0 PI) h1) (- h2 h3)) (pow (* h0 PI) (/ (- h2 h3) h0)) (pow h1 (/ (- h2 h3) h0)) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (exp (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (* (* h0 PI) h1) (* (* h0 PI) h1) (+ (+ (log h0) (log PI)) (log h1)) (+ (log (* h0 PI)) (log h1)) (log (* (* h0 PI) h1)) (exp (* (* h0 PI) h1)) (* (* (* (* h0 h0) h0) (* (* PI PI) PI)) (* (* h1 h1) h1)) (* (* (* (* h0 PI) (* h0 PI)) (* h0 PI)) (* (* h1 h1) h1)) (* (cbrt (* (* h0 PI) h1)) (cbrt (* (* h0 PI) h1))) (cbrt (* (* h0 PI) h1)) (* (* (* (* h0 PI) h1) (* (* h0 PI) h1)) (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (* (* h0 PI) (sqrt h1)) (* (* h0 PI) 1) (* PI h1) (* (* h0 PI) h1) (* (* h0 PI) h1) (+ (+ (log h0) (log PI)) (log h1)) (+ (log (* h0 PI)) (log h1)) (log (* (* h0 PI) h1)) (exp (* (* h0 PI) h1)) (* (* (* (* h0 h0) h0) (* (* PI PI) PI)) (* (* h1 h1) h1)) (* (* (* (* h0 PI) (* h0 PI)) (* h0 PI)) (* (* h1 h1) h1)) (* (cbrt (* (* h0 PI) h1)) (cbrt (* (* h0 PI) h1))) (cbrt (* (* h0 PI) h1)) (* (* (* (* h0 PI) h1) (* (* h0 PI) h1)) (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (* (* h0 PI) (sqrt h1)) (* (* h0 PI) 1) (* PI h1) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) 1.717 * * [simplify]: iteration 0 : 399 enodes (cost 798 ) 1.724 * * [simplify]: iteration 1 : 1625 enodes (cost 738 ) 1.756 * * [simplify]: iteration 2 : 5001 enodes (cost 694 ) 1.760 * * * [progress]: adding candidates to table 2.111 * * [progress]: iteration 3 / 4 2.111 * * * [progress]: picking best candidate 2.130 * * * * [pick]: Picked # 2.130 * * * [progress]: localizing error 2.155 * * * [progress]: generating rewritten candidates 2.155 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1) 2.257 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 2.277 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 1 2) 2.278 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1 1 2 2) 2.283 * * * [progress]: generating series expansions 2.283 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1) 2.284 * [backup-simplify]: Simplify (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 2.284 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.284 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.284 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.284 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.284 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.284 * [taylor]: Taking taylor expansion of 0.5 in k 2.284 * [backup-simplify]: Simplify 0.5 into 0.5 2.284 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.284 * [taylor]: Taking taylor expansion of 1.0 in k 2.284 * [backup-simplify]: Simplify 1.0 into 1.0 2.284 * [taylor]: Taking taylor expansion of k in k 2.284 * [backup-simplify]: Simplify 0 into 0 2.284 * [backup-simplify]: Simplify 1 into 1 2.284 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.284 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.284 * [taylor]: Taking taylor expansion of 2.0 in k 2.284 * [backup-simplify]: Simplify 2.0 into 2.0 2.284 * [taylor]: Taking taylor expansion of (* n PI) in k 2.284 * [taylor]: Taking taylor expansion of n in k 2.284 * [backup-simplify]: Simplify n into n 2.284 * [taylor]: Taking taylor expansion of PI in k 2.284 * [backup-simplify]: Simplify PI into PI 2.284 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.284 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.284 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.284 * [backup-simplify]: Simplify (- 0) into 0 2.285 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.285 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.285 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.285 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.285 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.285 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.285 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.285 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.285 * [taylor]: Taking taylor expansion of 0.5 in n 2.285 * [backup-simplify]: Simplify 0.5 into 0.5 2.285 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.285 * [taylor]: Taking taylor expansion of 1.0 in n 2.285 * [backup-simplify]: Simplify 1.0 into 1.0 2.285 * [taylor]: Taking taylor expansion of k in n 2.285 * [backup-simplify]: Simplify k into k 2.285 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.285 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.285 * [taylor]: Taking taylor expansion of 2.0 in n 2.285 * [backup-simplify]: Simplify 2.0 into 2.0 2.285 * [taylor]: Taking taylor expansion of (* n PI) in n 2.285 * [taylor]: Taking taylor expansion of n in n 2.285 * [backup-simplify]: Simplify 0 into 0 2.285 * [backup-simplify]: Simplify 1 into 1 2.285 * [taylor]: Taking taylor expansion of PI in n 2.285 * [backup-simplify]: Simplify PI into PI 2.286 * [backup-simplify]: Simplify (* 0 PI) into 0 2.286 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.287 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.288 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.288 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.289 * [backup-simplify]: Simplify (- k) into (- k) 2.289 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.289 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.289 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.290 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.291 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.291 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.291 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.291 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.291 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.291 * [taylor]: Taking taylor expansion of 0.5 in n 2.291 * [backup-simplify]: Simplify 0.5 into 0.5 2.291 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.291 * [taylor]: Taking taylor expansion of 1.0 in n 2.291 * [backup-simplify]: Simplify 1.0 into 1.0 2.291 * [taylor]: Taking taylor expansion of k in n 2.291 * [backup-simplify]: Simplify k into k 2.291 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.291 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.291 * [taylor]: Taking taylor expansion of 2.0 in n 2.291 * [backup-simplify]: Simplify 2.0 into 2.0 2.291 * [taylor]: Taking taylor expansion of (* n PI) in n 2.291 * [taylor]: Taking taylor expansion of n in n 2.291 * [backup-simplify]: Simplify 0 into 0 2.291 * [backup-simplify]: Simplify 1 into 1 2.291 * [taylor]: Taking taylor expansion of PI in n 2.291 * [backup-simplify]: Simplify PI into PI 2.291 * [backup-simplify]: Simplify (* 0 PI) into 0 2.292 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.293 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.293 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.294 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.294 * [backup-simplify]: Simplify (- k) into (- k) 2.294 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.294 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.295 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.296 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.296 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.296 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.296 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.296 * [taylor]: Taking taylor expansion of 0.5 in k 2.296 * [backup-simplify]: Simplify 0.5 into 0.5 2.296 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.297 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.297 * [taylor]: Taking taylor expansion of 1.0 in k 2.297 * [backup-simplify]: Simplify 1.0 into 1.0 2.297 * [taylor]: Taking taylor expansion of k in k 2.297 * [backup-simplify]: Simplify 0 into 0 2.297 * [backup-simplify]: Simplify 1 into 1 2.297 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.297 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.297 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.297 * [taylor]: Taking taylor expansion of 2.0 in k 2.297 * [backup-simplify]: Simplify 2.0 into 2.0 2.297 * [taylor]: Taking taylor expansion of PI in k 2.297 * [backup-simplify]: Simplify PI into PI 2.297 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.298 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.298 * [taylor]: Taking taylor expansion of (log n) in k 2.298 * [taylor]: Taking taylor expansion of n in k 2.298 * [backup-simplify]: Simplify n into n 2.298 * [backup-simplify]: Simplify (log n) into (log n) 2.298 * [backup-simplify]: Simplify (- 0) into 0 2.298 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.299 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.300 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.300 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 2.301 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.302 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.302 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.303 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.304 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.304 * [backup-simplify]: Simplify (- 0) into 0 2.304 * [backup-simplify]: Simplify (+ 0 0) into 0 2.305 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 2.305 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.306 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.307 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.307 * [taylor]: Taking taylor expansion of 0 in k 2.307 * [backup-simplify]: Simplify 0 into 0 2.307 * [backup-simplify]: Simplify 0 into 0 2.308 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.309 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.309 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.310 * [backup-simplify]: Simplify (+ 0 0) into 0 2.310 * [backup-simplify]: Simplify (- 1) into -1 2.310 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.311 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.312 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2.314 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 2.316 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 2.317 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.317 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.319 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.319 * [backup-simplify]: Simplify (- 0) into 0 2.319 * [backup-simplify]: Simplify (+ 0 0) into 0 2.320 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.321 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.321 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.323 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.323 * [taylor]: Taking taylor expansion of 0 in k 2.323 * [backup-simplify]: Simplify 0 into 0 2.323 * [backup-simplify]: Simplify 0 into 0 2.323 * [backup-simplify]: Simplify 0 into 0 2.324 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.326 * [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 2.327 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.327 * [backup-simplify]: Simplify (+ 0 0) into 0 2.328 * [backup-simplify]: Simplify (- 0) into 0 2.328 * [backup-simplify]: Simplify (+ 0 0) into 0 2.329 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.331 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.338 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.341 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.347 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.347 * [backup-simplify]: Simplify (pow (* (* (* 2.0 PI) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 2.347 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.348 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.348 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.348 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.348 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.348 * [taylor]: Taking taylor expansion of 0.5 in k 2.348 * [backup-simplify]: Simplify 0.5 into 0.5 2.348 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.348 * [taylor]: Taking taylor expansion of 1.0 in k 2.348 * [backup-simplify]: Simplify 1.0 into 1.0 2.348 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.348 * [taylor]: Taking taylor expansion of k in k 2.348 * [backup-simplify]: Simplify 0 into 0 2.348 * [backup-simplify]: Simplify 1 into 1 2.348 * [backup-simplify]: Simplify (/ 1 1) into 1 2.348 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.348 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.348 * [taylor]: Taking taylor expansion of 2.0 in k 2.348 * [backup-simplify]: Simplify 2.0 into 2.0 2.348 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.348 * [taylor]: Taking taylor expansion of PI in k 2.348 * [backup-simplify]: Simplify PI into PI 2.348 * [taylor]: Taking taylor expansion of n in k 2.348 * [backup-simplify]: Simplify n into n 2.348 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.349 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.349 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.349 * [backup-simplify]: Simplify (- 1) into -1 2.349 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.349 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.349 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.350 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.350 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.350 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.350 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.350 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.350 * [taylor]: Taking taylor expansion of 0.5 in n 2.350 * [backup-simplify]: Simplify 0.5 into 0.5 2.350 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.350 * [taylor]: Taking taylor expansion of 1.0 in n 2.350 * [backup-simplify]: Simplify 1.0 into 1.0 2.350 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.350 * [taylor]: Taking taylor expansion of k in n 2.350 * [backup-simplify]: Simplify k into k 2.350 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.350 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.350 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.350 * [taylor]: Taking taylor expansion of 2.0 in n 2.350 * [backup-simplify]: Simplify 2.0 into 2.0 2.350 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.350 * [taylor]: Taking taylor expansion of PI in n 2.350 * [backup-simplify]: Simplify PI into PI 2.350 * [taylor]: Taking taylor expansion of n in n 2.350 * [backup-simplify]: Simplify 0 into 0 2.350 * [backup-simplify]: Simplify 1 into 1 2.350 * [backup-simplify]: Simplify (/ PI 1) into PI 2.351 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.351 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.351 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.351 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.351 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.352 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.353 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.354 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.354 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.354 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.354 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.354 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.354 * [taylor]: Taking taylor expansion of 0.5 in n 2.354 * [backup-simplify]: Simplify 0.5 into 0.5 2.354 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.354 * [taylor]: Taking taylor expansion of 1.0 in n 2.354 * [backup-simplify]: Simplify 1.0 into 1.0 2.354 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.354 * [taylor]: Taking taylor expansion of k in n 2.354 * [backup-simplify]: Simplify k into k 2.354 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.354 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.354 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.354 * [taylor]: Taking taylor expansion of 2.0 in n 2.354 * [backup-simplify]: Simplify 2.0 into 2.0 2.354 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.354 * [taylor]: Taking taylor expansion of PI in n 2.354 * [backup-simplify]: Simplify PI into PI 2.354 * [taylor]: Taking taylor expansion of n in n 2.354 * [backup-simplify]: Simplify 0 into 0 2.354 * [backup-simplify]: Simplify 1 into 1 2.354 * [backup-simplify]: Simplify (/ PI 1) into PI 2.355 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.355 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.355 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.355 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.355 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.356 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.357 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.358 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.358 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.358 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.358 * [taylor]: Taking taylor expansion of 0.5 in k 2.358 * [backup-simplify]: Simplify 0.5 into 0.5 2.358 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.358 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.358 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.358 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.358 * [taylor]: Taking taylor expansion of 2.0 in k 2.358 * [backup-simplify]: Simplify 2.0 into 2.0 2.358 * [taylor]: Taking taylor expansion of PI in k 2.358 * [backup-simplify]: Simplify PI into PI 2.358 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.359 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.359 * [taylor]: Taking taylor expansion of (log n) in k 2.359 * [taylor]: Taking taylor expansion of n in k 2.359 * [backup-simplify]: Simplify n into n 2.359 * [backup-simplify]: Simplify (log n) into (log n) 2.359 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.359 * [taylor]: Taking taylor expansion of 1.0 in k 2.359 * [backup-simplify]: Simplify 1.0 into 1.0 2.359 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.359 * [taylor]: Taking taylor expansion of k in k 2.359 * [backup-simplify]: Simplify 0 into 0 2.359 * [backup-simplify]: Simplify 1 into 1 2.360 * [backup-simplify]: Simplify (/ 1 1) into 1 2.360 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.360 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.360 * [backup-simplify]: Simplify (- 1) into -1 2.361 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.361 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.362 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.363 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.363 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.364 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.364 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.365 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.365 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.366 * [backup-simplify]: Simplify (- 0) into 0 2.366 * [backup-simplify]: Simplify (+ 0 0) into 0 2.366 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.367 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.368 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.369 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.369 * [taylor]: Taking taylor expansion of 0 in k 2.369 * [backup-simplify]: Simplify 0 into 0 2.369 * [backup-simplify]: Simplify 0 into 0 2.369 * [backup-simplify]: Simplify 0 into 0 2.370 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.370 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.372 * [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 2.372 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.372 * [backup-simplify]: Simplify (- 0) into 0 2.372 * [backup-simplify]: Simplify (+ 0 0) into 0 2.373 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.374 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.375 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.376 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.376 * [taylor]: Taking taylor expansion of 0 in k 2.376 * [backup-simplify]: Simplify 0 into 0 2.376 * [backup-simplify]: Simplify 0 into 0 2.376 * [backup-simplify]: Simplify 0 into 0 2.376 * [backup-simplify]: Simplify 0 into 0 2.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.378 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.380 * [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 2.381 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.381 * [backup-simplify]: Simplify (- 0) into 0 2.381 * [backup-simplify]: Simplify (+ 0 0) into 0 2.382 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.383 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.384 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.385 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.385 * [taylor]: Taking taylor expansion of 0 in k 2.385 * [backup-simplify]: Simplify 0 into 0 2.385 * [backup-simplify]: Simplify 0 into 0 2.386 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.387 * [backup-simplify]: Simplify (pow (* (* (* 2.0 PI) (* (cbrt (/ 1 (- n))) (cbrt (/ 1 (- n))))) (cbrt (/ 1 (- n)))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) 2.387 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.387 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.387 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in k 2.387 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in k 2.387 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.387 * [taylor]: Taking taylor expansion of 0.5 in k 2.387 * [backup-simplify]: Simplify 0.5 into 0.5 2.387 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.387 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.387 * [taylor]: Taking taylor expansion of k in k 2.387 * [backup-simplify]: Simplify 0 into 0 2.387 * [backup-simplify]: Simplify 1 into 1 2.387 * [backup-simplify]: Simplify (/ 1 1) into 1 2.387 * [taylor]: Taking taylor expansion of 1.0 in k 2.387 * [backup-simplify]: Simplify 1.0 into 1.0 2.387 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in k 2.387 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in k 2.387 * [taylor]: Taking taylor expansion of 2.0 in k 2.388 * [backup-simplify]: Simplify 2.0 into 2.0 2.388 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in k 2.388 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in k 2.388 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in k 2.388 * [taylor]: Taking taylor expansion of (cbrt -1) in k 2.388 * [taylor]: Taking taylor expansion of -1 in k 2.388 * [backup-simplify]: Simplify -1 into -1 2.388 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.388 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.389 * [taylor]: Taking taylor expansion of PI in k 2.389 * [backup-simplify]: Simplify PI into PI 2.389 * [taylor]: Taking taylor expansion of n in k 2.389 * [backup-simplify]: Simplify n into n 2.389 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 2.391 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 2.392 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 2.392 * [backup-simplify]: Simplify (/ (* -1 PI) n) into (* -1 (/ PI n)) 2.392 * [backup-simplify]: Simplify (* 2.0 (* -1 (/ PI n))) into (* -2.0 (/ PI n)) 2.392 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.392 * [backup-simplify]: Simplify (+ 1 0) into 1 2.392 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.393 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.394 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.394 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.394 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 2.394 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 2.394 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.394 * [taylor]: Taking taylor expansion of 0.5 in n 2.394 * [backup-simplify]: Simplify 0.5 into 0.5 2.394 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.394 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.394 * [taylor]: Taking taylor expansion of k in n 2.394 * [backup-simplify]: Simplify k into k 2.394 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.394 * [taylor]: Taking taylor expansion of 1.0 in n 2.394 * [backup-simplify]: Simplify 1.0 into 1.0 2.394 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 2.394 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 2.394 * [taylor]: Taking taylor expansion of 2.0 in n 2.394 * [backup-simplify]: Simplify 2.0 into 2.0 2.394 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 2.394 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 2.394 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 2.394 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.394 * [taylor]: Taking taylor expansion of -1 in n 2.394 * [backup-simplify]: Simplify -1 into -1 2.394 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.395 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.395 * [taylor]: Taking taylor expansion of PI in n 2.395 * [backup-simplify]: Simplify PI into PI 2.395 * [taylor]: Taking taylor expansion of n in n 2.395 * [backup-simplify]: Simplify 0 into 0 2.395 * [backup-simplify]: Simplify 1 into 1 2.396 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 2.397 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 2.398 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 2.398 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 2.399 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 2.400 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.400 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.400 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.401 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.402 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.402 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.402 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.402 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 2.402 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 2.402 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.402 * [taylor]: Taking taylor expansion of 0.5 in n 2.402 * [backup-simplify]: Simplify 0.5 into 0.5 2.402 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.402 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.402 * [taylor]: Taking taylor expansion of k in n 2.402 * [backup-simplify]: Simplify k into k 2.402 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.403 * [taylor]: Taking taylor expansion of 1.0 in n 2.403 * [backup-simplify]: Simplify 1.0 into 1.0 2.403 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 2.403 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 2.403 * [taylor]: Taking taylor expansion of 2.0 in n 2.403 * [backup-simplify]: Simplify 2.0 into 2.0 2.403 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 2.403 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 2.403 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 2.403 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.403 * [taylor]: Taking taylor expansion of -1 in n 2.403 * [backup-simplify]: Simplify -1 into -1 2.403 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.403 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.403 * [taylor]: Taking taylor expansion of PI in n 2.403 * [backup-simplify]: Simplify PI into PI 2.403 * [taylor]: Taking taylor expansion of n in n 2.403 * [backup-simplify]: Simplify 0 into 0 2.403 * [backup-simplify]: Simplify 1 into 1 2.404 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 2.405 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 2.406 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 2.407 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 2.408 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 2.408 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.408 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.408 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.409 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.410 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.411 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.411 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.411 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.411 * [taylor]: Taking taylor expansion of 0.5 in k 2.411 * [backup-simplify]: Simplify 0.5 into 0.5 2.411 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.411 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.411 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.411 * [taylor]: Taking taylor expansion of k in k 2.411 * [backup-simplify]: Simplify 0 into 0 2.411 * [backup-simplify]: Simplify 1 into 1 2.411 * [backup-simplify]: Simplify (/ 1 1) into 1 2.411 * [taylor]: Taking taylor expansion of 1.0 in k 2.411 * [backup-simplify]: Simplify 1.0 into 1.0 2.411 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.411 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.411 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.411 * [taylor]: Taking taylor expansion of -2.0 in k 2.411 * [backup-simplify]: Simplify -2.0 into -2.0 2.411 * [taylor]: Taking taylor expansion of PI in k 2.411 * [backup-simplify]: Simplify PI into PI 2.412 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.412 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.412 * [taylor]: Taking taylor expansion of (log n) in k 2.412 * [taylor]: Taking taylor expansion of n in k 2.412 * [backup-simplify]: Simplify n into n 2.412 * [backup-simplify]: Simplify (log n) into (log n) 2.413 * [backup-simplify]: Simplify (+ 1 0) into 1 2.413 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.413 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.414 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.415 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.415 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.416 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.416 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (cbrt -1))) into 0 2.417 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow (cbrt -1) 2))) into 0 2.418 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (* 0 PI)) into 0 2.418 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)))) into 0 2.419 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* -1 PI))) into 0 2.420 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.420 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.420 * [backup-simplify]: Simplify (+ 0 0) into 0 2.420 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.421 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.422 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.423 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.423 * [taylor]: Taking taylor expansion of 0 in k 2.423 * [backup-simplify]: Simplify 0 into 0 2.423 * [backup-simplify]: Simplify 0 into 0 2.423 * [backup-simplify]: Simplify 0 into 0 2.424 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.425 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (cbrt -1)))) into 0 2.426 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2)))) into 0 2.426 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (* 0 PI))) into 0 2.427 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.434 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* -1 PI)))) into 0 2.436 * [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 2.436 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.436 * [backup-simplify]: Simplify (+ 0 0) into 0 2.437 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.437 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.438 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.440 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.440 * [taylor]: Taking taylor expansion of 0 in k 2.440 * [backup-simplify]: Simplify 0 into 0 2.440 * [backup-simplify]: Simplify 0 into 0 2.440 * [backup-simplify]: Simplify 0 into 0 2.440 * [backup-simplify]: Simplify 0 into 0 2.441 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.441 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1))))) into 0 2.442 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2))))) into 0 2.443 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.444 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.444 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* -1 PI))))) into 0 2.447 * [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 2.447 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.448 * [backup-simplify]: Simplify (+ 0 0) into 0 2.448 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.449 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.450 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.452 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.452 * [taylor]: Taking taylor expansion of 0 in k 2.452 * [backup-simplify]: Simplify 0 into 0 2.452 * [backup-simplify]: Simplify 0 into 0 2.453 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.453 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 2.453 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 2.453 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.453 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.453 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.453 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.453 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.453 * [taylor]: Taking taylor expansion of 0.5 in k 2.453 * [backup-simplify]: Simplify 0.5 into 0.5 2.454 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.454 * [taylor]: Taking taylor expansion of 1.0 in k 2.454 * [backup-simplify]: Simplify 1.0 into 1.0 2.454 * [taylor]: Taking taylor expansion of k in k 2.454 * [backup-simplify]: Simplify 0 into 0 2.454 * [backup-simplify]: Simplify 1 into 1 2.454 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.454 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.454 * [taylor]: Taking taylor expansion of 2.0 in k 2.454 * [backup-simplify]: Simplify 2.0 into 2.0 2.454 * [taylor]: Taking taylor expansion of (* n PI) in k 2.454 * [taylor]: Taking taylor expansion of n in k 2.454 * [backup-simplify]: Simplify n into n 2.454 * [taylor]: Taking taylor expansion of PI in k 2.454 * [backup-simplify]: Simplify PI into PI 2.454 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.454 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.454 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.454 * [backup-simplify]: Simplify (- 0) into 0 2.454 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.455 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.455 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.455 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.455 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.455 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.455 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.455 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.455 * [taylor]: Taking taylor expansion of 0.5 in n 2.455 * [backup-simplify]: Simplify 0.5 into 0.5 2.455 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.455 * [taylor]: Taking taylor expansion of 1.0 in n 2.455 * [backup-simplify]: Simplify 1.0 into 1.0 2.455 * [taylor]: Taking taylor expansion of k in n 2.455 * [backup-simplify]: Simplify k into k 2.455 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.455 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.455 * [taylor]: Taking taylor expansion of 2.0 in n 2.455 * [backup-simplify]: Simplify 2.0 into 2.0 2.455 * [taylor]: Taking taylor expansion of (* n PI) in n 2.455 * [taylor]: Taking taylor expansion of n in n 2.455 * [backup-simplify]: Simplify 0 into 0 2.455 * [backup-simplify]: Simplify 1 into 1 2.455 * [taylor]: Taking taylor expansion of PI in n 2.455 * [backup-simplify]: Simplify PI into PI 2.455 * [backup-simplify]: Simplify (* 0 PI) into 0 2.456 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.456 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.457 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.458 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.458 * [backup-simplify]: Simplify (- k) into (- k) 2.458 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.458 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.459 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.460 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.461 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.461 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.461 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.461 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.461 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.461 * [taylor]: Taking taylor expansion of 0.5 in n 2.461 * [backup-simplify]: Simplify 0.5 into 0.5 2.461 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.461 * [taylor]: Taking taylor expansion of 1.0 in n 2.461 * [backup-simplify]: Simplify 1.0 into 1.0 2.461 * [taylor]: Taking taylor expansion of k in n 2.461 * [backup-simplify]: Simplify k into k 2.461 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.461 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.461 * [taylor]: Taking taylor expansion of 2.0 in n 2.461 * [backup-simplify]: Simplify 2.0 into 2.0 2.461 * [taylor]: Taking taylor expansion of (* n PI) in n 2.461 * [taylor]: Taking taylor expansion of n in n 2.461 * [backup-simplify]: Simplify 0 into 0 2.461 * [backup-simplify]: Simplify 1 into 1 2.461 * [taylor]: Taking taylor expansion of PI in n 2.461 * [backup-simplify]: Simplify PI into PI 2.461 * [backup-simplify]: Simplify (* 0 PI) into 0 2.462 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.463 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.464 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.464 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.464 * [backup-simplify]: Simplify (- k) into (- k) 2.464 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.464 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.465 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.466 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.466 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.466 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.467 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.467 * [taylor]: Taking taylor expansion of 0.5 in k 2.467 * [backup-simplify]: Simplify 0.5 into 0.5 2.467 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.467 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.467 * [taylor]: Taking taylor expansion of 1.0 in k 2.467 * [backup-simplify]: Simplify 1.0 into 1.0 2.467 * [taylor]: Taking taylor expansion of k in k 2.467 * [backup-simplify]: Simplify 0 into 0 2.467 * [backup-simplify]: Simplify 1 into 1 2.467 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.467 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.467 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.467 * [taylor]: Taking taylor expansion of 2.0 in k 2.467 * [backup-simplify]: Simplify 2.0 into 2.0 2.467 * [taylor]: Taking taylor expansion of PI in k 2.467 * [backup-simplify]: Simplify PI into PI 2.467 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.468 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.468 * [taylor]: Taking taylor expansion of (log n) in k 2.468 * [taylor]: Taking taylor expansion of n in k 2.468 * [backup-simplify]: Simplify n into n 2.468 * [backup-simplify]: Simplify (log n) into (log n) 2.468 * [backup-simplify]: Simplify (- 0) into 0 2.468 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.469 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.470 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.470 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 2.471 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.471 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.472 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.473 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.474 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.474 * [backup-simplify]: Simplify (- 0) into 0 2.474 * [backup-simplify]: Simplify (+ 0 0) into 0 2.474 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 2.475 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.476 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.477 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.477 * [taylor]: Taking taylor expansion of 0 in k 2.477 * [backup-simplify]: Simplify 0 into 0 2.477 * [backup-simplify]: Simplify 0 into 0 2.477 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.478 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.479 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.479 * [backup-simplify]: Simplify (+ 0 0) into 0 2.479 * [backup-simplify]: Simplify (- 1) into -1 2.480 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.480 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.482 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2.483 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 2.485 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 2.486 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.487 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.488 * [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 2.489 * [backup-simplify]: Simplify (- 0) into 0 2.489 * [backup-simplify]: Simplify (+ 0 0) into 0 2.489 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.490 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.491 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.492 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.492 * [taylor]: Taking taylor expansion of 0 in k 2.492 * [backup-simplify]: Simplify 0 into 0 2.492 * [backup-simplify]: Simplify 0 into 0 2.492 * [backup-simplify]: Simplify 0 into 0 2.493 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.495 * [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 2.496 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.496 * [backup-simplify]: Simplify (+ 0 0) into 0 2.496 * [backup-simplify]: Simplify (- 0) into 0 2.496 * [backup-simplify]: Simplify (+ 0 0) into 0 2.497 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.499 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.501 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.505 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.510 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.511 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 2.511 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.511 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.511 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.511 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.511 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.511 * [taylor]: Taking taylor expansion of 0.5 in k 2.511 * [backup-simplify]: Simplify 0.5 into 0.5 2.511 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.511 * [taylor]: Taking taylor expansion of 1.0 in k 2.511 * [backup-simplify]: Simplify 1.0 into 1.0 2.511 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.511 * [taylor]: Taking taylor expansion of k in k 2.511 * [backup-simplify]: Simplify 0 into 0 2.511 * [backup-simplify]: Simplify 1 into 1 2.512 * [backup-simplify]: Simplify (/ 1 1) into 1 2.512 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.512 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.512 * [taylor]: Taking taylor expansion of 2.0 in k 2.512 * [backup-simplify]: Simplify 2.0 into 2.0 2.512 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.512 * [taylor]: Taking taylor expansion of PI in k 2.512 * [backup-simplify]: Simplify PI into PI 2.512 * [taylor]: Taking taylor expansion of n in k 2.512 * [backup-simplify]: Simplify n into n 2.512 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.512 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.512 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.512 * [backup-simplify]: Simplify (- 1) into -1 2.512 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.513 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.513 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.513 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.513 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.513 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.513 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.513 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.513 * [taylor]: Taking taylor expansion of 0.5 in n 2.513 * [backup-simplify]: Simplify 0.5 into 0.5 2.513 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.513 * [taylor]: Taking taylor expansion of 1.0 in n 2.513 * [backup-simplify]: Simplify 1.0 into 1.0 2.513 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.513 * [taylor]: Taking taylor expansion of k in n 2.513 * [backup-simplify]: Simplify k into k 2.513 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.513 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.513 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.513 * [taylor]: Taking taylor expansion of 2.0 in n 2.513 * [backup-simplify]: Simplify 2.0 into 2.0 2.513 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.513 * [taylor]: Taking taylor expansion of PI in n 2.513 * [backup-simplify]: Simplify PI into PI 2.513 * [taylor]: Taking taylor expansion of n in n 2.513 * [backup-simplify]: Simplify 0 into 0 2.513 * [backup-simplify]: Simplify 1 into 1 2.513 * [backup-simplify]: Simplify (/ PI 1) into PI 2.514 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.514 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.514 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.514 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.515 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.515 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.516 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.517 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.517 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.517 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.517 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.517 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.517 * [taylor]: Taking taylor expansion of 0.5 in n 2.517 * [backup-simplify]: Simplify 0.5 into 0.5 2.517 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.517 * [taylor]: Taking taylor expansion of 1.0 in n 2.517 * [backup-simplify]: Simplify 1.0 into 1.0 2.517 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.517 * [taylor]: Taking taylor expansion of k in n 2.517 * [backup-simplify]: Simplify k into k 2.517 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.517 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.517 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.517 * [taylor]: Taking taylor expansion of 2.0 in n 2.517 * [backup-simplify]: Simplify 2.0 into 2.0 2.517 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.517 * [taylor]: Taking taylor expansion of PI in n 2.517 * [backup-simplify]: Simplify PI into PI 2.517 * [taylor]: Taking taylor expansion of n in n 2.517 * [backup-simplify]: Simplify 0 into 0 2.517 * [backup-simplify]: Simplify 1 into 1 2.517 * [backup-simplify]: Simplify (/ PI 1) into PI 2.518 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.518 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.518 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.518 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.519 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.519 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.520 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.521 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.521 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.521 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.521 * [taylor]: Taking taylor expansion of 0.5 in k 2.521 * [backup-simplify]: Simplify 0.5 into 0.5 2.521 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.521 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.521 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.521 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.521 * [taylor]: Taking taylor expansion of 2.0 in k 2.521 * [backup-simplify]: Simplify 2.0 into 2.0 2.521 * [taylor]: Taking taylor expansion of PI in k 2.521 * [backup-simplify]: Simplify PI into PI 2.521 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.522 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.522 * [taylor]: Taking taylor expansion of (log n) in k 2.522 * [taylor]: Taking taylor expansion of n in k 2.522 * [backup-simplify]: Simplify n into n 2.522 * [backup-simplify]: Simplify (log n) into (log n) 2.522 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.522 * [taylor]: Taking taylor expansion of 1.0 in k 2.522 * [backup-simplify]: Simplify 1.0 into 1.0 2.522 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.522 * [taylor]: Taking taylor expansion of k in k 2.522 * [backup-simplify]: Simplify 0 into 0 2.522 * [backup-simplify]: Simplify 1 into 1 2.522 * [backup-simplify]: Simplify (/ 1 1) into 1 2.522 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.529 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.530 * [backup-simplify]: Simplify (- 1) into -1 2.530 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.531 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.531 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.532 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.533 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.533 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.534 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.535 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.535 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.535 * [backup-simplify]: Simplify (- 0) into 0 2.535 * [backup-simplify]: Simplify (+ 0 0) into 0 2.536 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.536 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.537 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.538 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.538 * [taylor]: Taking taylor expansion of 0 in k 2.538 * [backup-simplify]: Simplify 0 into 0 2.538 * [backup-simplify]: Simplify 0 into 0 2.538 * [backup-simplify]: Simplify 0 into 0 2.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.539 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.541 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.541 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.541 * [backup-simplify]: Simplify (- 0) into 0 2.542 * [backup-simplify]: Simplify (+ 0 0) into 0 2.542 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.543 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.544 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.545 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.545 * [taylor]: Taking taylor expansion of 0 in k 2.545 * [backup-simplify]: Simplify 0 into 0 2.545 * [backup-simplify]: Simplify 0 into 0 2.545 * [backup-simplify]: Simplify 0 into 0 2.545 * [backup-simplify]: Simplify 0 into 0 2.546 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.546 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.549 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 2.549 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.550 * [backup-simplify]: Simplify (- 0) into 0 2.550 * [backup-simplify]: Simplify (+ 0 0) into 0 2.551 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.551 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.553 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.554 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.554 * [taylor]: Taking taylor expansion of 0 in k 2.554 * [backup-simplify]: Simplify 0 into 0 2.554 * [backup-simplify]: Simplify 0 into 0 2.555 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.555 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 2.555 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.555 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.555 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.555 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.556 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.556 * [taylor]: Taking taylor expansion of 0.5 in k 2.556 * [backup-simplify]: Simplify 0.5 into 0.5 2.556 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.556 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.556 * [taylor]: Taking taylor expansion of k in k 2.556 * [backup-simplify]: Simplify 0 into 0 2.556 * [backup-simplify]: Simplify 1 into 1 2.556 * [backup-simplify]: Simplify (/ 1 1) into 1 2.556 * [taylor]: Taking taylor expansion of 1.0 in k 2.556 * [backup-simplify]: Simplify 1.0 into 1.0 2.556 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.556 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.556 * [taylor]: Taking taylor expansion of -2.0 in k 2.556 * [backup-simplify]: Simplify -2.0 into -2.0 2.556 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.556 * [taylor]: Taking taylor expansion of PI in k 2.556 * [backup-simplify]: Simplify PI into PI 2.556 * [taylor]: Taking taylor expansion of n in k 2.556 * [backup-simplify]: Simplify n into n 2.556 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.556 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.556 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.556 * [backup-simplify]: Simplify (+ 1 0) into 1 2.557 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.557 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.557 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.557 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.557 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.557 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.557 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.557 * [taylor]: Taking taylor expansion of 0.5 in n 2.557 * [backup-simplify]: Simplify 0.5 into 0.5 2.557 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.557 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.557 * [taylor]: Taking taylor expansion of k in n 2.557 * [backup-simplify]: Simplify k into k 2.557 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.557 * [taylor]: Taking taylor expansion of 1.0 in n 2.557 * [backup-simplify]: Simplify 1.0 into 1.0 2.557 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.557 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.557 * [taylor]: Taking taylor expansion of -2.0 in n 2.557 * [backup-simplify]: Simplify -2.0 into -2.0 2.557 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.557 * [taylor]: Taking taylor expansion of PI in n 2.557 * [backup-simplify]: Simplify PI into PI 2.557 * [taylor]: Taking taylor expansion of n in n 2.557 * [backup-simplify]: Simplify 0 into 0 2.557 * [backup-simplify]: Simplify 1 into 1 2.558 * [backup-simplify]: Simplify (/ PI 1) into PI 2.558 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.558 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.559 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.559 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.560 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.561 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.561 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.561 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.561 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.561 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.561 * [taylor]: Taking taylor expansion of 0.5 in n 2.561 * [backup-simplify]: Simplify 0.5 into 0.5 2.561 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.561 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.561 * [taylor]: Taking taylor expansion of k in n 2.561 * [backup-simplify]: Simplify k into k 2.561 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.561 * [taylor]: Taking taylor expansion of 1.0 in n 2.561 * [backup-simplify]: Simplify 1.0 into 1.0 2.561 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.561 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.561 * [taylor]: Taking taylor expansion of -2.0 in n 2.561 * [backup-simplify]: Simplify -2.0 into -2.0 2.561 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.561 * [taylor]: Taking taylor expansion of PI in n 2.561 * [backup-simplify]: Simplify PI into PI 2.561 * [taylor]: Taking taylor expansion of n in n 2.561 * [backup-simplify]: Simplify 0 into 0 2.561 * [backup-simplify]: Simplify 1 into 1 2.562 * [backup-simplify]: Simplify (/ PI 1) into PI 2.562 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.563 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.563 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.563 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.564 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.564 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.565 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.565 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.565 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.565 * [taylor]: Taking taylor expansion of 0.5 in k 2.565 * [backup-simplify]: Simplify 0.5 into 0.5 2.565 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.565 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.565 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.565 * [taylor]: Taking taylor expansion of k in k 2.565 * [backup-simplify]: Simplify 0 into 0 2.565 * [backup-simplify]: Simplify 1 into 1 2.565 * [backup-simplify]: Simplify (/ 1 1) into 1 2.565 * [taylor]: Taking taylor expansion of 1.0 in k 2.566 * [backup-simplify]: Simplify 1.0 into 1.0 2.566 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.566 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.566 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.566 * [taylor]: Taking taylor expansion of -2.0 in k 2.566 * [backup-simplify]: Simplify -2.0 into -2.0 2.566 * [taylor]: Taking taylor expansion of PI in k 2.566 * [backup-simplify]: Simplify PI into PI 2.566 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.566 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.567 * [taylor]: Taking taylor expansion of (log n) in k 2.567 * [taylor]: Taking taylor expansion of n in k 2.567 * [backup-simplify]: Simplify n into n 2.567 * [backup-simplify]: Simplify (log n) into (log n) 2.567 * [backup-simplify]: Simplify (+ 1 0) into 1 2.567 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.567 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.568 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.569 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.569 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.570 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.571 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.571 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.572 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.572 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.572 * [backup-simplify]: Simplify (+ 0 0) into 0 2.573 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.574 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.574 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.575 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.575 * [taylor]: Taking taylor expansion of 0 in k 2.575 * [backup-simplify]: Simplify 0 into 0 2.575 * [backup-simplify]: Simplify 0 into 0 2.575 * [backup-simplify]: Simplify 0 into 0 2.576 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.577 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.578 * [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 2.578 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.579 * [backup-simplify]: Simplify (+ 0 0) into 0 2.579 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.580 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.581 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.582 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.582 * [taylor]: Taking taylor expansion of 0 in k 2.582 * [backup-simplify]: Simplify 0 into 0 2.582 * [backup-simplify]: Simplify 0 into 0 2.582 * [backup-simplify]: Simplify 0 into 0 2.582 * [backup-simplify]: Simplify 0 into 0 2.583 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.584 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.586 * [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 2.587 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.587 * [backup-simplify]: Simplify (+ 0 0) into 0 2.588 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.588 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.589 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.591 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.591 * [taylor]: Taking taylor expansion of 0 in k 2.591 * [backup-simplify]: Simplify 0 into 0 2.591 * [backup-simplify]: Simplify 0 into 0 2.592 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.592 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 1 2) 2.592 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 2.592 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 2.592 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.592 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.592 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.592 * [taylor]: Taking taylor expansion of 1/3 in n 2.592 * [backup-simplify]: Simplify 1/3 into 1/3 2.592 * [taylor]: Taking taylor expansion of (log n) in n 2.592 * [taylor]: Taking taylor expansion of n in n 2.592 * [backup-simplify]: Simplify 0 into 0 2.592 * [backup-simplify]: Simplify 1 into 1 2.592 * [backup-simplify]: Simplify (log 1) into 0 2.593 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.593 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.593 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.593 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.593 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.593 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.593 * [taylor]: Taking taylor expansion of 1/3 in n 2.593 * [backup-simplify]: Simplify 1/3 into 1/3 2.593 * [taylor]: Taking taylor expansion of (log n) in n 2.593 * [taylor]: Taking taylor expansion of n in n 2.593 * [backup-simplify]: Simplify 0 into 0 2.593 * [backup-simplify]: Simplify 1 into 1 2.593 * [backup-simplify]: Simplify (log 1) into 0 2.594 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.594 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.594 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.594 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.595 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.595 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.595 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 2.596 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.596 * [backup-simplify]: Simplify 0 into 0 2.597 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.597 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.598 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 2.599 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.599 * [backup-simplify]: Simplify 0 into 0 2.601 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 2.602 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.602 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 2.603 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.603 * [backup-simplify]: Simplify 0 into 0 2.608 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 2.609 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.610 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 2.611 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.611 * [backup-simplify]: Simplify 0 into 0 2.625 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 2.626 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.627 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 2.629 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.629 * [backup-simplify]: Simplify 0 into 0 2.643 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 2.644 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.645 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 2.648 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.648 * [backup-simplify]: Simplify 0 into 0 2.648 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.648 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 2.648 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 2.648 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.648 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.648 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.648 * [taylor]: Taking taylor expansion of 1/3 in n 2.648 * [backup-simplify]: Simplify 1/3 into 1/3 2.648 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.648 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.648 * [taylor]: Taking taylor expansion of n in n 2.648 * [backup-simplify]: Simplify 0 into 0 2.648 * [backup-simplify]: Simplify 1 into 1 2.649 * [backup-simplify]: Simplify (/ 1 1) into 1 2.649 * [backup-simplify]: Simplify (log 1) into 0 2.649 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.649 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.649 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.649 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.649 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.649 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.649 * [taylor]: Taking taylor expansion of 1/3 in n 2.649 * [backup-simplify]: Simplify 1/3 into 1/3 2.649 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.649 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.649 * [taylor]: Taking taylor expansion of n in n 2.649 * [backup-simplify]: Simplify 0 into 0 2.649 * [backup-simplify]: Simplify 1 into 1 2.650 * [backup-simplify]: Simplify (/ 1 1) into 1 2.650 * [backup-simplify]: Simplify (log 1) into 0 2.650 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.650 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.650 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.650 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 2.651 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.652 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.652 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.652 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 2.653 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.653 * [backup-simplify]: Simplify 0 into 0 2.653 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.655 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.655 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.655 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 2.656 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.656 * [backup-simplify]: Simplify 0 into 0 2.657 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.659 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 2.659 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.660 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 2.661 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.661 * [backup-simplify]: Simplify 0 into 0 2.662 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.667 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 2.667 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.668 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 2.669 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.669 * [backup-simplify]: Simplify 0 into 0 2.670 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.678 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 2.678 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.680 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 2.681 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.682 * [backup-simplify]: Simplify 0 into 0 2.682 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.704 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 2.704 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.706 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 2.708 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.708 * [backup-simplify]: Simplify 0 into 0 2.709 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 2.709 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.709 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 2.709 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.709 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.709 * [taylor]: Taking taylor expansion of -1 in n 2.709 * [backup-simplify]: Simplify -1 into -1 2.709 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.709 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.710 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.710 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.710 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.710 * [taylor]: Taking taylor expansion of 1/3 in n 2.710 * [backup-simplify]: Simplify 1/3 into 1/3 2.710 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.710 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.710 * [taylor]: Taking taylor expansion of n in n 2.710 * [backup-simplify]: Simplify 0 into 0 2.710 * [backup-simplify]: Simplify 1 into 1 2.710 * [backup-simplify]: Simplify (/ 1 1) into 1 2.710 * [backup-simplify]: Simplify (log 1) into 0 2.710 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.710 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.711 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.711 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.711 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.711 * [taylor]: Taking taylor expansion of -1 in n 2.711 * [backup-simplify]: Simplify -1 into -1 2.711 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.711 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.711 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.711 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.712 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.712 * [taylor]: Taking taylor expansion of 1/3 in n 2.712 * [backup-simplify]: Simplify 1/3 into 1/3 2.712 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.712 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.712 * [taylor]: Taking taylor expansion of n in n 2.712 * [backup-simplify]: Simplify 0 into 0 2.712 * [backup-simplify]: Simplify 1 into 1 2.712 * [backup-simplify]: Simplify (/ 1 1) into 1 2.712 * [backup-simplify]: Simplify (log 1) into 0 2.712 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.712 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.712 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.713 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.713 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.714 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.714 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.715 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.715 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 2.716 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.716 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 2.716 * [backup-simplify]: Simplify 0 into 0 2.716 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.718 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.718 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.719 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 2.719 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.720 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.721 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 2.721 * [backup-simplify]: Simplify 0 into 0 2.721 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.724 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 2.724 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.725 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 2.726 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.727 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.727 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 2.727 * [backup-simplify]: Simplify 0 into 0 2.728 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.733 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 2.733 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.734 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 2.736 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.736 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.737 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 2.738 * [backup-simplify]: Simplify 0 into 0 2.738 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.746 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 2.746 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.748 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 2.749 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.750 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.751 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 2.751 * [backup-simplify]: Simplify 0 into 0 2.752 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.767 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 2.767 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.768 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 2.771 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.772 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.774 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 2.774 * [backup-simplify]: Simplify 0 into 0 2.774 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 2.774 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1 1 2 2) 2.774 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 2.774 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 2.774 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.774 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.774 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.774 * [taylor]: Taking taylor expansion of 1/3 in n 2.774 * [backup-simplify]: Simplify 1/3 into 1/3 2.774 * [taylor]: Taking taylor expansion of (log n) in n 2.774 * [taylor]: Taking taylor expansion of n in n 2.774 * [backup-simplify]: Simplify 0 into 0 2.774 * [backup-simplify]: Simplify 1 into 1 2.775 * [backup-simplify]: Simplify (log 1) into 0 2.775 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.775 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.775 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.775 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.775 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.775 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.775 * [taylor]: Taking taylor expansion of 1/3 in n 2.775 * [backup-simplify]: Simplify 1/3 into 1/3 2.775 * [taylor]: Taking taylor expansion of (log n) in n 2.775 * [taylor]: Taking taylor expansion of n in n 2.775 * [backup-simplify]: Simplify 0 into 0 2.775 * [backup-simplify]: Simplify 1 into 1 2.775 * [backup-simplify]: Simplify (log 1) into 0 2.776 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.776 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.776 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.776 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.777 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.777 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.783 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 2.784 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.784 * [backup-simplify]: Simplify 0 into 0 2.786 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.786 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.787 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 2.787 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.787 * [backup-simplify]: Simplify 0 into 0 2.790 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 2.790 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.791 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 2.792 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.792 * [backup-simplify]: Simplify 0 into 0 2.797 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 2.797 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.798 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 2.800 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.800 * [backup-simplify]: Simplify 0 into 0 2.808 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 2.809 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.810 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 2.812 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.812 * [backup-simplify]: Simplify 0 into 0 2.826 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 2.827 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.828 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 2.831 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.831 * [backup-simplify]: Simplify 0 into 0 2.831 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.831 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 2.831 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 2.831 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.831 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.831 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.831 * [taylor]: Taking taylor expansion of 1/3 in n 2.831 * [backup-simplify]: Simplify 1/3 into 1/3 2.831 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.831 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.831 * [taylor]: Taking taylor expansion of n in n 2.831 * [backup-simplify]: Simplify 0 into 0 2.831 * [backup-simplify]: Simplify 1 into 1 2.832 * [backup-simplify]: Simplify (/ 1 1) into 1 2.832 * [backup-simplify]: Simplify (log 1) into 0 2.832 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.832 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.832 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.832 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.832 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.832 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.832 * [taylor]: Taking taylor expansion of 1/3 in n 2.832 * [backup-simplify]: Simplify 1/3 into 1/3 2.832 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.832 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.832 * [taylor]: Taking taylor expansion of n in n 2.832 * [backup-simplify]: Simplify 0 into 0 2.832 * [backup-simplify]: Simplify 1 into 1 2.833 * [backup-simplify]: Simplify (/ 1 1) into 1 2.833 * [backup-simplify]: Simplify (log 1) into 0 2.833 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.833 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.833 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.833 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 2.834 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.834 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.835 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.835 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 2.836 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.836 * [backup-simplify]: Simplify 0 into 0 2.836 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.837 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.838 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.838 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 2.839 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.839 * [backup-simplify]: Simplify 0 into 0 2.839 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.842 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 2.842 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.843 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 2.844 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.844 * [backup-simplify]: Simplify 0 into 0 2.844 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.849 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 2.850 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.850 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 2.852 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.852 * [backup-simplify]: Simplify 0 into 0 2.852 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.866 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 2.867 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.868 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 2.870 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.870 * [backup-simplify]: Simplify 0 into 0 2.870 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.885 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 2.885 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.887 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 2.889 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.890 * [backup-simplify]: Simplify 0 into 0 2.890 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 2.890 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.890 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 2.890 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.890 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.890 * [taylor]: Taking taylor expansion of -1 in n 2.890 * [backup-simplify]: Simplify -1 into -1 2.890 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.891 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.891 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.891 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.891 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.891 * [taylor]: Taking taylor expansion of 1/3 in n 2.891 * [backup-simplify]: Simplify 1/3 into 1/3 2.891 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.891 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.891 * [taylor]: Taking taylor expansion of n in n 2.891 * [backup-simplify]: Simplify 0 into 0 2.891 * [backup-simplify]: Simplify 1 into 1 2.891 * [backup-simplify]: Simplify (/ 1 1) into 1 2.891 * [backup-simplify]: Simplify (log 1) into 0 2.892 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.892 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.892 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.892 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.892 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.892 * [taylor]: Taking taylor expansion of -1 in n 2.892 * [backup-simplify]: Simplify -1 into -1 2.892 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.892 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.892 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.892 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.893 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.893 * [taylor]: Taking taylor expansion of 1/3 in n 2.893 * [backup-simplify]: Simplify 1/3 into 1/3 2.893 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.893 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.893 * [taylor]: Taking taylor expansion of n in n 2.893 * [backup-simplify]: Simplify 0 into 0 2.893 * [backup-simplify]: Simplify 1 into 1 2.893 * [backup-simplify]: Simplify (/ 1 1) into 1 2.893 * [backup-simplify]: Simplify (log 1) into 0 2.893 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.893 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.893 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.894 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.894 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.895 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.895 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.896 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.896 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 2.896 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.897 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 2.897 * [backup-simplify]: Simplify 0 into 0 2.898 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.899 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.899 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.900 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 2.901 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.901 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.902 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 2.902 * [backup-simplify]: Simplify 0 into 0 2.903 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.905 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 2.905 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.906 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 2.907 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.908 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.909 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 2.909 * [backup-simplify]: Simplify 0 into 0 2.909 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.914 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 2.915 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.916 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 2.917 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.918 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.919 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 2.919 * [backup-simplify]: Simplify 0 into 0 2.920 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.928 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 2.928 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.929 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 2.931 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.932 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.933 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 2.933 * [backup-simplify]: Simplify 0 into 0 2.934 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.955 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 2.956 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.957 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 2.960 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.961 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.962 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 2.962 * [backup-simplify]: Simplify 0 into 0 2.963 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 2.963 * * * [progress]: simplifying candidates 2.965 * [simplify]: Simplifying: (* (+ (+ (+ (log 2.0) (log PI)) (+ (log (cbrt n)) (log (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (+ (log 2.0) (log PI)) (log (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (log (* 2.0 PI)) (+ (log (cbrt n)) (log (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (log (* 2.0 PI)) (log (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (log (* (* 2.0 PI) (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (log (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n))) (/ (- 1.0 k) 2.0)) (* (log (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 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) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1.0 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ k 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) 1) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (- 1.0 k)) (pow (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (log (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (exp (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (+ (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)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (- (+ (* 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)))))) (- (+ (* 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)))))) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) 2.965 * [simplify]: Sending expressions to egg_math: (* (+ (+ (+ (log h0) (log PI)) (+ (log (cbrt h1)) (log (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (+ (+ (log h0) (log PI)) (log (* (cbrt h1) (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (+ (log (* h0 PI)) (+ (log (cbrt h1)) (log (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (+ (log (* h0 PI)) (log (* (cbrt h1) (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (log (* (* h0 PI) (* (cbrt h1) (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (log (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1))) (/ (- h2 h3) h0)) (* (log (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1))) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ h2 h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ h3 h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (sqrt (/ (- h2 h3) h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (sqrt (- h2 h3)) 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) 1) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (- h2 h3)) (pow (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (/ (- h2 h3) h0)) (pow (cbrt h1) (/ (- h2 h3) h0)) (log (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (exp (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (cbrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0)))) (cbrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (* (* (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (sqrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (sqrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (/ (- h2 h3) h0) 2)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (/ (- h2 h3) h0) 2)) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ h2 h0)) (pow (* (* h0 PI) h1) (/ h3 h0)) (pow (* (* h0 PI) h1) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* h0 PI) h1) (sqrt (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) 1) (pow (* (* h0 PI) h1) (- h2 h3)) (pow (* h0 PI) (/ (- h2 h3) h0)) (pow h1 (/ (- h2 h3) h0)) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (exp (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (log (cbrt h1)) (exp (cbrt h1)) (cbrt (* (cbrt h1) (cbrt h1))) (cbrt (cbrt h1)) (cbrt (sqrt h1)) (cbrt (sqrt h1)) (cbrt 1) (cbrt h1) (* (cbrt (cbrt h1)) (cbrt (cbrt h1))) (cbrt (cbrt h1)) (* (* (cbrt h1) (cbrt h1)) (cbrt h1)) (sqrt (cbrt h1)) (sqrt (cbrt h1)) (log (cbrt h1)) (exp (cbrt h1)) (cbrt (* (cbrt h1) (cbrt h1))) (cbrt (cbrt h1)) (cbrt (sqrt h1)) (cbrt (sqrt h1)) (cbrt 1) (cbrt h1) (* (cbrt (cbrt h1)) (cbrt (cbrt h1))) (cbrt (cbrt h1)) (* (* (cbrt h1) (cbrt h1)) (cbrt h1)) (sqrt (cbrt h1)) (sqrt (cbrt h1)) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (pow h1 1/3) (pow (/ 1 h1) -1/3) (* (pow (* -1 h1) 1/3) (cbrt -1)) (pow h1 1/3) (pow (/ 1 h1) -1/3) (* (pow (* -1 h1) 1/3) (cbrt -1)) 2.972 * * [simplify]: iteration 0 : 501 enodes (cost 956 ) 2.979 * * [simplify]: iteration 1 : 1597 enodes (cost 898 ) 3.007 * * [simplify]: iteration 2 : 5001 enodes (cost 687 ) 3.011 * * * [progress]: adding candidates to table 3.421 * * [progress]: iteration 4 / 4 3.421 * * * [progress]: picking best candidate 3.433 * * * * [pick]: Picked # 3.433 * * * [progress]: localizing error 3.448 * * * [progress]: generating rewritten candidates 3.449 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.470 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 3.498 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 3.515 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 3.554 * * * [progress]: generating series expansions 3.555 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.555 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 3.555 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.555 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.555 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.555 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.555 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.556 * [taylor]: Taking taylor expansion of 0.5 in k 3.556 * [backup-simplify]: Simplify 0.5 into 0.5 3.556 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.556 * [taylor]: Taking taylor expansion of 1.0 in k 3.556 * [backup-simplify]: Simplify 1.0 into 1.0 3.556 * [taylor]: Taking taylor expansion of k in k 3.556 * [backup-simplify]: Simplify 0 into 0 3.556 * [backup-simplify]: Simplify 1 into 1 3.556 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.556 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.556 * [taylor]: Taking taylor expansion of 2.0 in k 3.556 * [backup-simplify]: Simplify 2.0 into 2.0 3.556 * [taylor]: Taking taylor expansion of (* n PI) in k 3.556 * [taylor]: Taking taylor expansion of n in k 3.556 * [backup-simplify]: Simplify n into n 3.556 * [taylor]: Taking taylor expansion of PI in k 3.556 * [backup-simplify]: Simplify PI into PI 3.556 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.556 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.556 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.556 * [backup-simplify]: Simplify (- 0) into 0 3.556 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.557 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.557 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.557 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.557 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.557 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.557 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.557 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.557 * [taylor]: Taking taylor expansion of 0.5 in n 3.557 * [backup-simplify]: Simplify 0.5 into 0.5 3.557 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.557 * [taylor]: Taking taylor expansion of 1.0 in n 3.557 * [backup-simplify]: Simplify 1.0 into 1.0 3.557 * [taylor]: Taking taylor expansion of k in n 3.557 * [backup-simplify]: Simplify k into k 3.557 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.557 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.557 * [taylor]: Taking taylor expansion of 2.0 in n 3.557 * [backup-simplify]: Simplify 2.0 into 2.0 3.557 * [taylor]: Taking taylor expansion of (* n PI) in n 3.557 * [taylor]: Taking taylor expansion of n in n 3.557 * [backup-simplify]: Simplify 0 into 0 3.557 * [backup-simplify]: Simplify 1 into 1 3.557 * [taylor]: Taking taylor expansion of PI in n 3.557 * [backup-simplify]: Simplify PI into PI 3.558 * [backup-simplify]: Simplify (* 0 PI) into 0 3.558 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.559 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.560 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.560 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.560 * [backup-simplify]: Simplify (- k) into (- k) 3.560 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.560 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.561 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.562 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.563 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 3.563 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.563 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.563 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.563 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.563 * [taylor]: Taking taylor expansion of 0.5 in n 3.563 * [backup-simplify]: Simplify 0.5 into 0.5 3.563 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.563 * [taylor]: Taking taylor expansion of 1.0 in n 3.563 * [backup-simplify]: Simplify 1.0 into 1.0 3.563 * [taylor]: Taking taylor expansion of k in n 3.563 * [backup-simplify]: Simplify k into k 3.563 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.563 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.563 * [taylor]: Taking taylor expansion of 2.0 in n 3.563 * [backup-simplify]: Simplify 2.0 into 2.0 3.563 * [taylor]: Taking taylor expansion of (* n PI) in n 3.563 * [taylor]: Taking taylor expansion of n in n 3.563 * [backup-simplify]: Simplify 0 into 0 3.563 * [backup-simplify]: Simplify 1 into 1 3.563 * [taylor]: Taking taylor expansion of PI in n 3.563 * [backup-simplify]: Simplify PI into PI 3.563 * [backup-simplify]: Simplify (* 0 PI) into 0 3.564 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.564 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.565 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.566 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.566 * [backup-simplify]: Simplify (- k) into (- k) 3.566 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.566 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.567 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.567 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.568 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 3.568 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.568 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.568 * [taylor]: Taking taylor expansion of 0.5 in k 3.568 * [backup-simplify]: Simplify 0.5 into 0.5 3.568 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.568 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.568 * [taylor]: Taking taylor expansion of 1.0 in k 3.568 * [backup-simplify]: Simplify 1.0 into 1.0 3.568 * [taylor]: Taking taylor expansion of k in k 3.568 * [backup-simplify]: Simplify 0 into 0 3.568 * [backup-simplify]: Simplify 1 into 1 3.568 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.568 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.568 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.568 * [taylor]: Taking taylor expansion of 2.0 in k 3.568 * [backup-simplify]: Simplify 2.0 into 2.0 3.568 * [taylor]: Taking taylor expansion of PI in k 3.568 * [backup-simplify]: Simplify PI into PI 3.569 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.569 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.569 * [taylor]: Taking taylor expansion of (log n) in k 3.569 * [taylor]: Taking taylor expansion of n in k 3.569 * [backup-simplify]: Simplify n into n 3.569 * [backup-simplify]: Simplify (log n) into (log n) 3.570 * [backup-simplify]: Simplify (- 0) into 0 3.570 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.571 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.571 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.572 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 3.573 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.573 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.574 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.574 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.575 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.576 * [backup-simplify]: Simplify (- 0) into 0 3.576 * [backup-simplify]: Simplify (+ 0 0) into 0 3.576 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.577 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.577 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.579 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.579 * [taylor]: Taking taylor expansion of 0 in k 3.579 * [backup-simplify]: Simplify 0 into 0 3.579 * [backup-simplify]: Simplify 0 into 0 3.579 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.580 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.581 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.581 * [backup-simplify]: Simplify (+ 0 0) into 0 3.581 * [backup-simplify]: Simplify (- 1) into -1 3.581 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.582 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.583 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3.585 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 3.587 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 3.588 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.588 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.590 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.590 * [backup-simplify]: Simplify (- 0) into 0 3.591 * [backup-simplify]: Simplify (+ 0 0) into 0 3.591 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.592 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.593 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.594 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.595 * [taylor]: Taking taylor expansion of 0 in k 3.595 * [backup-simplify]: Simplify 0 into 0 3.595 * [backup-simplify]: Simplify 0 into 0 3.595 * [backup-simplify]: Simplify 0 into 0 3.595 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.597 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.598 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.599 * [backup-simplify]: Simplify (+ 0 0) into 0 3.599 * [backup-simplify]: Simplify (- 0) into 0 3.599 * [backup-simplify]: Simplify (+ 0 0) into 0 3.600 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.602 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 3.604 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 3.607 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 3.613 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 3.613 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 3.613 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.613 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.613 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.613 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.613 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.613 * [taylor]: Taking taylor expansion of 0.5 in k 3.613 * [backup-simplify]: Simplify 0.5 into 0.5 3.613 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.614 * [taylor]: Taking taylor expansion of 1.0 in k 3.614 * [backup-simplify]: Simplify 1.0 into 1.0 3.614 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.614 * [taylor]: Taking taylor expansion of k in k 3.614 * [backup-simplify]: Simplify 0 into 0 3.614 * [backup-simplify]: Simplify 1 into 1 3.614 * [backup-simplify]: Simplify (/ 1 1) into 1 3.614 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.614 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.614 * [taylor]: Taking taylor expansion of 2.0 in k 3.614 * [backup-simplify]: Simplify 2.0 into 2.0 3.614 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.614 * [taylor]: Taking taylor expansion of PI in k 3.614 * [backup-simplify]: Simplify PI into PI 3.614 * [taylor]: Taking taylor expansion of n in k 3.614 * [backup-simplify]: Simplify n into n 3.614 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.614 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.614 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.614 * [backup-simplify]: Simplify (- 1) into -1 3.615 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.615 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.615 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.615 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 3.615 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.615 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.615 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.615 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.615 * [taylor]: Taking taylor expansion of 0.5 in n 3.615 * [backup-simplify]: Simplify 0.5 into 0.5 3.615 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.615 * [taylor]: Taking taylor expansion of 1.0 in n 3.615 * [backup-simplify]: Simplify 1.0 into 1.0 3.615 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.615 * [taylor]: Taking taylor expansion of k in n 3.615 * [backup-simplify]: Simplify k into k 3.615 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.615 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.615 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.615 * [taylor]: Taking taylor expansion of 2.0 in n 3.615 * [backup-simplify]: Simplify 2.0 into 2.0 3.615 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.615 * [taylor]: Taking taylor expansion of PI in n 3.615 * [backup-simplify]: Simplify PI into PI 3.616 * [taylor]: Taking taylor expansion of n in n 3.616 * [backup-simplify]: Simplify 0 into 0 3.616 * [backup-simplify]: Simplify 1 into 1 3.616 * [backup-simplify]: Simplify (/ PI 1) into PI 3.616 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.617 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.617 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.617 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.617 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.618 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.618 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 3.619 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 3.619 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.619 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.619 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.619 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.619 * [taylor]: Taking taylor expansion of 0.5 in n 3.619 * [backup-simplify]: Simplify 0.5 into 0.5 3.619 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.619 * [taylor]: Taking taylor expansion of 1.0 in n 3.619 * [backup-simplify]: Simplify 1.0 into 1.0 3.619 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.619 * [taylor]: Taking taylor expansion of k in n 3.619 * [backup-simplify]: Simplify k into k 3.619 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.619 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.619 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.619 * [taylor]: Taking taylor expansion of 2.0 in n 3.619 * [backup-simplify]: Simplify 2.0 into 2.0 3.619 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.620 * [taylor]: Taking taylor expansion of PI in n 3.620 * [backup-simplify]: Simplify PI into PI 3.620 * [taylor]: Taking taylor expansion of n in n 3.620 * [backup-simplify]: Simplify 0 into 0 3.620 * [backup-simplify]: Simplify 1 into 1 3.620 * [backup-simplify]: Simplify (/ PI 1) into PI 3.620 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.621 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.621 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.621 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.621 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.622 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.629 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 3.630 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 3.630 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.630 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.630 * [taylor]: Taking taylor expansion of 0.5 in k 3.630 * [backup-simplify]: Simplify 0.5 into 0.5 3.630 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.630 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.630 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.630 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.630 * [taylor]: Taking taylor expansion of 2.0 in k 3.630 * [backup-simplify]: Simplify 2.0 into 2.0 3.630 * [taylor]: Taking taylor expansion of PI in k 3.630 * [backup-simplify]: Simplify PI into PI 3.631 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.631 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.631 * [taylor]: Taking taylor expansion of (log n) in k 3.631 * [taylor]: Taking taylor expansion of n in k 3.631 * [backup-simplify]: Simplify n into n 3.631 * [backup-simplify]: Simplify (log n) into (log n) 3.631 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.631 * [taylor]: Taking taylor expansion of 1.0 in k 3.632 * [backup-simplify]: Simplify 1.0 into 1.0 3.632 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.632 * [taylor]: Taking taylor expansion of k in k 3.632 * [backup-simplify]: Simplify 0 into 0 3.632 * [backup-simplify]: Simplify 1 into 1 3.632 * [backup-simplify]: Simplify (/ 1 1) into 1 3.632 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.633 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 3.633 * [backup-simplify]: Simplify (- 1) into -1 3.633 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.634 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 3.634 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 3.635 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 3.636 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 3.636 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.637 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.638 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.638 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.638 * [backup-simplify]: Simplify (- 0) into 0 3.638 * [backup-simplify]: Simplify (+ 0 0) into 0 3.638 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.639 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.640 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.641 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.641 * [taylor]: Taking taylor expansion of 0 in k 3.641 * [backup-simplify]: Simplify 0 into 0 3.641 * [backup-simplify]: Simplify 0 into 0 3.641 * [backup-simplify]: Simplify 0 into 0 3.642 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.643 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.644 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.645 * [backup-simplify]: Simplify (- 0) into 0 3.645 * [backup-simplify]: Simplify (+ 0 0) into 0 3.645 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 3.646 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.647 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 3.648 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.648 * [taylor]: Taking taylor expansion of 0 in k 3.649 * [backup-simplify]: Simplify 0 into 0 3.649 * [backup-simplify]: Simplify 0 into 0 3.649 * [backup-simplify]: Simplify 0 into 0 3.649 * [backup-simplify]: Simplify 0 into 0 3.649 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.650 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.652 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 3.653 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.653 * [backup-simplify]: Simplify (- 0) into 0 3.653 * [backup-simplify]: Simplify (+ 0 0) into 0 3.654 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 3.655 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.656 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 3.657 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.657 * [taylor]: Taking taylor expansion of 0 in k 3.657 * [backup-simplify]: Simplify 0 into 0 3.657 * [backup-simplify]: Simplify 0 into 0 3.658 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 3.659 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 3.659 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.659 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.659 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.659 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.659 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.659 * [taylor]: Taking taylor expansion of 0.5 in k 3.659 * [backup-simplify]: Simplify 0.5 into 0.5 3.659 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.659 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.659 * [taylor]: Taking taylor expansion of k in k 3.659 * [backup-simplify]: Simplify 0 into 0 3.659 * [backup-simplify]: Simplify 1 into 1 3.659 * [backup-simplify]: Simplify (/ 1 1) into 1 3.659 * [taylor]: Taking taylor expansion of 1.0 in k 3.659 * [backup-simplify]: Simplify 1.0 into 1.0 3.659 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.659 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.659 * [taylor]: Taking taylor expansion of -2.0 in k 3.659 * [backup-simplify]: Simplify -2.0 into -2.0 3.659 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.659 * [taylor]: Taking taylor expansion of PI in k 3.659 * [backup-simplify]: Simplify PI into PI 3.659 * [taylor]: Taking taylor expansion of n in k 3.659 * [backup-simplify]: Simplify n into n 3.659 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.659 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.659 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.660 * [backup-simplify]: Simplify (+ 1 0) into 1 3.660 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.660 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.660 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 3.660 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.660 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.660 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.660 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.660 * [taylor]: Taking taylor expansion of 0.5 in n 3.660 * [backup-simplify]: Simplify 0.5 into 0.5 3.660 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.660 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.660 * [taylor]: Taking taylor expansion of k in n 3.660 * [backup-simplify]: Simplify k into k 3.660 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.660 * [taylor]: Taking taylor expansion of 1.0 in n 3.660 * [backup-simplify]: Simplify 1.0 into 1.0 3.660 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.660 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.660 * [taylor]: Taking taylor expansion of -2.0 in n 3.660 * [backup-simplify]: Simplify -2.0 into -2.0 3.660 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.660 * [taylor]: Taking taylor expansion of PI in n 3.660 * [backup-simplify]: Simplify PI into PI 3.660 * [taylor]: Taking taylor expansion of n in n 3.661 * [backup-simplify]: Simplify 0 into 0 3.661 * [backup-simplify]: Simplify 1 into 1 3.661 * [backup-simplify]: Simplify (/ PI 1) into PI 3.661 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.662 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.662 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.662 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.663 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.663 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 3.664 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 3.664 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.665 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.665 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.665 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.665 * [taylor]: Taking taylor expansion of 0.5 in n 3.665 * [backup-simplify]: Simplify 0.5 into 0.5 3.665 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.665 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.665 * [taylor]: Taking taylor expansion of k in n 3.665 * [backup-simplify]: Simplify k into k 3.665 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.665 * [taylor]: Taking taylor expansion of 1.0 in n 3.665 * [backup-simplify]: Simplify 1.0 into 1.0 3.665 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.665 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.665 * [taylor]: Taking taylor expansion of -2.0 in n 3.665 * [backup-simplify]: Simplify -2.0 into -2.0 3.665 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.665 * [taylor]: Taking taylor expansion of PI in n 3.665 * [backup-simplify]: Simplify PI into PI 3.665 * [taylor]: Taking taylor expansion of n in n 3.665 * [backup-simplify]: Simplify 0 into 0 3.665 * [backup-simplify]: Simplify 1 into 1 3.665 * [backup-simplify]: Simplify (/ PI 1) into PI 3.665 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.666 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.666 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.666 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.667 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.668 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 3.668 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 3.669 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 3.669 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 3.669 * [taylor]: Taking taylor expansion of 0.5 in k 3.669 * [backup-simplify]: Simplify 0.5 into 0.5 3.669 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 3.669 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.669 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.669 * [taylor]: Taking taylor expansion of k in k 3.669 * [backup-simplify]: Simplify 0 into 0 3.669 * [backup-simplify]: Simplify 1 into 1 3.669 * [backup-simplify]: Simplify (/ 1 1) into 1 3.669 * [taylor]: Taking taylor expansion of 1.0 in k 3.669 * [backup-simplify]: Simplify 1.0 into 1.0 3.669 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.669 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.669 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.669 * [taylor]: Taking taylor expansion of -2.0 in k 3.669 * [backup-simplify]: Simplify -2.0 into -2.0 3.669 * [taylor]: Taking taylor expansion of PI in k 3.669 * [backup-simplify]: Simplify PI into PI 3.669 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.670 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.670 * [taylor]: Taking taylor expansion of (log n) in k 3.670 * [taylor]: Taking taylor expansion of n in k 3.670 * [backup-simplify]: Simplify n into n 3.670 * [backup-simplify]: Simplify (log n) into (log n) 3.670 * [backup-simplify]: Simplify (+ 1 0) into 1 3.670 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.671 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 3.672 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 3.672 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 3.673 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 3.674 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 3.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.675 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.676 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.676 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.676 * [backup-simplify]: Simplify (+ 0 0) into 0 3.676 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.677 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.678 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.679 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.679 * [taylor]: Taking taylor expansion of 0 in k 3.679 * [backup-simplify]: Simplify 0 into 0 3.679 * [backup-simplify]: Simplify 0 into 0 3.679 * [backup-simplify]: Simplify 0 into 0 3.679 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.680 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.682 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 3.682 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.682 * [backup-simplify]: Simplify (+ 0 0) into 0 3.682 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 3.683 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.684 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 3.686 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.686 * [taylor]: Taking taylor expansion of 0 in k 3.686 * [backup-simplify]: Simplify 0 into 0 3.686 * [backup-simplify]: Simplify 0 into 0 3.686 * [backup-simplify]: Simplify 0 into 0 3.686 * [backup-simplify]: Simplify 0 into 0 3.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.687 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.690 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 3.690 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.690 * [backup-simplify]: Simplify (+ 0 0) into 0 3.691 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 3.692 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.694 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 3.695 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.695 * [taylor]: Taking taylor expansion of 0 in k 3.695 * [backup-simplify]: Simplify 0 into 0 3.695 * [backup-simplify]: Simplify 0 into 0 3.696 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 3.696 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 3.696 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k))) 3.696 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.696 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.696 * [taylor]: Taking taylor expansion of 1.0 in k 3.696 * [backup-simplify]: Simplify 1.0 into 1.0 3.696 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.696 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.696 * [taylor]: Taking taylor expansion of k in k 3.696 * [backup-simplify]: Simplify 0 into 0 3.696 * [backup-simplify]: Simplify 1 into 1 3.697 * [backup-simplify]: Simplify (/ 1 1) into 1 3.697 * [backup-simplify]: Simplify (sqrt 0) into 0 3.698 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.698 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.698 * [taylor]: Taking taylor expansion of 1.0 in k 3.698 * [backup-simplify]: Simplify 1.0 into 1.0 3.698 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.698 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.698 * [taylor]: Taking taylor expansion of k in k 3.698 * [backup-simplify]: Simplify 0 into 0 3.698 * [backup-simplify]: Simplify 1 into 1 3.698 * [backup-simplify]: Simplify (/ 1 1) into 1 3.698 * [backup-simplify]: Simplify (sqrt 0) into 0 3.699 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.699 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.699 * [backup-simplify]: Simplify 0 into 0 3.700 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.700 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.701 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.702 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.703 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.704 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.704 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.706 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.707 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.707 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.708 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 3.708 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k)) 3.708 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.708 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.708 * [taylor]: Taking taylor expansion of 1.0 in k 3.708 * [backup-simplify]: Simplify 1.0 into 1.0 3.708 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.708 * [taylor]: Taking taylor expansion of k in k 3.709 * [backup-simplify]: Simplify 0 into 0 3.709 * [backup-simplify]: Simplify 1 into 1 3.709 * [backup-simplify]: Simplify (sqrt 0) into 0 3.709 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.709 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.709 * [taylor]: Taking taylor expansion of 1.0 in k 3.710 * [backup-simplify]: Simplify 1.0 into 1.0 3.710 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.710 * [taylor]: Taking taylor expansion of k in k 3.710 * [backup-simplify]: Simplify 0 into 0 3.710 * [backup-simplify]: Simplify 1 into 1 3.710 * [backup-simplify]: Simplify (sqrt 0) into 0 3.710 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.711 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.711 * [backup-simplify]: Simplify 0 into 0 3.712 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.712 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.713 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.715 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.715 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.723 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.724 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.724 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.725 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 3.726 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k))) 3.726 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.726 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.726 * [taylor]: Taking taylor expansion of 1.0 in k 3.726 * [backup-simplify]: Simplify 1.0 into 1.0 3.726 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.726 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.726 * [taylor]: Taking taylor expansion of -1 in k 3.726 * [backup-simplify]: Simplify -1 into -1 3.726 * [taylor]: Taking taylor expansion of k in k 3.726 * [backup-simplify]: Simplify 0 into 0 3.726 * [backup-simplify]: Simplify 1 into 1 3.726 * [backup-simplify]: Simplify (/ -1 1) into -1 3.726 * [backup-simplify]: Simplify (sqrt 0) into 0 3.727 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.727 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.727 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.727 * [taylor]: Taking taylor expansion of 1.0 in k 3.727 * [backup-simplify]: Simplify 1.0 into 1.0 3.728 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.728 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.728 * [taylor]: Taking taylor expansion of -1 in k 3.728 * [backup-simplify]: Simplify -1 into -1 3.728 * [taylor]: Taking taylor expansion of k in k 3.728 * [backup-simplify]: Simplify 0 into 0 3.728 * [backup-simplify]: Simplify 1 into 1 3.728 * [backup-simplify]: Simplify (/ -1 1) into -1 3.728 * [backup-simplify]: Simplify (sqrt 0) into 0 3.729 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.729 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.729 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.731 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.733 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.733 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.734 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.736 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.738 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 3.738 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.739 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 3.739 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 3.739 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.739 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.739 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.739 * [taylor]: Taking taylor expansion of 2.0 in n 3.739 * [backup-simplify]: Simplify 2.0 into 2.0 3.739 * [taylor]: Taking taylor expansion of (* n PI) in n 3.740 * [taylor]: Taking taylor expansion of n in n 3.740 * [backup-simplify]: Simplify 0 into 0 3.740 * [backup-simplify]: Simplify 1 into 1 3.740 * [taylor]: Taking taylor expansion of PI in n 3.740 * [backup-simplify]: Simplify PI into PI 3.740 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.740 * [taylor]: Taking taylor expansion of 2.0 in n 3.740 * [backup-simplify]: Simplify 2.0 into 2.0 3.740 * [taylor]: Taking taylor expansion of (* n PI) in n 3.740 * [taylor]: Taking taylor expansion of n in n 3.740 * [backup-simplify]: Simplify 0 into 0 3.740 * [backup-simplify]: Simplify 1 into 1 3.740 * [taylor]: Taking taylor expansion of PI in n 3.740 * [backup-simplify]: Simplify PI into PI 3.740 * [backup-simplify]: Simplify (* 0 PI) into 0 3.740 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.740 * [backup-simplify]: Simplify 0 into 0 3.741 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.742 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.743 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.743 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.744 * [backup-simplify]: Simplify 0 into 0 3.744 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.745 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.745 * [backup-simplify]: Simplify 0 into 0 3.746 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.747 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.747 * [backup-simplify]: Simplify 0 into 0 3.747 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.748 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 3.748 * [backup-simplify]: Simplify 0 into 0 3.749 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.750 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 3.750 * [backup-simplify]: Simplify 0 into 0 3.751 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 3.752 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 3.752 * [backup-simplify]: Simplify 0 into 0 3.752 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.753 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 3.753 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.753 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.753 * [taylor]: Taking taylor expansion of 2.0 in n 3.753 * [backup-simplify]: Simplify 2.0 into 2.0 3.753 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.753 * [taylor]: Taking taylor expansion of PI in n 3.753 * [backup-simplify]: Simplify PI into PI 3.753 * [taylor]: Taking taylor expansion of n in n 3.753 * [backup-simplify]: Simplify 0 into 0 3.753 * [backup-simplify]: Simplify 1 into 1 3.753 * [backup-simplify]: Simplify (/ PI 1) into PI 3.753 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.753 * [taylor]: Taking taylor expansion of 2.0 in n 3.753 * [backup-simplify]: Simplify 2.0 into 2.0 3.753 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.753 * [taylor]: Taking taylor expansion of PI in n 3.753 * [backup-simplify]: Simplify PI into PI 3.753 * [taylor]: Taking taylor expansion of n in n 3.753 * [backup-simplify]: Simplify 0 into 0 3.753 * [backup-simplify]: Simplify 1 into 1 3.754 * [backup-simplify]: Simplify (/ PI 1) into PI 3.754 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.754 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.755 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.755 * [backup-simplify]: Simplify 0 into 0 3.756 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.756 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.756 * [backup-simplify]: Simplify 0 into 0 3.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.757 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.757 * [backup-simplify]: Simplify 0 into 0 3.758 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.759 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.759 * [backup-simplify]: Simplify 0 into 0 3.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.760 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.760 * [backup-simplify]: Simplify 0 into 0 3.761 * [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 3.762 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.762 * [backup-simplify]: Simplify 0 into 0 3.762 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 3.762 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 3.762 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.762 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.762 * [taylor]: Taking taylor expansion of -2.0 in n 3.762 * [backup-simplify]: Simplify -2.0 into -2.0 3.762 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.762 * [taylor]: Taking taylor expansion of PI in n 3.762 * [backup-simplify]: Simplify PI into PI 3.762 * [taylor]: Taking taylor expansion of n in n 3.763 * [backup-simplify]: Simplify 0 into 0 3.763 * [backup-simplify]: Simplify 1 into 1 3.763 * [backup-simplify]: Simplify (/ PI 1) into PI 3.763 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.763 * [taylor]: Taking taylor expansion of -2.0 in n 3.763 * [backup-simplify]: Simplify -2.0 into -2.0 3.763 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.763 * [taylor]: Taking taylor expansion of PI in n 3.763 * [backup-simplify]: Simplify PI into PI 3.763 * [taylor]: Taking taylor expansion of n in n 3.763 * [backup-simplify]: Simplify 0 into 0 3.763 * [backup-simplify]: Simplify 1 into 1 3.763 * [backup-simplify]: Simplify (/ PI 1) into PI 3.764 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.764 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.764 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.765 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.765 * [backup-simplify]: Simplify 0 into 0 3.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.766 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.766 * [backup-simplify]: Simplify 0 into 0 3.767 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.767 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.767 * [backup-simplify]: Simplify 0 into 0 3.768 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.769 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.769 * [backup-simplify]: Simplify 0 into 0 3.769 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.770 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.770 * [backup-simplify]: Simplify 0 into 0 3.771 * [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 3.772 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.772 * [backup-simplify]: Simplify 0 into 0 3.772 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 3.772 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 3.772 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4)) 3.772 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 3.772 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 3.772 * [taylor]: Taking taylor expansion of 1.0 in k 3.772 * [backup-simplify]: Simplify 1.0 into 1.0 3.772 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 3.772 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 3.772 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 3.772 * [taylor]: Taking taylor expansion of 1/4 in k 3.772 * [backup-simplify]: Simplify 1/4 into 1/4 3.772 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.772 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.772 * [taylor]: Taking taylor expansion of k in k 3.772 * [backup-simplify]: Simplify 0 into 0 3.772 * [backup-simplify]: Simplify 1 into 1 3.773 * [backup-simplify]: Simplify (/ 1 1) into 1 3.773 * [backup-simplify]: Simplify (log 1) into 0 3.773 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.773 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 3.773 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 3.773 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 3.773 * [taylor]: Taking taylor expansion of 1.0 in k 3.773 * [backup-simplify]: Simplify 1.0 into 1.0 3.773 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 3.773 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 3.773 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 3.773 * [taylor]: Taking taylor expansion of 1/4 in k 3.773 * [backup-simplify]: Simplify 1/4 into 1/4 3.773 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.773 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.773 * [taylor]: Taking taylor expansion of k in k 3.773 * [backup-simplify]: Simplify 0 into 0 3.773 * [backup-simplify]: Simplify 1 into 1 3.774 * [backup-simplify]: Simplify (/ 1 1) into 1 3.774 * [backup-simplify]: Simplify (log 1) into 0 3.774 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.774 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 3.774 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 3.774 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 3.774 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 3.775 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.776 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.776 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.776 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 3.777 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 3.777 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0 3.777 * [backup-simplify]: Simplify 0 into 0 3.778 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.779 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 3.779 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.780 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 3.780 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.781 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0 3.781 * [backup-simplify]: Simplify 0 into 0 3.782 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.784 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 3.784 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.785 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 3.786 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.787 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0 3.787 * [backup-simplify]: Simplify 0 into 0 3.787 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.792 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 3.793 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.793 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 3.795 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.796 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0 3.796 * [backup-simplify]: Simplify 0 into 0 3.796 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.805 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 3.805 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.812 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 3.814 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.815 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0 3.815 * [backup-simplify]: Simplify 0 into 0 3.816 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.830 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 3.831 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.832 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 3.835 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.836 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0 3.836 * [backup-simplify]: Simplify 0 into 0 3.836 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 3.836 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4)) 3.837 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 3.837 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 3.837 * [taylor]: Taking taylor expansion of 1.0 in k 3.837 * [backup-simplify]: Simplify 1.0 into 1.0 3.837 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 3.837 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 3.837 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 3.837 * [taylor]: Taking taylor expansion of 1/4 in k 3.837 * [backup-simplify]: Simplify 1/4 into 1/4 3.837 * [taylor]: Taking taylor expansion of (log k) in k 3.837 * [taylor]: Taking taylor expansion of k in k 3.837 * [backup-simplify]: Simplify 0 into 0 3.837 * [backup-simplify]: Simplify 1 into 1 3.837 * [backup-simplify]: Simplify (log 1) into 0 3.837 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.837 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 3.837 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 3.837 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 3.837 * [taylor]: Taking taylor expansion of 1.0 in k 3.837 * [backup-simplify]: Simplify 1.0 into 1.0 3.837 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 3.837 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 3.837 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 3.837 * [taylor]: Taking taylor expansion of 1/4 in k 3.837 * [backup-simplify]: Simplify 1/4 into 1/4 3.837 * [taylor]: Taking taylor expansion of (log k) in k 3.837 * [taylor]: Taking taylor expansion of k in k 3.837 * [backup-simplify]: Simplify 0 into 0 3.838 * [backup-simplify]: Simplify 1 into 1 3.838 * [backup-simplify]: Simplify (log 1) into 0 3.838 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.838 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 3.838 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 3.838 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 3.838 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 3.839 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.839 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.840 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 3.840 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 3.840 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0 3.840 * [backup-simplify]: Simplify 0 into 0 3.842 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 3.842 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.843 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 3.844 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.844 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 3.844 * [backup-simplify]: Simplify 0 into 0 3.847 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 3.847 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.847 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 3.848 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.849 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 3.849 * [backup-simplify]: Simplify 0 into 0 3.854 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 3.854 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.855 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 3.856 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.857 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0 3.858 * [backup-simplify]: Simplify 0 into 0 3.866 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 3.866 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.867 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 3.869 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.871 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0 3.871 * [backup-simplify]: Simplify 0 into 0 3.885 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 3.886 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.893 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 3.896 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.898 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0 3.898 * [backup-simplify]: Simplify 0 into 0 3.898 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 3.898 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) 3.898 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 3.898 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 3.898 * [taylor]: Taking taylor expansion of 1.0 in k 3.898 * [backup-simplify]: Simplify 1.0 into 1.0 3.898 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 3.898 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 3.898 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.898 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.898 * [taylor]: Taking taylor expansion of -1 in k 3.898 * [backup-simplify]: Simplify -1 into -1 3.898 * [taylor]: Taking taylor expansion of k in k 3.898 * [backup-simplify]: Simplify 0 into 0 3.898 * [backup-simplify]: Simplify 1 into 1 3.899 * [backup-simplify]: Simplify (/ -1 1) into -1 3.899 * [backup-simplify]: Simplify (sqrt 0) into 0 3.900 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.900 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 3.900 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 3.901 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.902 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.903 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.905 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 3.905 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 3.905 * [taylor]: Taking taylor expansion of 1.0 in k 3.905 * [backup-simplify]: Simplify 1.0 into 1.0 3.905 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 3.905 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 3.905 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.905 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.905 * [taylor]: Taking taylor expansion of -1 in k 3.905 * [backup-simplify]: Simplify -1 into -1 3.905 * [taylor]: Taking taylor expansion of k in k 3.905 * [backup-simplify]: Simplify 0 into 0 3.905 * [backup-simplify]: Simplify 1 into 1 3.905 * [backup-simplify]: Simplify (/ -1 1) into -1 3.905 * [backup-simplify]: Simplify (sqrt 0) into 0 3.906 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.906 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 3.907 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 3.907 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.909 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.910 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.911 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 3.911 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 3.912 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 3.914 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 3.915 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 3.915 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.917 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.919 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 3.922 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 3.929 * [backup-simplify]: Simplify (+ (* 1.0 (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) 3.934 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) 3.940 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (sqrt +nan.0)))) (/ 1 (- k))) (* 1.0 (sqrt +nan.0)))) into (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) 3.941 * * * [progress]: simplifying candidates 3.949 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (- (- (log 1.0) (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (- (log (/ 1.0 (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (log (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (exp (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- 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(cbrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt k)))) (* (sqrt (sqrt k)) (sqrt (sqrt k))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt (sqrt k)))) (log (/ 1.0 (sqrt (sqrt k)))) (exp (/ 1.0 (sqrt (sqrt k)))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (cbrt (/ 1.0 (sqrt (sqrt k)))) (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (- 1.0) (- (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 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+nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) 3.952 * [simplify]: Sending expressions to egg_math: (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ h2 h0)) (pow (* (* h0 PI) h1) (/ h3 h0)) (pow (* (* h0 PI) h1) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* h0 PI) h1) (sqrt (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) 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(sqrt h3)) (cbrt (sqrt h3))))) (/ (sqrt h2) (sqrt (cbrt (sqrt h3)))) (/ (sqrt h2) (sqrt (sqrt (* (cbrt h3) (cbrt h3))))) (/ (sqrt h2) (sqrt (sqrt (cbrt h3)))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt (sqrt 1))) (/ (sqrt h2) (sqrt (sqrt h3))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt 1)) (/ (sqrt h2) (sqrt (sqrt h3))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt (sqrt (sqrt h3)))) (/ (sqrt h2) 1) (/ (sqrt h2) (sqrt (sqrt h3))) (/ 1 (* (cbrt (sqrt (sqrt h3))) (cbrt (sqrt (sqrt h3))))) (/ h2 (cbrt (sqrt (sqrt h3)))) (/ 1 (sqrt (* (cbrt (sqrt h3)) (cbrt (sqrt h3))))) (/ h2 (sqrt (cbrt (sqrt h3)))) (/ 1 (sqrt (sqrt (* (cbrt h3) (cbrt h3))))) (/ h2 (sqrt (sqrt (cbrt h3)))) (/ 1 (sqrt (sqrt (sqrt h3)))) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ 1 (sqrt (sqrt 1))) (/ h2 (sqrt (sqrt h3))) (/ 1 (sqrt (sqrt (sqrt h3)))) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ 1 (sqrt 1)) (/ h2 (sqrt (sqrt h3))) (/ 1 (sqrt (sqrt (sqrt h3)))) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ 1 1) (/ h2 (sqrt (sqrt h3))) (/ 1 (sqrt (sqrt h3))) (/ (sqrt (sqrt h3)) h2) (/ h2 (* (cbrt (sqrt (sqrt h3))) (cbrt (sqrt (sqrt h3))))) (/ h2 (sqrt (* (cbrt (sqrt h3)) (cbrt (sqrt h3))))) (/ h2 (sqrt (sqrt (* (cbrt h3) (cbrt h3))))) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ h2 (sqrt (sqrt 1))) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt (sqrt h3)))) (/ h2 1) (/ (sqrt (sqrt h3)) (cbrt h2)) (/ (sqrt (sqrt h3)) (sqrt h2)) (/ (sqrt (sqrt h3)) h2) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (- (+ (* h8 h3) (- (+ (* h8 (pow h3 2)) (- h8))))) (- (+ (* h8 (/ 1 (pow h3 2))) (- (+ (* h8 (/ 1 h3)) (- (* h8 (/ 1 (pow h3 3)))))))) (- (+ (* h8 (/ 1 (pow h3 2))) (- (+ (* h8 (/ 1 h3)) (- h8))))) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h2 (pow (/ 1 h3) 1/4)) (* h2 (pow (/ 1 h3) 1/4)) (- (* h2 (sqrt h8)) (+ (* h8 (/ 1 (* (sqrt h8) (pow h3 2)))) (- (+ (* h8 (/ 1 (* (sqrt h8) h3))) (- (* h8 (/ 1 (* (pow (sqrt h8) 3) (pow h3 2))))))))) 3.968 * * [simplify]: iteration 0 : 1334 enodes (cost 5795 ) 3.989 * * [simplify]: iteration 1 : 5001 enodes (cost 5011 ) 4.017 * * * [progress]: adding candidates to table 4.733 * [progress]: [Phase 3 of 3] Extracting. 4.733 * * [regime]: Finding splitpoints for: (# # # # # # # #) 4.740 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 4.740 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 4.773 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 4.810 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 4.845 * * * [regime]: Found split indices: #