10.446 * [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 ) 0.085 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.088 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.094 * * [simplify]: iteration 4 : 1044 enodes (cost 8 ) 0.117 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.118 * * [progress]: iteration 1 / 4 0.118 * * * [progress]: picking best candidate 0.120 * * * * [pick]: Picked # 0.120 * * * [progress]: localizing error 0.136 * * * [progress]: generating rewritten candidates 0.136 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.159 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.177 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.183 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.232 * * * [progress]: generating series expansions 0.232 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.233 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 0.233 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.233 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.233 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.233 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.233 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.233 * [taylor]: Taking taylor expansion of 0.5 in k 0.233 * [backup-simplify]: Simplify 0.5 into 0.5 0.233 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.233 * [taylor]: Taking taylor expansion of 1.0 in k 0.233 * [backup-simplify]: Simplify 1.0 into 1.0 0.233 * [taylor]: Taking taylor expansion of k in k 0.233 * [backup-simplify]: Simplify 0 into 0 0.233 * [backup-simplify]: Simplify 1 into 1 0.233 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.233 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.233 * [taylor]: Taking taylor expansion of 2.0 in k 0.233 * [backup-simplify]: Simplify 2.0 into 2.0 0.233 * [taylor]: Taking taylor expansion of (* n PI) in k 0.233 * [taylor]: Taking taylor expansion of n in k 0.233 * [backup-simplify]: Simplify n into n 0.233 * [taylor]: Taking taylor expansion of PI in k 0.233 * [backup-simplify]: Simplify PI into PI 0.233 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.233 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.233 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.234 * [backup-simplify]: Simplify (- 0) into 0 0.234 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.234 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.234 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.234 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.234 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.234 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.234 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.234 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.234 * [taylor]: Taking taylor expansion of 0.5 in n 0.234 * [backup-simplify]: Simplify 0.5 into 0.5 0.234 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.234 * [taylor]: Taking taylor expansion of 1.0 in n 0.234 * [backup-simplify]: Simplify 1.0 into 1.0 0.235 * [taylor]: Taking taylor expansion of k in n 0.235 * [backup-simplify]: Simplify k into k 0.235 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.235 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.235 * [taylor]: Taking taylor expansion of 2.0 in n 0.235 * [backup-simplify]: Simplify 2.0 into 2.0 0.235 * [taylor]: Taking taylor expansion of (* n PI) in n 0.235 * [taylor]: Taking taylor expansion of n in n 0.235 * [backup-simplify]: Simplify 0 into 0 0.235 * [backup-simplify]: Simplify 1 into 1 0.235 * [taylor]: Taking taylor expansion of PI in n 0.235 * [backup-simplify]: Simplify PI into PI 0.235 * [backup-simplify]: Simplify (* 0 PI) into 0 0.235 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.236 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.237 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.238 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.238 * [backup-simplify]: Simplify (- k) into (- k) 0.238 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.238 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.239 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.239 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.240 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.240 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.240 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.240 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.240 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.240 * [taylor]: Taking taylor expansion of 0.5 in n 0.240 * [backup-simplify]: Simplify 0.5 into 0.5 0.240 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.240 * [taylor]: Taking taylor expansion of 1.0 in n 0.240 * [backup-simplify]: Simplify 1.0 into 1.0 0.240 * [taylor]: Taking taylor expansion of k in n 0.240 * [backup-simplify]: Simplify k into k 0.240 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.240 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.240 * [taylor]: Taking taylor expansion of 2.0 in n 0.240 * [backup-simplify]: Simplify 2.0 into 2.0 0.240 * [taylor]: Taking taylor expansion of (* n PI) in n 0.240 * [taylor]: Taking taylor expansion of n in n 0.240 * [backup-simplify]: Simplify 0 into 0 0.240 * [backup-simplify]: Simplify 1 into 1 0.240 * [taylor]: Taking taylor expansion of PI in n 0.240 * [backup-simplify]: Simplify PI into PI 0.241 * [backup-simplify]: Simplify (* 0 PI) into 0 0.241 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.242 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.243 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.243 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.243 * [backup-simplify]: Simplify (- k) into (- k) 0.243 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.243 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.244 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.245 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.245 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.246 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.246 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.246 * [taylor]: Taking taylor expansion of 0.5 in k 0.246 * [backup-simplify]: Simplify 0.5 into 0.5 0.246 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.246 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.246 * [taylor]: Taking taylor expansion of 1.0 in k 0.246 * [backup-simplify]: Simplify 1.0 into 1.0 0.246 * [taylor]: Taking taylor expansion of k in k 0.246 * [backup-simplify]: Simplify 0 into 0 0.246 * [backup-simplify]: Simplify 1 into 1 0.246 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.246 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.246 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.246 * [taylor]: Taking taylor expansion of 2.0 in k 0.246 * [backup-simplify]: Simplify 2.0 into 2.0 0.246 * [taylor]: Taking taylor expansion of PI in k 0.246 * [backup-simplify]: Simplify PI into PI 0.246 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.247 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.247 * [taylor]: Taking taylor expansion of (log n) in k 0.247 * [taylor]: Taking taylor expansion of n in k 0.247 * [backup-simplify]: Simplify n into n 0.247 * [backup-simplify]: Simplify (log n) into (log n) 0.247 * [backup-simplify]: Simplify (- 0) into 0 0.247 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.248 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.249 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.249 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.250 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.251 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.251 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.252 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.253 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.253 * [backup-simplify]: Simplify (- 0) into 0 0.253 * [backup-simplify]: Simplify (+ 0 0) into 0 0.253 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 0.254 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.255 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.256 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.256 * [taylor]: Taking taylor expansion of 0 in k 0.256 * [backup-simplify]: Simplify 0 into 0 0.256 * [backup-simplify]: Simplify 0 into 0 0.257 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.257 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.258 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.258 * [backup-simplify]: Simplify (+ 0 0) into 0 0.258 * [backup-simplify]: Simplify (- 1) into -1 0.259 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.260 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.261 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 0.263 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0.269 * [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)))))) 0.269 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.270 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.272 * [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 0.272 * [backup-simplify]: Simplify (- 0) into 0 0.272 * [backup-simplify]: Simplify (+ 0 0) into 0 0.273 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 0.273 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.274 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.276 * [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 0.276 * [taylor]: Taking taylor expansion of 0 in k 0.276 * [backup-simplify]: Simplify 0 into 0 0.276 * [backup-simplify]: Simplify 0 into 0 0.276 * [backup-simplify]: Simplify 0 into 0 0.276 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.278 * [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 0.279 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 0.279 * [backup-simplify]: Simplify (+ 0 0) into 0 0.280 * [backup-simplify]: Simplify (- 0) into 0 0.280 * [backup-simplify]: Simplify (+ 0 0) into 0 0.281 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.282 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 0.284 * [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)))))) 0.287 * [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)))))) 0.293 * [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)))))) 0.294 * [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)))) 0.294 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.294 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.294 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.294 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.294 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.294 * [taylor]: Taking taylor expansion of 0.5 in k 0.294 * [backup-simplify]: Simplify 0.5 into 0.5 0.294 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.294 * [taylor]: Taking taylor expansion of 1.0 in k 0.294 * [backup-simplify]: Simplify 1.0 into 1.0 0.294 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.294 * [taylor]: Taking taylor expansion of k in k 0.294 * [backup-simplify]: Simplify 0 into 0 0.294 * [backup-simplify]: Simplify 1 into 1 0.294 * [backup-simplify]: Simplify (/ 1 1) into 1 0.294 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.294 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.294 * [taylor]: Taking taylor expansion of 2.0 in k 0.294 * [backup-simplify]: Simplify 2.0 into 2.0 0.294 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.294 * [taylor]: Taking taylor expansion of PI in k 0.294 * [backup-simplify]: Simplify PI into PI 0.294 * [taylor]: Taking taylor expansion of n in k 0.294 * [backup-simplify]: Simplify n into n 0.294 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.294 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.294 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.295 * [backup-simplify]: Simplify (- 1) into -1 0.295 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.295 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.295 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.295 * [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))))) 0.295 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.295 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.295 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.296 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.296 * [taylor]: Taking taylor expansion of 0.5 in n 0.296 * [backup-simplify]: Simplify 0.5 into 0.5 0.296 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.296 * [taylor]: Taking taylor expansion of 1.0 in n 0.296 * [backup-simplify]: Simplify 1.0 into 1.0 0.296 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.296 * [taylor]: Taking taylor expansion of k in n 0.296 * [backup-simplify]: Simplify k into k 0.296 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.296 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.296 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.296 * [taylor]: Taking taylor expansion of 2.0 in n 0.296 * [backup-simplify]: Simplify 2.0 into 2.0 0.296 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.296 * [taylor]: Taking taylor expansion of PI in n 0.296 * [backup-simplify]: Simplify PI into PI 0.296 * [taylor]: Taking taylor expansion of n in n 0.296 * [backup-simplify]: Simplify 0 into 0 0.296 * [backup-simplify]: Simplify 1 into 1 0.296 * [backup-simplify]: Simplify (/ PI 1) into PI 0.296 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.297 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.297 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.297 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.297 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.298 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.299 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.299 * [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))))) 0.299 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.299 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.299 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.299 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.300 * [taylor]: Taking taylor expansion of 0.5 in n 0.300 * [backup-simplify]: Simplify 0.5 into 0.5 0.300 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.300 * [taylor]: Taking taylor expansion of 1.0 in n 0.300 * [backup-simplify]: Simplify 1.0 into 1.0 0.300 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.300 * [taylor]: Taking taylor expansion of k in n 0.300 * [backup-simplify]: Simplify k into k 0.300 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.300 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.300 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.300 * [taylor]: Taking taylor expansion of 2.0 in n 0.300 * [backup-simplify]: Simplify 2.0 into 2.0 0.300 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.300 * [taylor]: Taking taylor expansion of PI in n 0.300 * [backup-simplify]: Simplify PI into PI 0.300 * [taylor]: Taking taylor expansion of n in n 0.300 * [backup-simplify]: Simplify 0 into 0 0.300 * [backup-simplify]: Simplify 1 into 1 0.300 * [backup-simplify]: Simplify (/ PI 1) into PI 0.300 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.301 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.301 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.301 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.301 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.302 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.303 * [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)))) 0.303 * [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))))) 0.304 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.304 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.304 * [taylor]: Taking taylor expansion of 0.5 in k 0.304 * [backup-simplify]: Simplify 0.5 into 0.5 0.304 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.304 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.304 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.304 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.304 * [taylor]: Taking taylor expansion of 2.0 in k 0.304 * [backup-simplify]: Simplify 2.0 into 2.0 0.304 * [taylor]: Taking taylor expansion of PI in k 0.304 * [backup-simplify]: Simplify PI into PI 0.304 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.305 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.305 * [taylor]: Taking taylor expansion of (log n) in k 0.305 * [taylor]: Taking taylor expansion of n in k 0.305 * [backup-simplify]: Simplify n into n 0.305 * [backup-simplify]: Simplify (log n) into (log n) 0.305 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.305 * [taylor]: Taking taylor expansion of 1.0 in k 0.305 * [backup-simplify]: Simplify 1.0 into 1.0 0.305 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.305 * [taylor]: Taking taylor expansion of k in k 0.305 * [backup-simplify]: Simplify 0 into 0 0.305 * [backup-simplify]: Simplify 1 into 1 0.305 * [backup-simplify]: Simplify (/ 1 1) into 1 0.305 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.306 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.306 * [backup-simplify]: Simplify (- 1) into -1 0.306 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.307 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.307 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 0.308 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.309 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.310 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.311 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.311 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.311 * [backup-simplify]: Simplify (- 0) into 0 0.311 * [backup-simplify]: Simplify (+ 0 0) into 0 0.312 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.312 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.313 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.314 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.314 * [taylor]: Taking taylor expansion of 0 in k 0.314 * [backup-simplify]: Simplify 0 into 0 0.314 * [backup-simplify]: Simplify 0 into 0 0.314 * [backup-simplify]: Simplify 0 into 0 0.315 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.315 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.317 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.317 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.317 * [backup-simplify]: Simplify (- 0) into 0 0.318 * [backup-simplify]: Simplify (+ 0 0) into 0 0.318 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 0.319 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.320 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 0.321 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.321 * [taylor]: Taking taylor expansion of 0 in k 0.321 * [backup-simplify]: Simplify 0 into 0 0.321 * [backup-simplify]: Simplify 0 into 0 0.321 * [backup-simplify]: Simplify 0 into 0 0.321 * [backup-simplify]: Simplify 0 into 0 0.322 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.323 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.325 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 0.326 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.326 * [backup-simplify]: Simplify (- 0) into 0 0.326 * [backup-simplify]: Simplify (+ 0 0) into 0 0.327 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 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 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 0.330 * [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 0.330 * [taylor]: Taking taylor expansion of 0 in k 0.330 * [backup-simplify]: Simplify 0 into 0 0.330 * [backup-simplify]: Simplify 0 into 0 0.331 * [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)))) 0.332 * [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))) 0.332 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.332 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.332 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.332 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.332 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.332 * [taylor]: Taking taylor expansion of 0.5 in k 0.332 * [backup-simplify]: Simplify 0.5 into 0.5 0.332 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.332 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.332 * [taylor]: Taking taylor expansion of k in k 0.332 * [backup-simplify]: Simplify 0 into 0 0.332 * [backup-simplify]: Simplify 1 into 1 0.332 * [backup-simplify]: Simplify (/ 1 1) into 1 0.332 * [taylor]: Taking taylor expansion of 1.0 in k 0.332 * [backup-simplify]: Simplify 1.0 into 1.0 0.332 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.332 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.332 * [taylor]: Taking taylor expansion of -2.0 in k 0.332 * [backup-simplify]: Simplify -2.0 into -2.0 0.332 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.332 * [taylor]: Taking taylor expansion of PI in k 0.332 * [backup-simplify]: Simplify PI into PI 0.332 * [taylor]: Taking taylor expansion of n in k 0.332 * [backup-simplify]: Simplify n into n 0.332 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.332 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.332 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.333 * [backup-simplify]: Simplify (+ 1 0) into 1 0.333 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.333 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.333 * [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)))))) 0.333 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.333 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.333 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.333 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.333 * [taylor]: Taking taylor expansion of 0.5 in n 0.333 * [backup-simplify]: Simplify 0.5 into 0.5 0.333 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.333 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.333 * [taylor]: Taking taylor expansion of k in n 0.333 * [backup-simplify]: Simplify k into k 0.333 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.333 * [taylor]: Taking taylor expansion of 1.0 in n 0.333 * [backup-simplify]: Simplify 1.0 into 1.0 0.333 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.333 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.333 * [taylor]: Taking taylor expansion of -2.0 in n 0.334 * [backup-simplify]: Simplify -2.0 into -2.0 0.334 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.334 * [taylor]: Taking taylor expansion of PI in n 0.334 * [backup-simplify]: Simplify PI into PI 0.334 * [taylor]: Taking taylor expansion of n in n 0.334 * [backup-simplify]: Simplify 0 into 0 0.334 * [backup-simplify]: Simplify 1 into 1 0.334 * [backup-simplify]: Simplify (/ PI 1) into PI 0.334 * [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 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.335 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.336 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.336 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.337 * [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))))) 0.337 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.337 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.337 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.337 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.337 * [taylor]: Taking taylor expansion of 0.5 in n 0.337 * [backup-simplify]: Simplify 0.5 into 0.5 0.337 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.337 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.337 * [taylor]: Taking taylor expansion of k in n 0.337 * [backup-simplify]: Simplify k into k 0.337 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.337 * [taylor]: Taking taylor expansion of 1.0 in n 0.337 * [backup-simplify]: Simplify 1.0 into 1.0 0.337 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.337 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.337 * [taylor]: Taking taylor expansion of -2.0 in n 0.337 * [backup-simplify]: Simplify -2.0 into -2.0 0.337 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.337 * [taylor]: Taking taylor expansion of PI in n 0.337 * [backup-simplify]: Simplify PI into PI 0.337 * [taylor]: Taking taylor expansion of n in n 0.337 * [backup-simplify]: Simplify 0 into 0 0.338 * [backup-simplify]: Simplify 1 into 1 0.338 * [backup-simplify]: Simplify (/ PI 1) into PI 0.338 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.339 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.339 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.339 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.340 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.340 * [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)))) 0.341 * [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))))) 0.341 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.341 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.341 * [taylor]: Taking taylor expansion of 0.5 in k 0.341 * [backup-simplify]: Simplify 0.5 into 0.5 0.341 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.341 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.341 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.341 * [taylor]: Taking taylor expansion of k in k 0.341 * [backup-simplify]: Simplify 0 into 0 0.341 * [backup-simplify]: Simplify 1 into 1 0.342 * [backup-simplify]: Simplify (/ 1 1) into 1 0.342 * [taylor]: Taking taylor expansion of 1.0 in k 0.342 * [backup-simplify]: Simplify 1.0 into 1.0 0.342 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.342 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.342 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.342 * [taylor]: Taking taylor expansion of -2.0 in k 0.342 * [backup-simplify]: Simplify -2.0 into -2.0 0.342 * [taylor]: Taking taylor expansion of PI in k 0.342 * [backup-simplify]: Simplify PI into PI 0.342 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.343 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.343 * [taylor]: Taking taylor expansion of (log n) in k 0.343 * [taylor]: Taking taylor expansion of n in k 0.343 * [backup-simplify]: Simplify n into n 0.343 * [backup-simplify]: Simplify (log n) into (log n) 0.343 * [backup-simplify]: Simplify (+ 1 0) into 1 0.343 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.344 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 0.344 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 0.345 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 0.346 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.346 * [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))))) 0.347 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.347 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.348 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.348 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.348 * [backup-simplify]: Simplify (+ 0 0) into 0 0.349 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 0.350 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.351 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.352 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.352 * [taylor]: Taking taylor expansion of 0 in k 0.352 * [backup-simplify]: Simplify 0 into 0 0.352 * [backup-simplify]: Simplify 0 into 0 0.352 * [backup-simplify]: Simplify 0 into 0 0.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.353 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.354 * [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 0.355 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.355 * [backup-simplify]: Simplify (+ 0 0) into 0 0.355 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 0.356 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.360 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 0.362 * [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 0.362 * [taylor]: Taking taylor expansion of 0 in k 0.362 * [backup-simplify]: Simplify 0 into 0 0.362 * [backup-simplify]: Simplify 0 into 0 0.362 * [backup-simplify]: Simplify 0 into 0 0.362 * [backup-simplify]: Simplify 0 into 0 0.362 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.363 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.366 * [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 0.366 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.366 * [backup-simplify]: Simplify (+ 0 0) into 0 0.367 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.368 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.369 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 0.370 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 0.370 * [taylor]: Taking taylor expansion of 0 in k 0.370 * [backup-simplify]: Simplify 0 into 0 0.370 * [backup-simplify]: Simplify 0 into 0 0.371 * [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)))))) 0.371 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.372 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.372 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.372 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.372 * [taylor]: Taking taylor expansion of 2.0 in n 0.372 * [backup-simplify]: Simplify 2.0 into 2.0 0.372 * [taylor]: Taking taylor expansion of (* n PI) in n 0.372 * [taylor]: Taking taylor expansion of n in n 0.372 * [backup-simplify]: Simplify 0 into 0 0.372 * [backup-simplify]: Simplify 1 into 1 0.372 * [taylor]: Taking taylor expansion of PI in n 0.372 * [backup-simplify]: Simplify PI into PI 0.372 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.372 * [taylor]: Taking taylor expansion of 2.0 in n 0.372 * [backup-simplify]: Simplify 2.0 into 2.0 0.372 * [taylor]: Taking taylor expansion of (* n PI) in n 0.372 * [taylor]: Taking taylor expansion of n in n 0.372 * [backup-simplify]: Simplify 0 into 0 0.372 * [backup-simplify]: Simplify 1 into 1 0.372 * [taylor]: Taking taylor expansion of PI in n 0.372 * [backup-simplify]: Simplify PI into PI 0.372 * [backup-simplify]: Simplify (* 0 PI) into 0 0.373 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.373 * [backup-simplify]: Simplify 0 into 0 0.373 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.374 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.375 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.375 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.376 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.376 * [backup-simplify]: Simplify 0 into 0 0.376 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.377 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.377 * [backup-simplify]: Simplify 0 into 0 0.378 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.378 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.378 * [backup-simplify]: Simplify 0 into 0 0.379 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.380 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 0.380 * [backup-simplify]: Simplify 0 into 0 0.381 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.382 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.382 * [backup-simplify]: Simplify 0 into 0 0.383 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.384 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.384 * [backup-simplify]: Simplify 0 into 0 0.384 * [backup-simplify]: Simplify (* (* 2.0 PI) 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 0.385 * [backup-simplify]: Simplify 0 into 0 0.385 * [backup-simplify]: Simplify 1 into 1 0.385 * [backup-simplify]: Simplify (/ PI 1) into PI 0.385 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.385 * [taylor]: Taking taylor expansion of 2.0 in n 0.385 * [backup-simplify]: Simplify 2.0 into 2.0 0.385 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.385 * [taylor]: Taking taylor expansion of PI in n 0.385 * [backup-simplify]: Simplify PI into PI 0.385 * [taylor]: Taking taylor expansion of n in n 0.385 * [backup-simplify]: Simplify 0 into 0 0.385 * [backup-simplify]: Simplify 1 into 1 0.385 * [backup-simplify]: Simplify (/ PI 1) into PI 0.386 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.386 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.386 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.387 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.387 * [backup-simplify]: Simplify 0 into 0 0.387 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.388 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.388 * [backup-simplify]: Simplify 0 into 0 0.388 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.389 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.389 * [backup-simplify]: Simplify 0 into 0 0.390 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.390 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.390 * [backup-simplify]: Simplify 0 into 0 0.391 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.392 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.392 * [backup-simplify]: Simplify 0 into 0 0.392 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.393 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.393 * [backup-simplify]: Simplify 0 into 0 0.394 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.394 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.394 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.394 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.394 * [taylor]: Taking taylor expansion of -2.0 in n 0.394 * [backup-simplify]: Simplify -2.0 into -2.0 0.394 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.394 * [taylor]: Taking taylor expansion of PI in n 0.394 * [backup-simplify]: Simplify PI into PI 0.394 * [taylor]: Taking taylor expansion of n in n 0.394 * [backup-simplify]: Simplify 0 into 0 0.394 * [backup-simplify]: Simplify 1 into 1 0.394 * [backup-simplify]: Simplify (/ PI 1) into PI 0.394 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.394 * [taylor]: Taking taylor expansion of -2.0 in n 0.394 * [backup-simplify]: Simplify -2.0 into -2.0 0.394 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.394 * [taylor]: Taking taylor expansion of PI in n 0.394 * [backup-simplify]: Simplify PI into PI 0.394 * [taylor]: Taking taylor expansion of n in n 0.394 * [backup-simplify]: Simplify 0 into 0 0.395 * [backup-simplify]: Simplify 1 into 1 0.395 * [backup-simplify]: Simplify (/ PI 1) into PI 0.395 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.395 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.396 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.396 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.396 * [backup-simplify]: Simplify 0 into 0 0.397 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.397 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.397 * [backup-simplify]: Simplify 0 into 0 0.398 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.399 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.399 * [backup-simplify]: Simplify 0 into 0 0.399 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.400 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.400 * [backup-simplify]: Simplify 0 into 0 0.400 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.401 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.401 * [backup-simplify]: Simplify 0 into 0 0.402 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.403 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.403 * [backup-simplify]: Simplify 0 into 0 0.403 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.403 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.403 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.403 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.403 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.403 * [taylor]: Taking taylor expansion of 1.0 in k 0.403 * [backup-simplify]: Simplify 1.0 into 1.0 0.403 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.403 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.403 * [taylor]: Taking taylor expansion of k in k 0.403 * [backup-simplify]: Simplify 0 into 0 0.403 * [backup-simplify]: Simplify 1 into 1 0.404 * [backup-simplify]: Simplify (/ 1 1) into 1 0.404 * [backup-simplify]: Simplify (sqrt 0) into 0 0.405 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.405 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.405 * [taylor]: Taking taylor expansion of 1.0 in k 0.405 * [backup-simplify]: Simplify 1.0 into 1.0 0.405 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.405 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.405 * [taylor]: Taking taylor expansion of k in k 0.405 * [backup-simplify]: Simplify 0 into 0 0.405 * [backup-simplify]: Simplify 1 into 1 0.405 * [backup-simplify]: Simplify (/ 1 1) into 1 0.405 * [backup-simplify]: Simplify (sqrt 0) into 0 0.406 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.406 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.406 * [backup-simplify]: Simplify 0 into 0 0.407 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.407 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.408 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.409 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.410 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.411 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.411 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.413 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.414 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.414 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.415 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 0.416 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 0.416 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.416 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.416 * [taylor]: Taking taylor expansion of 1.0 in k 0.416 * [backup-simplify]: Simplify 1.0 into 1.0 0.416 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.416 * [taylor]: Taking taylor expansion of k in k 0.416 * [backup-simplify]: Simplify 0 into 0 0.416 * [backup-simplify]: Simplify 1 into 1 0.416 * [backup-simplify]: Simplify (sqrt 0) into 0 0.417 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.417 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.417 * [taylor]: Taking taylor expansion of 1.0 in k 0.417 * [backup-simplify]: Simplify 1.0 into 1.0 0.417 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.417 * [taylor]: Taking taylor expansion of k in k 0.417 * [backup-simplify]: Simplify 0 into 0 0.417 * [backup-simplify]: Simplify 1 into 1 0.417 * [backup-simplify]: Simplify (sqrt 0) into 0 0.418 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.418 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.418 * [backup-simplify]: Simplify 0 into 0 0.419 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.419 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.421 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.422 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.422 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.424 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.425 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.425 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.426 * [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)))))))) 0.427 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.427 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.427 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.427 * [taylor]: Taking taylor expansion of 1.0 in k 0.427 * [backup-simplify]: Simplify 1.0 into 1.0 0.427 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.427 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.427 * [taylor]: Taking taylor expansion of -1 in k 0.427 * [backup-simplify]: Simplify -1 into -1 0.427 * [taylor]: Taking taylor expansion of k in k 0.427 * [backup-simplify]: Simplify 0 into 0 0.427 * [backup-simplify]: Simplify 1 into 1 0.427 * [backup-simplify]: Simplify (/ -1 1) into -1 0.427 * [backup-simplify]: Simplify (sqrt 0) into 0 0.428 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.428 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.428 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.428 * [taylor]: Taking taylor expansion of 1.0 in k 0.428 * [backup-simplify]: Simplify 1.0 into 1.0 0.428 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.428 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.428 * [taylor]: Taking taylor expansion of -1 in k 0.428 * [backup-simplify]: Simplify -1 into -1 0.428 * [taylor]: Taking taylor expansion of k in k 0.428 * [backup-simplify]: Simplify 0 into 0 0.428 * [backup-simplify]: Simplify 1 into 1 0.429 * [backup-simplify]: Simplify (/ -1 1) into -1 0.429 * [backup-simplify]: Simplify (sqrt 0) into 0 0.430 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.430 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.430 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.432 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.434 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 0.434 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.434 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.436 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.439 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 0.439 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.440 * [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))))) 0.440 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.440 * [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))))) 0.440 * [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 0.440 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.440 * [taylor]: Taking taylor expansion of 1.0 in n 0.440 * [backup-simplify]: Simplify 1.0 into 1.0 0.440 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.440 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.440 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.440 * [taylor]: Taking taylor expansion of k in n 0.440 * [backup-simplify]: Simplify k into k 0.440 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.440 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 0.440 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.441 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 0.441 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.441 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.441 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.441 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.441 * [taylor]: Taking taylor expansion of 0.5 in n 0.441 * [backup-simplify]: Simplify 0.5 into 0.5 0.441 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.441 * [taylor]: Taking taylor expansion of 1.0 in n 0.441 * [backup-simplify]: Simplify 1.0 into 1.0 0.441 * [taylor]: Taking taylor expansion of k in n 0.441 * [backup-simplify]: Simplify k into k 0.441 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.441 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.441 * [taylor]: Taking taylor expansion of 2.0 in n 0.441 * [backup-simplify]: Simplify 2.0 into 2.0 0.441 * [taylor]: Taking taylor expansion of (* n PI) in n 0.441 * [taylor]: Taking taylor expansion of n in n 0.441 * [backup-simplify]: Simplify 0 into 0 0.441 * [backup-simplify]: Simplify 1 into 1 0.441 * [taylor]: Taking taylor expansion of PI in n 0.441 * [backup-simplify]: Simplify PI into PI 0.441 * [backup-simplify]: Simplify (* 0 PI) into 0 0.441 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.442 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.443 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.444 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.444 * [backup-simplify]: Simplify (- k) into (- k) 0.444 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.444 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.448 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.449 * [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)))) 0.450 * [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))))) 0.450 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.450 * [taylor]: Taking taylor expansion of 1.0 in k 0.450 * [backup-simplify]: Simplify 1.0 into 1.0 0.450 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.450 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.450 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.450 * [taylor]: Taking taylor expansion of k in k 0.450 * [backup-simplify]: Simplify 0 into 0 0.450 * [backup-simplify]: Simplify 1 into 1 0.450 * [backup-simplify]: Simplify (/ 1 1) into 1 0.450 * [backup-simplify]: Simplify (sqrt 0) into 0 0.451 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.451 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.451 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.451 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.451 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.451 * [taylor]: Taking taylor expansion of 0.5 in k 0.451 * [backup-simplify]: Simplify 0.5 into 0.5 0.451 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.451 * [taylor]: Taking taylor expansion of 1.0 in k 0.451 * [backup-simplify]: Simplify 1.0 into 1.0 0.451 * [taylor]: Taking taylor expansion of k in k 0.451 * [backup-simplify]: Simplify 0 into 0 0.451 * [backup-simplify]: Simplify 1 into 1 0.451 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.451 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.451 * [taylor]: Taking taylor expansion of 2.0 in k 0.451 * [backup-simplify]: Simplify 2.0 into 2.0 0.451 * [taylor]: Taking taylor expansion of (* n PI) in k 0.451 * [taylor]: Taking taylor expansion of n in k 0.451 * [backup-simplify]: Simplify n into n 0.451 * [taylor]: Taking taylor expansion of PI in k 0.451 * [backup-simplify]: Simplify PI into PI 0.451 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.451 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.451 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.452 * [backup-simplify]: Simplify (- 0) into 0 0.452 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.452 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.452 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.452 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.452 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.452 * [taylor]: Taking taylor expansion of 1.0 in k 0.452 * [backup-simplify]: Simplify 1.0 into 1.0 0.452 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.452 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.452 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.452 * [taylor]: Taking taylor expansion of k in k 0.452 * [backup-simplify]: Simplify 0 into 0 0.453 * [backup-simplify]: Simplify 1 into 1 0.453 * [backup-simplify]: Simplify (/ 1 1) into 1 0.453 * [backup-simplify]: Simplify (sqrt 0) into 0 0.454 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.454 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.454 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.454 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.454 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.454 * [taylor]: Taking taylor expansion of 0.5 in k 0.454 * [backup-simplify]: Simplify 0.5 into 0.5 0.454 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.454 * [taylor]: Taking taylor expansion of 1.0 in k 0.454 * [backup-simplify]: Simplify 1.0 into 1.0 0.454 * [taylor]: Taking taylor expansion of k in k 0.454 * [backup-simplify]: Simplify 0 into 0 0.454 * [backup-simplify]: Simplify 1 into 1 0.454 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.454 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.454 * [taylor]: Taking taylor expansion of 2.0 in k 0.454 * [backup-simplify]: Simplify 2.0 into 2.0 0.454 * [taylor]: Taking taylor expansion of (* n PI) in k 0.454 * [taylor]: Taking taylor expansion of n in k 0.454 * [backup-simplify]: Simplify n into n 0.454 * [taylor]: Taking taylor expansion of PI in k 0.454 * [backup-simplify]: Simplify PI into PI 0.454 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.454 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.454 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.454 * [backup-simplify]: Simplify (- 0) into 0 0.455 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.455 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.455 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.455 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.455 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 0.456 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.456 * [taylor]: Taking taylor expansion of 0 in n 0.456 * [backup-simplify]: Simplify 0 into 0 0.456 * [backup-simplify]: Simplify 0 into 0 0.456 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 0.456 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 0.457 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 0.457 * [backup-simplify]: Simplify (- 1) into -1 0.457 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.458 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 0.459 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 0.459 * [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))) 0.460 * [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))) 0.461 * [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))) 0.461 * [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 0.461 * [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 0.461 * [taylor]: Taking taylor expansion of +nan.0 in n 0.461 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.461 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.461 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.461 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.461 * [taylor]: Taking taylor expansion of 0.5 in n 0.461 * [backup-simplify]: Simplify 0.5 into 0.5 0.461 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.461 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.461 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.461 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.461 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.461 * [taylor]: Taking taylor expansion of 1.0 in n 0.461 * [backup-simplify]: Simplify 1.0 into 1.0 0.461 * [taylor]: Taking taylor expansion of (log PI) in n 0.461 * [taylor]: Taking taylor expansion of PI in n 0.461 * [backup-simplify]: Simplify PI into PI 0.461 * [backup-simplify]: Simplify (log PI) into (log PI) 0.462 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.463 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.463 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.463 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.463 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.463 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.463 * [taylor]: Taking taylor expansion of 1.0 in n 0.463 * [backup-simplify]: Simplify 1.0 into 1.0 0.463 * [taylor]: Taking taylor expansion of (log n) in n 0.463 * [taylor]: Taking taylor expansion of n in n 0.463 * [backup-simplify]: Simplify 0 into 0 0.463 * [backup-simplify]: Simplify 1 into 1 0.463 * [backup-simplify]: Simplify (log 1) into 0 0.464 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.464 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.464 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.464 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.464 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.464 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.464 * [taylor]: Taking taylor expansion of 1.0 in n 0.464 * [backup-simplify]: Simplify 1.0 into 1.0 0.464 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.464 * [taylor]: Taking taylor expansion of 2.0 in n 0.464 * [backup-simplify]: Simplify 2.0 into 2.0 0.464 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.465 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.465 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.466 * [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) 0.467 * [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) 0.467 * [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)) 0.468 * [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))) 0.469 * [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) 0.470 * [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)) 0.471 * [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))) 0.471 * [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))) 0.471 * [backup-simplify]: Simplify 0 into 0 0.472 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 0.472 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 0.473 * [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 0.474 * [backup-simplify]: Simplify (- 0) into 0 0.474 * [backup-simplify]: Simplify (+ 0 0) into 0 0.474 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.475 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 0.476 * [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))) 0.476 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.478 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.480 * [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)))))))) 0.483 * [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)))))))) 0.483 * [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 0.483 * [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 0.483 * [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 0.483 * [taylor]: Taking taylor expansion of +nan.0 in n 0.483 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.483 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.483 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.483 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.483 * [taylor]: Taking taylor expansion of 0.5 in n 0.483 * [backup-simplify]: Simplify 0.5 into 0.5 0.483 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.483 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.483 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.483 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.483 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.483 * [taylor]: Taking taylor expansion of 1.0 in n 0.483 * [backup-simplify]: Simplify 1.0 into 1.0 0.483 * [taylor]: Taking taylor expansion of (log PI) in n 0.483 * [taylor]: Taking taylor expansion of PI in n 0.483 * [backup-simplify]: Simplify PI into PI 0.483 * [backup-simplify]: Simplify (log PI) into (log PI) 0.484 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.485 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.485 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.485 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.485 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.485 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) 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 n) in n 0.485 * [taylor]: Taking taylor expansion of n in n 0.485 * [backup-simplify]: Simplify 0 into 0 0.485 * [backup-simplify]: Simplify 1 into 1 0.485 * [backup-simplify]: Simplify (log 1) into 0 0.486 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.486 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.486 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.486 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.486 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.486 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.486 * [taylor]: Taking taylor expansion of 1.0 in n 0.486 * [backup-simplify]: Simplify 1.0 into 1.0 0.486 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.486 * [taylor]: Taking taylor expansion of 2.0 in n 0.486 * [backup-simplify]: Simplify 2.0 into 2.0 0.486 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.487 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.487 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.488 * [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) 0.489 * [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) 0.489 * [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)) 0.490 * [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))) 0.491 * [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) 0.491 * [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 0.491 * [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 0.491 * [taylor]: Taking taylor expansion of +nan.0 in n 0.491 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.491 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 0.491 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.491 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.491 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.491 * [taylor]: Taking taylor expansion of 0.5 in n 0.491 * [backup-simplify]: Simplify 0.5 into 0.5 0.491 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.491 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.491 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.491 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.491 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.491 * [taylor]: Taking taylor expansion of 1.0 in n 0.491 * [backup-simplify]: Simplify 1.0 into 1.0 0.491 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.491 * [taylor]: Taking taylor expansion of 2.0 in n 0.491 * [backup-simplify]: Simplify 2.0 into 2.0 0.492 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.492 * [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 0.519 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 0.520 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 0.521 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 0.521 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.522 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.522 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 0.522 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 0.523 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 0.524 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 0.525 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 0.525 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 0.527 * [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 0.529 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 0.530 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 0.530 * [backup-simplify]: Simplify (- 0) into 0 0.530 * [backup-simplify]: Simplify 0 into 0 0.530 * [backup-simplify]: Simplify 0 into 0 0.531 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.532 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 0.533 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 0.534 * [backup-simplify]: Simplify (- 0) into 0 0.534 * [backup-simplify]: Simplify (+ 0 0) into 0 0.534 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 0.535 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 0.536 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.537 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.539 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.545 * [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)))))))) 0.552 * [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)))))))) 0.552 * [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 0.552 * [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 0.552 * [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 0.552 * [taylor]: Taking taylor expansion of +nan.0 in n 0.552 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.552 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.552 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.552 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.552 * [taylor]: Taking taylor expansion of 0.5 in n 0.552 * [backup-simplify]: Simplify 0.5 into 0.5 0.552 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.552 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.552 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.552 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.552 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.552 * [taylor]: Taking taylor expansion of 1.0 in n 0.553 * [backup-simplify]: Simplify 1.0 into 1.0 0.553 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.553 * [taylor]: Taking taylor expansion of 2.0 in n 0.553 * [backup-simplify]: Simplify 2.0 into 2.0 0.553 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.553 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.554 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.554 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.554 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.554 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.554 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.554 * [taylor]: Taking taylor expansion of 1.0 in n 0.554 * [backup-simplify]: Simplify 1.0 into 1.0 0.554 * [taylor]: Taking taylor expansion of (log n) in n 0.554 * [taylor]: Taking taylor expansion of n in n 0.554 * [backup-simplify]: Simplify 0 into 0 0.554 * [backup-simplify]: Simplify 1 into 1 0.555 * [backup-simplify]: Simplify (log 1) into 0 0.555 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.555 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.555 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.555 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.555 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.555 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.555 * [taylor]: Taking taylor expansion of 1.0 in n 0.555 * [backup-simplify]: Simplify 1.0 into 1.0 0.555 * [taylor]: Taking taylor expansion of (log PI) in n 0.555 * [taylor]: Taking taylor expansion of PI in n 0.555 * [backup-simplify]: Simplify PI into PI 0.555 * [backup-simplify]: Simplify (log PI) into (log PI) 0.556 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.557 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.557 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.558 * [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) 0.559 * [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)) 0.559 * [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))) 0.560 * [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) 0.560 * [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 0.560 * [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 0.560 * [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 0.560 * [taylor]: Taking taylor expansion of +nan.0 in n 0.560 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.560 * [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 0.560 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.560 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.561 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.561 * [taylor]: Taking taylor expansion of 0.5 in n 0.561 * [backup-simplify]: Simplify 0.5 into 0.5 0.561 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.561 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.561 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.561 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.561 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) 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 2.0) in n 0.561 * [taylor]: Taking taylor expansion of 2.0 in n 0.561 * [backup-simplify]: Simplify 2.0 into 2.0 0.561 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.561 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.562 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.562 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.562 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.562 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.562 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.562 * [taylor]: Taking taylor expansion of 1.0 in n 0.562 * [backup-simplify]: Simplify 1.0 into 1.0 0.562 * [taylor]: Taking taylor expansion of (log PI) in n 0.562 * [taylor]: Taking taylor expansion of PI in n 0.562 * [backup-simplify]: Simplify PI into PI 0.563 * [backup-simplify]: Simplify (log PI) into (log PI) 0.563 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.564 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.564 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.564 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.564 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.564 * [taylor]: Taking taylor expansion of 1.0 in n 0.564 * [backup-simplify]: Simplify 1.0 into 1.0 0.564 * [taylor]: Taking taylor expansion of (log n) in n 0.564 * [taylor]: Taking taylor expansion of n in n 0.564 * [backup-simplify]: Simplify 0 into 0 0.564 * [backup-simplify]: Simplify 1 into 1 0.565 * [backup-simplify]: Simplify (log 1) into 0 0.565 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.565 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.565 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.565 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.566 * [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) 0.567 * [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)) 0.568 * [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))) 0.568 * [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) 0.568 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.569 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) 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 * [taylor]: Taking taylor expansion of (* n PI) in n 0.569 * [taylor]: Taking taylor expansion of n in n 0.569 * [backup-simplify]: Simplify 0 into 0 0.569 * [backup-simplify]: Simplify 1 into 1 0.569 * [taylor]: Taking taylor expansion of PI in n 0.569 * [backup-simplify]: Simplify PI into PI 0.569 * [backup-simplify]: Simplify (* 0 PI) into 0 0.569 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.570 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.571 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.571 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.571 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 0.572 * [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 0.572 * [taylor]: Taking taylor expansion of +nan.0 in n 0.572 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.572 * [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 0.572 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.572 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.572 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.572 * [taylor]: Taking taylor expansion of 0.5 in n 0.572 * [backup-simplify]: Simplify 0.5 into 0.5 0.572 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.572 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.572 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.572 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.572 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.572 * [taylor]: Taking taylor expansion of 1.0 in n 0.572 * [backup-simplify]: Simplify 1.0 into 1.0 0.572 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.572 * [taylor]: Taking taylor expansion of 2.0 in n 0.572 * [backup-simplify]: Simplify 2.0 into 2.0 0.572 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.573 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.573 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.573 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.573 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.573 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.574 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.574 * [taylor]: Taking taylor expansion of 1.0 in n 0.574 * [backup-simplify]: Simplify 1.0 into 1.0 0.574 * [taylor]: Taking taylor expansion of (log PI) in n 0.574 * [taylor]: Taking taylor expansion of PI in n 0.574 * [backup-simplify]: Simplify PI into PI 0.574 * [backup-simplify]: Simplify (log PI) into (log PI) 0.574 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.575 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.575 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.575 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.575 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.575 * [taylor]: Taking taylor expansion of 1.0 in n 0.575 * [backup-simplify]: Simplify 1.0 into 1.0 0.575 * [taylor]: Taking taylor expansion of (log n) in n 0.575 * [taylor]: Taking taylor expansion of n in n 0.575 * [backup-simplify]: Simplify 0 into 0 0.575 * [backup-simplify]: Simplify 1 into 1 0.576 * [backup-simplify]: Simplify (log 1) into 0 0.576 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.576 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.576 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.576 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.577 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.578 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.579 * [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))) 0.580 * [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) 0.580 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.580 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.580 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.580 * [taylor]: Taking taylor expansion of 2.0 in n 0.580 * [backup-simplify]: Simplify 2.0 into 2.0 0.580 * [taylor]: Taking taylor expansion of (* n PI) in n 0.580 * [taylor]: Taking taylor expansion of n in n 0.580 * [backup-simplify]: Simplify 0 into 0 0.580 * [backup-simplify]: Simplify 1 into 1 0.580 * [taylor]: Taking taylor expansion of PI in n 0.580 * [backup-simplify]: Simplify PI into PI 0.580 * [backup-simplify]: Simplify (* 0 PI) into 0 0.580 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.581 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.582 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.583 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.584 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.585 * [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)) 0.585 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.587 * [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)) 0.588 * [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))) 0.589 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.590 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.591 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 0.593 * [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)) 0.594 * [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))) 0.596 * [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)))))))) 0.602 * [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)))))))))))) 0.610 * [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)))))))))))) 0.619 * [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)))))))))))))) 0.628 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 0.640 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 0.655 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) 0.656 * [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)))))) 0.656 * [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 0.656 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.656 * [taylor]: Taking taylor expansion of 1.0 in n 0.656 * [backup-simplify]: Simplify 1.0 into 1.0 0.656 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.656 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.656 * [taylor]: Taking taylor expansion of k in n 0.656 * [backup-simplify]: Simplify k into k 0.656 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 0.656 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 0.656 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.656 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.656 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.656 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.656 * [taylor]: Taking taylor expansion of 0.5 in n 0.656 * [backup-simplify]: Simplify 0.5 into 0.5 0.656 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.656 * [taylor]: Taking taylor expansion of 1.0 in n 0.656 * [backup-simplify]: Simplify 1.0 into 1.0 0.656 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.656 * [taylor]: Taking taylor expansion of k in n 0.656 * [backup-simplify]: Simplify k into k 0.656 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.656 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.656 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.656 * [taylor]: Taking taylor expansion of 2.0 in n 0.656 * [backup-simplify]: Simplify 2.0 into 2.0 0.656 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.656 * [taylor]: Taking taylor expansion of PI in n 0.656 * [backup-simplify]: Simplify PI into PI 0.656 * [taylor]: Taking taylor expansion of n in n 0.656 * [backup-simplify]: Simplify 0 into 0 0.656 * [backup-simplify]: Simplify 1 into 1 0.657 * [backup-simplify]: Simplify (/ PI 1) into PI 0.657 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.657 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.658 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.658 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.658 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.658 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.659 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.660 * [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))))) 0.660 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.660 * [taylor]: Taking taylor expansion of 1.0 in k 0.660 * [backup-simplify]: Simplify 1.0 into 1.0 0.660 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.660 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.660 * [taylor]: Taking taylor expansion of k in k 0.660 * [backup-simplify]: Simplify 0 into 0 0.660 * [backup-simplify]: Simplify 1 into 1 0.660 * [backup-simplify]: Simplify (sqrt 0) into 0 0.661 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.661 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.661 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.661 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.661 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.661 * [taylor]: Taking taylor expansion of 0.5 in k 0.661 * [backup-simplify]: Simplify 0.5 into 0.5 0.661 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.661 * [taylor]: Taking taylor expansion of 1.0 in k 0.661 * [backup-simplify]: Simplify 1.0 into 1.0 0.661 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.661 * [taylor]: Taking taylor expansion of k in k 0.661 * [backup-simplify]: Simplify 0 into 0 0.661 * [backup-simplify]: Simplify 1 into 1 0.661 * [backup-simplify]: Simplify (/ 1 1) into 1 0.662 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.662 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.662 * [taylor]: Taking taylor expansion of 2.0 in k 0.662 * [backup-simplify]: Simplify 2.0 into 2.0 0.662 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.662 * [taylor]: Taking taylor expansion of PI in k 0.662 * [backup-simplify]: Simplify PI into PI 0.662 * [taylor]: Taking taylor expansion of n in k 0.662 * [backup-simplify]: Simplify n into n 0.662 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.662 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.662 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.662 * [backup-simplify]: Simplify (- 1) into -1 0.662 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.663 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.663 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.663 * [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))))) 0.663 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.663 * [taylor]: Taking taylor expansion of 1.0 in k 0.663 * [backup-simplify]: Simplify 1.0 into 1.0 0.663 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.663 * [taylor]: Taking taylor expansion of (sqrt 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 (sqrt 0) into 0 0.664 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.664 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.664 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.664 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.664 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.664 * [taylor]: Taking taylor expansion of 0.5 in k 0.664 * [backup-simplify]: Simplify 0.5 into 0.5 0.664 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.664 * [taylor]: Taking taylor expansion of 1.0 in k 0.664 * [backup-simplify]: Simplify 1.0 into 1.0 0.664 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.664 * [taylor]: Taking taylor expansion of k in k 0.664 * [backup-simplify]: Simplify 0 into 0 0.664 * [backup-simplify]: Simplify 1 into 1 0.664 * [backup-simplify]: Simplify (/ 1 1) into 1 0.664 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.664 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.664 * [taylor]: Taking taylor expansion of 2.0 in k 0.664 * [backup-simplify]: Simplify 2.0 into 2.0 0.664 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.665 * [taylor]: Taking taylor expansion of PI in k 0.665 * [backup-simplify]: Simplify PI into PI 0.665 * [taylor]: Taking taylor expansion of n in k 0.665 * [backup-simplify]: Simplify n into n 0.665 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.665 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.665 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.665 * [backup-simplify]: Simplify (- 1) into -1 0.665 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.665 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.666 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.666 * [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))))) 0.666 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 0.666 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.666 * [taylor]: Taking taylor expansion of 0 in n 0.666 * [backup-simplify]: Simplify 0 into 0 0.666 * [backup-simplify]: Simplify 0 into 0 0.667 * [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))))))) 0.667 * [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))))))) 0.667 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.667 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.667 * [taylor]: Taking taylor expansion of +nan.0 in n 0.667 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.667 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.667 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.667 * [taylor]: Taking taylor expansion of 0.5 in n 0.667 * [backup-simplify]: Simplify 0.5 into 0.5 0.667 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.667 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.667 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.667 * [taylor]: Taking taylor expansion of 2.0 in n 0.667 * [backup-simplify]: Simplify 2.0 into 2.0 0.667 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.667 * [taylor]: Taking taylor expansion of PI in n 0.667 * [backup-simplify]: Simplify PI into PI 0.667 * [taylor]: Taking taylor expansion of n in n 0.667 * [backup-simplify]: Simplify 0 into 0 0.667 * [backup-simplify]: Simplify 1 into 1 0.668 * [backup-simplify]: Simplify (/ PI 1) into PI 0.668 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.669 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.669 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.669 * [taylor]: Taking taylor expansion of 1.0 in n 0.669 * [backup-simplify]: Simplify 1.0 into 1.0 0.669 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.669 * [taylor]: Taking taylor expansion of k in n 0.669 * [backup-simplify]: Simplify k into k 0.669 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.670 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.670 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.670 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.670 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.671 * [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)))) 0.672 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.672 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 0.673 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.674 * [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))))))) 0.674 * [backup-simplify]: Simplify 0 into 0 0.676 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.676 * [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))))))) 0.677 * [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))))))) 0.677 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.677 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.677 * [taylor]: Taking taylor expansion of +nan.0 in n 0.677 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.677 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.677 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.677 * [taylor]: Taking taylor expansion of 0.5 in n 0.677 * [backup-simplify]: Simplify 0.5 into 0.5 0.677 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.677 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.677 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.677 * [taylor]: Taking taylor expansion of 2.0 in n 0.677 * [backup-simplify]: Simplify 2.0 into 2.0 0.677 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.677 * [taylor]: Taking taylor expansion of PI in n 0.677 * [backup-simplify]: Simplify PI into PI 0.677 * [taylor]: Taking taylor expansion of n in n 0.677 * [backup-simplify]: Simplify 0 into 0 0.677 * [backup-simplify]: Simplify 1 into 1 0.678 * [backup-simplify]: Simplify (/ PI 1) into PI 0.678 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.678 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.678 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.679 * [taylor]: Taking taylor expansion of 1.0 in n 0.679 * [backup-simplify]: Simplify 1.0 into 1.0 0.679 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.679 * [taylor]: Taking taylor expansion of k in n 0.679 * [backup-simplify]: Simplify k into k 0.679 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.679 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.680 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.680 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.680 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.681 * [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)))) 0.682 * [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))))) 0.683 * [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)))))) 0.683 * [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))))))) 0.684 * [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))))))) 0.685 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.685 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.685 * [backup-simplify]: Simplify (- 0) into 0 0.686 * [backup-simplify]: Simplify (+ 0 0) into 0 0.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.686 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.687 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.688 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.689 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 0.690 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.691 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 0.691 * [backup-simplify]: Simplify (- 0) into 0 0.691 * [backup-simplify]: Simplify 0 into 0 0.691 * [backup-simplify]: Simplify 0 into 0 0.694 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.694 * [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))))))) 0.695 * [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))))))) 0.695 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.695 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.695 * [taylor]: Taking taylor expansion of +nan.0 in n 0.695 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.695 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.695 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.695 * [taylor]: Taking taylor expansion of 0.5 in n 0.695 * [backup-simplify]: Simplify 0.5 into 0.5 0.695 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.695 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.695 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.695 * [taylor]: Taking taylor expansion of 2.0 in n 0.695 * [backup-simplify]: Simplify 2.0 into 2.0 0.695 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.695 * [taylor]: Taking taylor expansion of PI in n 0.695 * [backup-simplify]: Simplify PI into PI 0.695 * [taylor]: Taking taylor expansion of n in n 0.695 * [backup-simplify]: Simplify 0 into 0 0.695 * [backup-simplify]: Simplify 1 into 1 0.696 * [backup-simplify]: Simplify (/ PI 1) into PI 0.696 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.697 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.697 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.697 * [taylor]: Taking taylor expansion of 1.0 in n 0.697 * [backup-simplify]: Simplify 1.0 into 1.0 0.697 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.697 * [taylor]: Taking taylor expansion of k in n 0.697 * [backup-simplify]: Simplify k into k 0.697 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.698 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.698 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.698 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.698 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.699 * [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)))) 0.700 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.701 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 0.701 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.702 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 0.705 * [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)))))))) 0.705 * [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)))) 0.705 * [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 0.705 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.705 * [taylor]: Taking taylor expansion of 1.0 in n 0.705 * [backup-simplify]: Simplify 1.0 into 1.0 0.705 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.705 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.705 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.705 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.706 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.706 * [taylor]: Taking taylor expansion of 0.5 in n 0.706 * [backup-simplify]: Simplify 0.5 into 0.5 0.706 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.706 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.706 * [taylor]: Taking taylor expansion of k in n 0.706 * [backup-simplify]: Simplify k into k 0.706 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.706 * [taylor]: Taking taylor expansion of 1.0 in n 0.706 * [backup-simplify]: Simplify 1.0 into 1.0 0.706 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.706 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.706 * [taylor]: Taking taylor expansion of -2.0 in n 0.706 * [backup-simplify]: Simplify -2.0 into -2.0 0.706 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.706 * [taylor]: Taking taylor expansion of PI in n 0.706 * [backup-simplify]: Simplify PI into PI 0.706 * [taylor]: Taking taylor expansion of n in n 0.706 * [backup-simplify]: Simplify 0 into 0 0.706 * [backup-simplify]: Simplify 1 into 1 0.706 * [backup-simplify]: Simplify (/ PI 1) into PI 0.706 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.707 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.707 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.707 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.708 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.709 * [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)))) 0.709 * [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))))) 0.709 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.709 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.709 * [taylor]: Taking taylor expansion of -1 in n 0.709 * [backup-simplify]: Simplify -1 into -1 0.709 * [taylor]: Taking taylor expansion of k in n 0.709 * [backup-simplify]: Simplify k into k 0.710 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 0.710 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 0.710 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 0.710 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 0.710 * [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))) 0.711 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.711 * [taylor]: Taking taylor expansion of 1.0 in k 0.711 * [backup-simplify]: Simplify 1.0 into 1.0 0.711 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.711 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.711 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.711 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.711 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.711 * [taylor]: Taking taylor expansion of 0.5 in k 0.711 * [backup-simplify]: Simplify 0.5 into 0.5 0.711 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.711 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.711 * [taylor]: Taking taylor expansion of k in k 0.711 * [backup-simplify]: Simplify 0 into 0 0.711 * [backup-simplify]: Simplify 1 into 1 0.711 * [backup-simplify]: Simplify (/ 1 1) into 1 0.711 * [taylor]: Taking taylor expansion of 1.0 in k 0.711 * [backup-simplify]: Simplify 1.0 into 1.0 0.711 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.711 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.711 * [taylor]: Taking taylor expansion of -2.0 in k 0.711 * [backup-simplify]: Simplify -2.0 into -2.0 0.711 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.711 * [taylor]: Taking taylor expansion of PI in k 0.711 * [backup-simplify]: Simplify PI into PI 0.711 * [taylor]: Taking taylor expansion of n in k 0.711 * [backup-simplify]: Simplify n into n 0.711 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.711 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.711 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.712 * [backup-simplify]: Simplify (+ 1 0) into 1 0.712 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.712 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.712 * [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)))))) 0.712 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.712 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.712 * [taylor]: Taking taylor expansion of -1 in k 0.712 * [backup-simplify]: Simplify -1 into -1 0.712 * [taylor]: Taking taylor expansion of k in k 0.712 * [backup-simplify]: Simplify 0 into 0 0.712 * [backup-simplify]: Simplify 1 into 1 0.712 * [backup-simplify]: Simplify (/ -1 1) into -1 0.713 * [backup-simplify]: Simplify (sqrt 0) into 0 0.713 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.714 * [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))))))) 0.714 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 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 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.714 * [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))) 0.715 * [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 0.717 * [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))))))) 0.717 * [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))))))) 0.717 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.717 * [taylor]: Taking taylor expansion of +nan.0 in n 0.717 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.717 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.717 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.717 * [taylor]: Taking taylor expansion of 0.5 in n 0.717 * [backup-simplify]: Simplify 0.5 into 0.5 0.717 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.717 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.717 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.717 * [taylor]: Taking taylor expansion of k in n 0.717 * [backup-simplify]: Simplify k into k 0.717 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.717 * [taylor]: Taking taylor expansion of 1.0 in n 0.717 * [backup-simplify]: Simplify 1.0 into 1.0 0.717 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.717 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.717 * [taylor]: Taking taylor expansion of -2.0 in n 0.717 * [backup-simplify]: Simplify -2.0 into -2.0 0.717 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.717 * [taylor]: Taking taylor expansion of PI in n 0.717 * [backup-simplify]: Simplify PI into PI 0.717 * [taylor]: Taking taylor expansion of n in n 0.717 * [backup-simplify]: Simplify 0 into 0 0.717 * [backup-simplify]: Simplify 1 into 1 0.718 * [backup-simplify]: Simplify (/ PI 1) into PI 0.718 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.718 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.719 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.719 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.720 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.721 * [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)))) 0.721 * [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))))) 0.722 * [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)))))) 0.723 * [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)))))) 0.723 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.725 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.726 * [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)))))))) 0.726 * [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)))))))) 0.726 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.726 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.726 * [taylor]: Taking taylor expansion of +nan.0 in n 0.726 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.726 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.726 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.726 * [taylor]: Taking taylor expansion of 0.5 in n 0.726 * [backup-simplify]: Simplify 0.5 into 0.5 0.726 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.726 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.726 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.726 * [taylor]: Taking taylor expansion of k in n 0.726 * [backup-simplify]: Simplify k into k 0.726 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.726 * [taylor]: Taking taylor expansion of 1.0 in n 0.726 * [backup-simplify]: Simplify 1.0 into 1.0 0.726 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.726 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.726 * [taylor]: Taking taylor expansion of -2.0 in n 0.726 * [backup-simplify]: Simplify -2.0 into -2.0 0.726 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.726 * [taylor]: Taking taylor expansion of PI in n 0.726 * [backup-simplify]: Simplify PI into PI 0.726 * [taylor]: Taking taylor expansion of n in n 0.727 * [backup-simplify]: Simplify 0 into 0 0.727 * [backup-simplify]: Simplify 1 into 1 0.727 * [backup-simplify]: Simplify (/ PI 1) into PI 0.727 * [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) 0.733 * [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))) 0.734 * [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)))) 0.735 * [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)))))) 0.736 * [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 (- (* +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 0.738 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.739 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.739 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.739 * [backup-simplify]: Simplify (+ 0 0) into 0 0.740 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.741 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 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 0.743 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.744 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 0.744 * [backup-simplify]: Simplify 0 into 0 0.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.746 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.747 * [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)))))))) 0.748 * [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)))))))) 0.748 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.748 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.748 * [taylor]: Taking taylor expansion of +nan.0 in n 0.748 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.748 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.748 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.748 * [taylor]: Taking taylor expansion of 0.5 in n 0.748 * [backup-simplify]: Simplify 0.5 into 0.5 0.748 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.748 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.748 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.748 * [taylor]: Taking taylor expansion of k in n 0.748 * [backup-simplify]: Simplify k into k 0.748 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.748 * [taylor]: Taking taylor expansion of 1.0 in n 0.748 * [backup-simplify]: Simplify 1.0 into 1.0 0.748 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.748 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.748 * [taylor]: Taking taylor expansion of -2.0 in n 0.748 * [backup-simplify]: Simplify -2.0 into -2.0 0.748 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.748 * [taylor]: Taking taylor expansion of PI in n 0.748 * [backup-simplify]: Simplify PI into PI 0.748 * [taylor]: Taking taylor expansion of n in n 0.748 * [backup-simplify]: Simplify 0 into 0 0.748 * [backup-simplify]: Simplify 1 into 1 0.748 * [backup-simplify]: Simplify (/ PI 1) into PI 0.749 * [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)) 0.751 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.752 * [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))))) 0.753 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 0.754 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 0.754 * [backup-simplify]: Simplify (- (* +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))))))) 0.757 * [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)))))))))))) 0.757 * * * [progress]: simplifying candidates 0.760 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 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2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (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) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) 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2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 0.761 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (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)) (expm1 (* (* h0 PI) h1)) (log1p (* (* h0 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) (expm1 (/ h2 (sqrt h3))) (log1p (/ h2 (sqrt h3))) (- (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 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(sqrt h3)) (cbrt (sqrt h3)))) (/ h2 (cbrt (sqrt h3))) (/ 1 (sqrt (* (cbrt h3) (cbrt h3)))) (/ h2 (sqrt (cbrt h3))) (/ 1 (sqrt (sqrt h3))) (/ h2 (sqrt (sqrt h3))) (/ 1 (sqrt 1)) (/ h2 (sqrt h3)) (/ 1 (sqrt (sqrt h3))) (/ h2 (sqrt (sqrt h3))) (/ 1 1) (/ h2 (sqrt h3)) (/ 1 (sqrt h3)) (/ (sqrt h3) h2) (/ h2 (* (cbrt (sqrt h3)) (cbrt (sqrt h3)))) (/ h2 (sqrt (* (cbrt h3) (cbrt h3)))) (/ h2 (sqrt (sqrt h3))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h3))) (/ h2 1) (/ (sqrt h3) (cbrt h2)) (/ (sqrt h3) (sqrt h2)) (/ (sqrt h3) h2) (expm1 (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (log1p (* (/ h2 (sqrt h3)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (+ (- (log h2) (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)))))))))))) 0.770 * * [simplify]: iteration 0 : 981 enodes (cost 1502 ) 0.787 * * [simplify]: iteration 1 : 4021 enodes (cost 1398 ) 0.852 * * [simplify]: iteration 2 : 5003 enodes (cost 1383 ) 0.859 * * * [progress]: adding candidates to table 1.287 * * [progress]: iteration 2 / 4 1.287 * * * [progress]: picking best candidate 1.304 * * * * [pick]: Picked # 1.304 * * * [progress]: localizing error 1.320 * * * [progress]: generating rewritten candidates 1.320 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 1.344 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 1.366 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 1) 1.384 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1) 1.408 * * * [progress]: generating series expansions 1.408 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 1.408 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.408 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.408 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.409 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.409 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.409 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.409 * [taylor]: Taking taylor expansion of 0.5 in k 1.409 * [backup-simplify]: Simplify 0.5 into 0.5 1.409 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.409 * [taylor]: Taking taylor expansion of 1.0 in k 1.409 * [backup-simplify]: Simplify 1.0 into 1.0 1.409 * [taylor]: Taking taylor expansion of k in k 1.409 * [backup-simplify]: Simplify 0 into 0 1.409 * [backup-simplify]: Simplify 1 into 1 1.409 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.409 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.409 * [taylor]: Taking taylor expansion of 2.0 in k 1.409 * [backup-simplify]: Simplify 2.0 into 2.0 1.409 * [taylor]: Taking taylor expansion of (* n PI) in k 1.409 * [taylor]: Taking taylor expansion of n in k 1.409 * [backup-simplify]: Simplify n into n 1.409 * [taylor]: Taking taylor expansion of PI in k 1.409 * [backup-simplify]: Simplify PI into PI 1.409 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.409 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.409 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.409 * [backup-simplify]: Simplify (- 0) into 0 1.410 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.410 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.410 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.410 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.410 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.410 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.410 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.410 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.410 * [taylor]: Taking taylor expansion of 0.5 in n 1.410 * [backup-simplify]: Simplify 0.5 into 0.5 1.410 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.410 * [taylor]: Taking taylor expansion of 1.0 in n 1.410 * [backup-simplify]: Simplify 1.0 into 1.0 1.411 * [taylor]: Taking taylor expansion of k in n 1.411 * [backup-simplify]: Simplify k into k 1.411 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.411 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.411 * [taylor]: Taking taylor expansion of 2.0 in n 1.411 * [backup-simplify]: Simplify 2.0 into 2.0 1.411 * [taylor]: Taking taylor expansion of (* n PI) in n 1.411 * [taylor]: Taking taylor expansion of n in n 1.411 * [backup-simplify]: Simplify 0 into 0 1.411 * [backup-simplify]: Simplify 1 into 1 1.411 * [taylor]: Taking taylor expansion of PI in n 1.411 * [backup-simplify]: Simplify PI into PI 1.411 * [backup-simplify]: Simplify (* 0 PI) into 0 1.411 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.412 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.413 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.414 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.414 * [backup-simplify]: Simplify (- k) into (- k) 1.414 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.414 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.415 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.415 * [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)))) 1.416 * [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))))) 1.416 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.416 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.416 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.416 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.416 * [taylor]: Taking taylor expansion of 0.5 in n 1.416 * [backup-simplify]: Simplify 0.5 into 0.5 1.416 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.416 * [taylor]: Taking taylor expansion of 1.0 in n 1.416 * [backup-simplify]: Simplify 1.0 into 1.0 1.416 * [taylor]: Taking taylor expansion of k in n 1.416 * [backup-simplify]: Simplify k into k 1.416 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.416 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.416 * [taylor]: Taking taylor expansion of 2.0 in n 1.416 * [backup-simplify]: Simplify 2.0 into 2.0 1.416 * [taylor]: Taking taylor expansion of (* n PI) in n 1.416 * [taylor]: Taking taylor expansion of n in n 1.416 * [backup-simplify]: Simplify 0 into 0 1.416 * [backup-simplify]: Simplify 1 into 1 1.416 * [taylor]: Taking taylor expansion of PI in n 1.416 * [backup-simplify]: Simplify PI into PI 1.417 * [backup-simplify]: Simplify (* 0 PI) into 0 1.417 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.418 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.419 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.419 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.419 * [backup-simplify]: Simplify (- k) into (- k) 1.419 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.419 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.420 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.421 * [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)))) 1.421 * [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))))) 1.422 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.422 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.422 * [taylor]: Taking taylor expansion of 0.5 in k 1.422 * [backup-simplify]: Simplify 0.5 into 0.5 1.422 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.422 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.422 * [taylor]: Taking taylor expansion of 1.0 in k 1.422 * [backup-simplify]: Simplify 1.0 into 1.0 1.422 * [taylor]: Taking taylor expansion of k in k 1.422 * [backup-simplify]: Simplify 0 into 0 1.422 * [backup-simplify]: Simplify 1 into 1 1.422 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.422 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.422 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.422 * [taylor]: Taking taylor expansion of 2.0 in k 1.422 * [backup-simplify]: Simplify 2.0 into 2.0 1.422 * [taylor]: Taking taylor expansion of PI in k 1.422 * [backup-simplify]: Simplify PI into PI 1.422 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.423 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.423 * [taylor]: Taking taylor expansion of (log n) in k 1.423 * [taylor]: Taking taylor expansion of n in k 1.423 * [backup-simplify]: Simplify n into n 1.423 * [backup-simplify]: Simplify (log n) into (log n) 1.423 * [backup-simplify]: Simplify (- 0) into 0 1.423 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.424 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.425 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.425 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.426 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.427 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.427 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.428 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.429 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.429 * [backup-simplify]: Simplify (- 0) into 0 1.429 * [backup-simplify]: Simplify (+ 0 0) into 0 1.429 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.430 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.431 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.432 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.432 * [taylor]: Taking taylor expansion of 0 in k 1.432 * [backup-simplify]: Simplify 0 into 0 1.432 * [backup-simplify]: Simplify 0 into 0 1.433 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.433 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.434 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.434 * [backup-simplify]: Simplify (+ 0 0) into 0 1.434 * [backup-simplify]: Simplify (- 1) into -1 1.435 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.436 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.437 * [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)))) 1.439 * [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)))))) 1.440 * [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)))))) 1.441 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.442 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.443 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.444 * [backup-simplify]: Simplify (- 0) into 0 1.444 * [backup-simplify]: Simplify (+ 0 0) into 0 1.444 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.445 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.446 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.447 * [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 1.447 * [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 1.448 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.450 * [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 1.451 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.451 * [backup-simplify]: Simplify (+ 0 0) into 0 1.451 * [backup-simplify]: Simplify (- 0) into 0 1.451 * [backup-simplify]: Simplify (+ 0 0) into 0 1.452 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.454 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.456 * [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)))))) 1.459 * [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)))))) 1.465 * [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)))))) 1.465 * [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)))) 1.465 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.465 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.465 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.465 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.465 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.465 * [taylor]: Taking taylor expansion of 0.5 in k 1.466 * [backup-simplify]: Simplify 0.5 into 0.5 1.466 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.466 * [taylor]: Taking taylor expansion of 1.0 in k 1.466 * [backup-simplify]: Simplify 1.0 into 1.0 1.466 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.466 * [taylor]: Taking taylor expansion of k in k 1.466 * [backup-simplify]: Simplify 0 into 0 1.466 * [backup-simplify]: Simplify 1 into 1 1.466 * [backup-simplify]: Simplify (/ 1 1) into 1 1.466 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.466 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.466 * [taylor]: Taking taylor expansion of 2.0 in k 1.466 * [backup-simplify]: Simplify 2.0 into 2.0 1.466 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.466 * [taylor]: Taking taylor expansion of PI in k 1.466 * [backup-simplify]: Simplify PI into PI 1.466 * [taylor]: Taking taylor expansion of n in k 1.466 * [backup-simplify]: Simplify n into n 1.466 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.466 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.466 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.466 * [backup-simplify]: Simplify (- 1) into -1 1.467 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.467 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.467 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.467 * [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))))) 1.467 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.467 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.467 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.467 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.467 * [taylor]: Taking taylor expansion of 0.5 in n 1.467 * [backup-simplify]: Simplify 0.5 into 0.5 1.467 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.467 * [taylor]: Taking taylor expansion of 1.0 in n 1.467 * [backup-simplify]: Simplify 1.0 into 1.0 1.467 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.467 * [taylor]: Taking taylor expansion of k in n 1.467 * [backup-simplify]: Simplify k into k 1.467 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.467 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.467 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.467 * [taylor]: Taking taylor expansion of 2.0 in n 1.467 * [backup-simplify]: Simplify 2.0 into 2.0 1.467 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.467 * [taylor]: Taking taylor expansion of PI in n 1.467 * [backup-simplify]: Simplify PI into PI 1.467 * [taylor]: Taking taylor expansion of n in n 1.468 * [backup-simplify]: Simplify 0 into 0 1.468 * [backup-simplify]: Simplify 1 into 1 1.468 * [backup-simplify]: Simplify (/ PI 1) into PI 1.468 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.469 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.469 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.469 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.469 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.470 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.470 * [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)))) 1.471 * [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))))) 1.471 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.471 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.471 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.471 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.471 * [taylor]: Taking taylor expansion of 0.5 in n 1.471 * [backup-simplify]: Simplify 0.5 into 0.5 1.471 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.471 * [taylor]: Taking taylor expansion of 1.0 in n 1.471 * [backup-simplify]: Simplify 1.0 into 1.0 1.471 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.471 * [taylor]: Taking taylor expansion of k in n 1.471 * [backup-simplify]: Simplify k into k 1.471 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.471 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.471 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.471 * [taylor]: Taking taylor expansion of 2.0 in n 1.471 * [backup-simplify]: Simplify 2.0 into 2.0 1.471 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.471 * [taylor]: Taking taylor expansion of PI in n 1.471 * [backup-simplify]: Simplify PI into PI 1.471 * [taylor]: Taking taylor expansion of n in n 1.471 * [backup-simplify]: Simplify 0 into 0 1.471 * [backup-simplify]: Simplify 1 into 1 1.472 * [backup-simplify]: Simplify (/ PI 1) into PI 1.472 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.473 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.473 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.473 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.473 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.474 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.474 * [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)))) 1.475 * [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))))) 1.475 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.475 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.475 * [taylor]: Taking taylor expansion of 0.5 in k 1.475 * [backup-simplify]: Simplify 0.5 into 0.5 1.475 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.475 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.475 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.475 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.475 * [taylor]: Taking taylor expansion of 2.0 in k 1.475 * [backup-simplify]: Simplify 2.0 into 2.0 1.475 * [taylor]: Taking taylor expansion of PI in k 1.475 * [backup-simplify]: Simplify PI into PI 1.476 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.477 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.477 * [taylor]: Taking taylor expansion of (log n) in k 1.477 * [taylor]: Taking taylor expansion of n in k 1.477 * [backup-simplify]: Simplify n into n 1.477 * [backup-simplify]: Simplify (log n) into (log n) 1.477 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.477 * [taylor]: Taking taylor expansion of 1.0 in k 1.477 * [backup-simplify]: Simplify 1.0 into 1.0 1.477 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.477 * [taylor]: Taking taylor expansion of k in k 1.477 * [backup-simplify]: Simplify 0 into 0 1.477 * [backup-simplify]: Simplify 1 into 1 1.477 * [backup-simplify]: Simplify (/ 1 1) into 1 1.477 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.478 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.478 * [backup-simplify]: Simplify (- 1) into -1 1.478 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.479 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.480 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.481 * [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))))) 1.481 * [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))))) 1.482 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.482 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.483 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.483 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.483 * [backup-simplify]: Simplify (- 0) into 0 1.484 * [backup-simplify]: Simplify (+ 0 0) into 0 1.484 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.485 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.489 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.490 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (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 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.491 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.493 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.493 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.493 * [backup-simplify]: Simplify (- 0) into 0 1.493 * [backup-simplify]: Simplify (+ 0 0) into 0 1.494 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.495 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.496 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.497 * [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 1.497 * [taylor]: Taking taylor expansion of 0 in k 1.497 * [backup-simplify]: Simplify 0 into 0 1.497 * [backup-simplify]: Simplify 0 into 0 1.497 * [backup-simplify]: Simplify 0 into 0 1.497 * [backup-simplify]: Simplify 0 into 0 1.498 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.498 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.501 * [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 1.501 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.501 * [backup-simplify]: Simplify (- 0) into 0 1.502 * [backup-simplify]: Simplify (+ 0 0) into 0 1.502 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.503 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.504 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.506 * [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 1.506 * [taylor]: Taking taylor expansion of 0 in k 1.506 * [backup-simplify]: Simplify 0 into 0 1.506 * [backup-simplify]: Simplify 0 into 0 1.507 * [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)))) 1.507 * [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))) 1.507 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.507 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.507 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.507 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.507 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.507 * [taylor]: Taking taylor expansion of 0.5 in k 1.507 * [backup-simplify]: Simplify 0.5 into 0.5 1.507 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.507 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.507 * [taylor]: Taking taylor expansion of k in k 1.507 * [backup-simplify]: Simplify 0 into 0 1.507 * [backup-simplify]: Simplify 1 into 1 1.508 * [backup-simplify]: Simplify (/ 1 1) into 1 1.508 * [taylor]: Taking taylor expansion of 1.0 in k 1.508 * [backup-simplify]: Simplify 1.0 into 1.0 1.508 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.508 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.508 * [taylor]: Taking taylor expansion of -2.0 in k 1.508 * [backup-simplify]: Simplify -2.0 into -2.0 1.508 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.508 * [taylor]: Taking taylor expansion of PI in k 1.508 * [backup-simplify]: Simplify PI into PI 1.508 * [taylor]: Taking taylor expansion of n in k 1.508 * [backup-simplify]: Simplify n into n 1.508 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.508 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.508 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.508 * [backup-simplify]: Simplify (+ 1 0) into 1 1.508 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.509 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.509 * [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)))))) 1.509 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.509 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.509 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.509 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.509 * [taylor]: Taking taylor expansion of 0.5 in n 1.509 * [backup-simplify]: Simplify 0.5 into 0.5 1.509 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.509 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.509 * [taylor]: Taking taylor expansion of k in n 1.509 * [backup-simplify]: Simplify k into k 1.509 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.509 * [taylor]: Taking taylor expansion of 1.0 in n 1.509 * [backup-simplify]: Simplify 1.0 into 1.0 1.509 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.509 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.509 * [taylor]: Taking taylor expansion of -2.0 in n 1.509 * [backup-simplify]: Simplify -2.0 into -2.0 1.509 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.509 * [taylor]: Taking taylor expansion of PI in n 1.509 * [backup-simplify]: Simplify PI into PI 1.509 * [taylor]: Taking taylor expansion of n in n 1.509 * [backup-simplify]: Simplify 0 into 0 1.509 * [backup-simplify]: Simplify 1 into 1 1.509 * [backup-simplify]: Simplify (/ PI 1) into PI 1.510 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.510 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.511 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.511 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.511 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.512 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.513 * [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))))) 1.513 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.513 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.513 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.513 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.513 * [taylor]: Taking taylor expansion of 0.5 in n 1.513 * [backup-simplify]: Simplify 0.5 into 0.5 1.513 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.513 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.513 * [taylor]: Taking taylor expansion of k in n 1.513 * [backup-simplify]: Simplify k into k 1.513 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.513 * [taylor]: Taking taylor expansion of 1.0 in n 1.513 * [backup-simplify]: Simplify 1.0 into 1.0 1.513 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.513 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.513 * [taylor]: Taking taylor expansion of -2.0 in n 1.513 * [backup-simplify]: Simplify -2.0 into -2.0 1.513 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.513 * [taylor]: Taking taylor expansion of PI in n 1.513 * [backup-simplify]: Simplify PI into PI 1.513 * [taylor]: Taking taylor expansion of n in n 1.513 * [backup-simplify]: Simplify 0 into 0 1.513 * [backup-simplify]: Simplify 1 into 1 1.514 * [backup-simplify]: Simplify (/ PI 1) into PI 1.514 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.514 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.515 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.515 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.515 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.516 * [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)))) 1.517 * [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))))) 1.517 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.517 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.517 * [taylor]: Taking taylor expansion of 0.5 in k 1.517 * [backup-simplify]: Simplify 0.5 into 0.5 1.517 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.517 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.517 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.517 * [taylor]: Taking taylor expansion of k in k 1.517 * [backup-simplify]: Simplify 0 into 0 1.517 * [backup-simplify]: Simplify 1 into 1 1.517 * [backup-simplify]: Simplify (/ 1 1) into 1 1.517 * [taylor]: Taking taylor expansion of 1.0 in k 1.517 * [backup-simplify]: Simplify 1.0 into 1.0 1.517 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.517 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.517 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.517 * [taylor]: Taking taylor expansion of -2.0 in k 1.517 * [backup-simplify]: Simplify -2.0 into -2.0 1.517 * [taylor]: Taking taylor expansion of PI in k 1.517 * [backup-simplify]: Simplify PI into PI 1.518 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.518 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.518 * [taylor]: Taking taylor expansion of (log n) in k 1.518 * [taylor]: Taking taylor expansion of n in k 1.518 * [backup-simplify]: Simplify n into n 1.518 * [backup-simplify]: Simplify (log n) into (log n) 1.519 * [backup-simplify]: Simplify (+ 1 0) into 1 1.519 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.519 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.520 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.521 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.521 * [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))))) 1.522 * [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))))) 1.523 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.523 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.524 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.524 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.524 * [backup-simplify]: Simplify (+ 0 0) into 0 1.524 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.525 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.526 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.527 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.527 * [taylor]: Taking taylor expansion of 0 in k 1.527 * [backup-simplify]: Simplify 0 into 0 1.527 * [backup-simplify]: Simplify 0 into 0 1.527 * [backup-simplify]: Simplify 0 into 0 1.528 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.529 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.530 * [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 1.530 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.530 * [backup-simplify]: Simplify (+ 0 0) into 0 1.531 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.532 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.533 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.534 * [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 1.534 * [taylor]: Taking taylor expansion of 0 in k 1.534 * [backup-simplify]: Simplify 0 into 0 1.534 * [backup-simplify]: Simplify 0 into 0 1.534 * [backup-simplify]: Simplify 0 into 0 1.534 * [backup-simplify]: Simplify 0 into 0 1.535 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.535 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.538 * [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 1.538 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.539 * [backup-simplify]: Simplify (+ 0 0) into 0 1.539 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.540 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.541 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.543 * [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 1.543 * [taylor]: Taking taylor expansion of 0 in k 1.543 * [backup-simplify]: Simplify 0 into 0 1.543 * [backup-simplify]: Simplify 0 into 0 1.544 * [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)))))) 1.544 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 1.544 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.544 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.544 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.544 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.544 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.544 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.544 * [taylor]: Taking taylor expansion of 0.5 in k 1.544 * [backup-simplify]: Simplify 0.5 into 0.5 1.544 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.544 * [taylor]: Taking taylor expansion of 1.0 in k 1.544 * [backup-simplify]: Simplify 1.0 into 1.0 1.544 * [taylor]: Taking taylor expansion of k in k 1.544 * [backup-simplify]: Simplify 0 into 0 1.544 * [backup-simplify]: Simplify 1 into 1 1.544 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.544 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.544 * [taylor]: Taking taylor expansion of 2.0 in k 1.544 * [backup-simplify]: Simplify 2.0 into 2.0 1.544 * [taylor]: Taking taylor expansion of (* n PI) in k 1.544 * [taylor]: Taking taylor expansion of n in k 1.544 * [backup-simplify]: Simplify n into n 1.544 * [taylor]: Taking taylor expansion of PI in k 1.544 * [backup-simplify]: Simplify PI into PI 1.544 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.545 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.545 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.545 * [backup-simplify]: Simplify (- 0) into 0 1.545 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.545 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.545 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.545 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.545 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.545 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.546 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.546 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.546 * [taylor]: Taking taylor expansion of 0.5 in n 1.546 * [backup-simplify]: Simplify 0.5 into 0.5 1.546 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.546 * [taylor]: Taking taylor expansion of 1.0 in n 1.546 * [backup-simplify]: Simplify 1.0 into 1.0 1.546 * [taylor]: Taking taylor expansion of k in n 1.546 * [backup-simplify]: Simplify k into k 1.546 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.546 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.546 * [taylor]: Taking taylor expansion of 2.0 in n 1.546 * [backup-simplify]: Simplify 2.0 into 2.0 1.546 * [taylor]: Taking taylor expansion of (* n PI) in n 1.546 * [taylor]: Taking taylor expansion of n in n 1.546 * [backup-simplify]: Simplify 0 into 0 1.546 * [backup-simplify]: Simplify 1 into 1 1.546 * [taylor]: Taking taylor expansion of PI in n 1.546 * [backup-simplify]: Simplify PI into PI 1.546 * [backup-simplify]: Simplify (* 0 PI) into 0 1.546 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.547 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.548 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.549 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.549 * [backup-simplify]: Simplify (- k) into (- k) 1.549 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.549 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.550 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.550 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.551 * [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))))) 1.551 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.551 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.551 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.551 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.551 * [taylor]: Taking taylor expansion of 0.5 in n 1.551 * [backup-simplify]: Simplify 0.5 into 0.5 1.551 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.551 * [taylor]: Taking taylor expansion of 1.0 in n 1.551 * [backup-simplify]: Simplify 1.0 into 1.0 1.551 * [taylor]: Taking taylor expansion of k in n 1.551 * [backup-simplify]: Simplify k into k 1.551 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.551 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.551 * [taylor]: Taking taylor expansion of 2.0 in n 1.551 * [backup-simplify]: Simplify 2.0 into 2.0 1.551 * [taylor]: Taking taylor expansion of (* n PI) in n 1.551 * [taylor]: Taking taylor expansion of n in n 1.551 * [backup-simplify]: Simplify 0 into 0 1.551 * [backup-simplify]: Simplify 1 into 1 1.551 * [taylor]: Taking taylor expansion of PI in n 1.551 * [backup-simplify]: Simplify PI into PI 1.551 * [backup-simplify]: Simplify (* 0 PI) into 0 1.552 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.553 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.553 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.554 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.554 * [backup-simplify]: Simplify (- k) into (- k) 1.554 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.554 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.555 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.556 * [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)))) 1.556 * [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))))) 1.556 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.556 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.556 * [taylor]: Taking taylor expansion of 0.5 in k 1.556 * [backup-simplify]: Simplify 0.5 into 0.5 1.556 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.556 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.556 * [taylor]: Taking taylor expansion of 1.0 in k 1.556 * [backup-simplify]: Simplify 1.0 into 1.0 1.557 * [taylor]: Taking taylor expansion of k in k 1.557 * [backup-simplify]: Simplify 0 into 0 1.557 * [backup-simplify]: Simplify 1 into 1 1.557 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.557 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.557 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.557 * [taylor]: Taking taylor expansion of 2.0 in k 1.557 * [backup-simplify]: Simplify 2.0 into 2.0 1.557 * [taylor]: Taking taylor expansion of PI in k 1.557 * [backup-simplify]: Simplify PI into PI 1.557 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.558 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.558 * [taylor]: Taking taylor expansion of (log n) in k 1.558 * [taylor]: Taking taylor expansion of n in k 1.558 * [backup-simplify]: Simplify n into n 1.558 * [backup-simplify]: Simplify (log n) into (log n) 1.558 * [backup-simplify]: Simplify (- 0) into 0 1.558 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.559 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.559 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.560 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.561 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.561 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.562 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.562 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.563 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.564 * [backup-simplify]: Simplify (- 0) into 0 1.564 * [backup-simplify]: Simplify (+ 0 0) into 0 1.564 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.565 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.566 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.567 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.567 * [taylor]: Taking taylor expansion of 0 in k 1.567 * [backup-simplify]: Simplify 0 into 0 1.567 * [backup-simplify]: Simplify 0 into 0 1.567 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.568 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.569 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.569 * [backup-simplify]: Simplify (+ 0 0) into 0 1.569 * [backup-simplify]: Simplify (- 1) into -1 1.569 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.570 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.571 * [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)))) 1.573 * [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)))))) 1.575 * [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)))))) 1.576 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.576 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.581 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.581 * [backup-simplify]: Simplify (- 0) into 0 1.582 * [backup-simplify]: Simplify (+ 0 0) into 0 1.582 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.583 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.584 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.585 * [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 1.585 * [taylor]: Taking taylor expansion of 0 in k 1.585 * [backup-simplify]: Simplify 0 into 0 1.585 * [backup-simplify]: Simplify 0 into 0 1.585 * [backup-simplify]: Simplify 0 into 0 1.586 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.587 * [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 1.588 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.589 * [backup-simplify]: Simplify (+ 0 0) into 0 1.589 * [backup-simplify]: Simplify (- 0) into 0 1.589 * [backup-simplify]: Simplify (+ 0 0) into 0 1.590 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.592 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.594 * [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)))))) 1.597 * [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)))))) 1.603 * [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)))))) 1.603 * [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)))) 1.603 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.603 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.603 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.603 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.603 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.603 * [taylor]: Taking taylor expansion of 0.5 in k 1.603 * [backup-simplify]: Simplify 0.5 into 0.5 1.603 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.603 * [taylor]: Taking taylor expansion of 1.0 in k 1.604 * [backup-simplify]: Simplify 1.0 into 1.0 1.604 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.604 * [taylor]: Taking taylor expansion of k in k 1.604 * [backup-simplify]: Simplify 0 into 0 1.604 * [backup-simplify]: Simplify 1 into 1 1.604 * [backup-simplify]: Simplify (/ 1 1) into 1 1.604 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.604 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.604 * [taylor]: Taking taylor expansion of 2.0 in k 1.604 * [backup-simplify]: Simplify 2.0 into 2.0 1.604 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.604 * [taylor]: Taking taylor expansion of PI in k 1.604 * [backup-simplify]: Simplify PI into PI 1.604 * [taylor]: Taking taylor expansion of n in k 1.604 * [backup-simplify]: Simplify n into n 1.604 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.604 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.604 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.604 * [backup-simplify]: Simplify (- 1) into -1 1.605 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.605 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.605 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.605 * [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))))) 1.605 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.605 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.605 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.605 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.605 * [taylor]: Taking taylor expansion of 0.5 in n 1.605 * [backup-simplify]: Simplify 0.5 into 0.5 1.605 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.605 * [taylor]: Taking taylor expansion of 1.0 in n 1.605 * [backup-simplify]: Simplify 1.0 into 1.0 1.605 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.605 * [taylor]: Taking taylor expansion of k in n 1.605 * [backup-simplify]: Simplify k into k 1.605 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.605 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.605 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.605 * [taylor]: Taking taylor expansion of 2.0 in n 1.605 * [backup-simplify]: Simplify 2.0 into 2.0 1.605 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.605 * [taylor]: Taking taylor expansion of PI in n 1.606 * [backup-simplify]: Simplify PI into PI 1.606 * [taylor]: Taking taylor expansion of n in n 1.606 * [backup-simplify]: Simplify 0 into 0 1.606 * [backup-simplify]: Simplify 1 into 1 1.606 * [backup-simplify]: Simplify (/ PI 1) into PI 1.606 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.607 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.607 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.607 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.607 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.608 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.608 * [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)))) 1.609 * [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))))) 1.609 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.609 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.609 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.609 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.609 * [taylor]: Taking taylor expansion of 0.5 in n 1.609 * [backup-simplify]: Simplify 0.5 into 0.5 1.609 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.609 * [taylor]: Taking taylor expansion of 1.0 in n 1.609 * [backup-simplify]: Simplify 1.0 into 1.0 1.609 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.609 * [taylor]: Taking taylor expansion of k in n 1.609 * [backup-simplify]: Simplify k into k 1.609 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.609 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.609 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.609 * [taylor]: Taking taylor expansion of 2.0 in n 1.609 * [backup-simplify]: Simplify 2.0 into 2.0 1.609 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.609 * [taylor]: Taking taylor expansion of PI in n 1.610 * [backup-simplify]: Simplify PI into PI 1.610 * [taylor]: Taking taylor expansion of n in n 1.610 * [backup-simplify]: Simplify 0 into 0 1.610 * [backup-simplify]: Simplify 1 into 1 1.610 * [backup-simplify]: Simplify (/ PI 1) into PI 1.610 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.611 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.611 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.611 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.611 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.612 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.612 * [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)))) 1.613 * [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))))) 1.613 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.613 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.613 * [taylor]: Taking taylor expansion of 0.5 in k 1.613 * [backup-simplify]: Simplify 0.5 into 0.5 1.613 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.613 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.613 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.613 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.613 * [taylor]: Taking taylor expansion of 2.0 in k 1.613 * [backup-simplify]: Simplify 2.0 into 2.0 1.613 * [taylor]: Taking taylor expansion of PI in k 1.613 * [backup-simplify]: Simplify PI into PI 1.614 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.614 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.614 * [taylor]: Taking taylor expansion of (log n) in k 1.614 * [taylor]: Taking taylor expansion of n in k 1.614 * [backup-simplify]: Simplify n into n 1.614 * [backup-simplify]: Simplify (log n) into (log n) 1.614 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.615 * [taylor]: Taking taylor expansion of 1.0 in k 1.615 * [backup-simplify]: Simplify 1.0 into 1.0 1.615 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.615 * [taylor]: Taking taylor expansion of k in k 1.615 * [backup-simplify]: Simplify 0 into 0 1.615 * [backup-simplify]: Simplify 1 into 1 1.615 * [backup-simplify]: Simplify (/ 1 1) into 1 1.615 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.615 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.616 * [backup-simplify]: Simplify (- 1) into -1 1.616 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.617 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.617 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.618 * [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))))) 1.619 * [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))))) 1.619 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.620 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.620 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.620 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.621 * [backup-simplify]: Simplify (- 0) into 0 1.621 * [backup-simplify]: Simplify (+ 0 0) into 0 1.621 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.622 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.623 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.624 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.624 * [taylor]: Taking taylor expansion of 0 in k 1.624 * [backup-simplify]: Simplify 0 into 0 1.624 * [backup-simplify]: Simplify 0 into 0 1.624 * [backup-simplify]: Simplify 0 into 0 1.625 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.625 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.627 * [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 1.627 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.627 * [backup-simplify]: Simplify (- 0) into 0 1.628 * [backup-simplify]: Simplify (+ 0 0) into 0 1.628 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.629 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.630 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.631 * [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 1.631 * [taylor]: Taking taylor expansion of 0 in k 1.631 * [backup-simplify]: Simplify 0 into 0 1.631 * [backup-simplify]: Simplify 0 into 0 1.631 * [backup-simplify]: Simplify 0 into 0 1.631 * [backup-simplify]: Simplify 0 into 0 1.632 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.632 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.635 * [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 1.635 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.636 * [backup-simplify]: Simplify (- 0) into 0 1.636 * [backup-simplify]: Simplify (+ 0 0) into 0 1.637 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.637 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.638 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.640 * [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 1.640 * [taylor]: Taking taylor expansion of 0 in k 1.640 * [backup-simplify]: Simplify 0 into 0 1.640 * [backup-simplify]: Simplify 0 into 0 1.641 * [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)))) 1.641 * [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))) 1.641 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.641 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.641 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.641 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.641 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.641 * [taylor]: Taking taylor expansion of 0.5 in k 1.641 * [backup-simplify]: Simplify 0.5 into 0.5 1.641 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.641 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.641 * [taylor]: Taking taylor expansion of k in k 1.641 * [backup-simplify]: Simplify 0 into 0 1.641 * [backup-simplify]: Simplify 1 into 1 1.642 * [backup-simplify]: Simplify (/ 1 1) into 1 1.642 * [taylor]: Taking taylor expansion of 1.0 in k 1.642 * [backup-simplify]: Simplify 1.0 into 1.0 1.642 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.642 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.642 * [taylor]: Taking taylor expansion of -2.0 in k 1.642 * [backup-simplify]: Simplify -2.0 into -2.0 1.642 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.642 * [taylor]: Taking taylor expansion of PI in k 1.642 * [backup-simplify]: Simplify PI into PI 1.642 * [taylor]: Taking taylor expansion of n in k 1.642 * [backup-simplify]: Simplify n into n 1.642 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.642 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.642 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.642 * [backup-simplify]: Simplify (+ 1 0) into 1 1.643 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.643 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.643 * [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)))))) 1.643 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.643 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.643 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.643 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.643 * [taylor]: Taking taylor expansion of 0.5 in n 1.643 * [backup-simplify]: Simplify 0.5 into 0.5 1.643 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.643 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.643 * [taylor]: Taking taylor expansion of k in n 1.643 * [backup-simplify]: Simplify k into k 1.643 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.643 * [taylor]: Taking taylor expansion of 1.0 in n 1.643 * [backup-simplify]: Simplify 1.0 into 1.0 1.643 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.643 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.643 * [taylor]: Taking taylor expansion of -2.0 in n 1.643 * [backup-simplify]: Simplify -2.0 into -2.0 1.643 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.643 * [taylor]: Taking taylor expansion of PI in n 1.643 * [backup-simplify]: Simplify PI into PI 1.643 * [taylor]: Taking taylor expansion of n in n 1.643 * [backup-simplify]: Simplify 0 into 0 1.643 * [backup-simplify]: Simplify 1 into 1 1.643 * [backup-simplify]: Simplify (/ PI 1) into PI 1.644 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.644 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.644 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.644 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.645 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.646 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.647 * [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))))) 1.647 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.647 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.647 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.647 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.647 * [taylor]: Taking taylor expansion of 0.5 in n 1.647 * [backup-simplify]: Simplify 0.5 into 0.5 1.647 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.647 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.647 * [taylor]: Taking taylor expansion of k in n 1.647 * [backup-simplify]: Simplify k into k 1.647 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.647 * [taylor]: Taking taylor expansion of 1.0 in n 1.647 * [backup-simplify]: Simplify 1.0 into 1.0 1.647 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.647 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.647 * [taylor]: Taking taylor expansion of -2.0 in n 1.647 * [backup-simplify]: Simplify -2.0 into -2.0 1.647 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.647 * [taylor]: Taking taylor expansion of PI in n 1.647 * [backup-simplify]: Simplify PI into PI 1.647 * [taylor]: Taking taylor expansion of n in n 1.647 * [backup-simplify]: Simplify 0 into 0 1.647 * [backup-simplify]: Simplify 1 into 1 1.647 * [backup-simplify]: Simplify (/ PI 1) into PI 1.648 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.648 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.648 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.648 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.649 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.650 * [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)))) 1.651 * [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))))) 1.651 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.651 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.651 * [taylor]: Taking taylor expansion of 0.5 in k 1.651 * [backup-simplify]: Simplify 0.5 into 0.5 1.651 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.651 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.651 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.651 * [taylor]: Taking taylor expansion of k in k 1.651 * [backup-simplify]: Simplify 0 into 0 1.651 * [backup-simplify]: Simplify 1 into 1 1.651 * [backup-simplify]: Simplify (/ 1 1) into 1 1.651 * [taylor]: Taking taylor expansion of 1.0 in k 1.651 * [backup-simplify]: Simplify 1.0 into 1.0 1.651 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.651 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.651 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.651 * [taylor]: Taking taylor expansion of -2.0 in k 1.651 * [backup-simplify]: Simplify -2.0 into -2.0 1.651 * [taylor]: Taking taylor expansion of PI in k 1.651 * [backup-simplify]: Simplify PI into PI 1.652 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.652 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.652 * [taylor]: Taking taylor expansion of (log n) in k 1.652 * [taylor]: Taking taylor expansion of n in k 1.652 * [backup-simplify]: Simplify n into n 1.652 * [backup-simplify]: Simplify (log n) into (log n) 1.653 * [backup-simplify]: Simplify (+ 1 0) into 1 1.653 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.653 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.654 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.654 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.655 * [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))))) 1.656 * [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))))) 1.656 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.657 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.658 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.658 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.658 * [backup-simplify]: Simplify (+ 0 0) into 0 1.658 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.659 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.660 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.661 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.661 * [taylor]: Taking taylor expansion of 0 in k 1.661 * [backup-simplify]: Simplify 0 into 0 1.661 * [backup-simplify]: Simplify 0 into 0 1.661 * [backup-simplify]: Simplify 0 into 0 1.662 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.662 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.664 * [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 1.664 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.664 * [backup-simplify]: Simplify (+ 0 0) into 0 1.665 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.666 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.666 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.671 * [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 1.671 * [taylor]: Taking taylor expansion of 0 in k 1.671 * [backup-simplify]: Simplify 0 into 0 1.671 * [backup-simplify]: Simplify 0 into 0 1.671 * [backup-simplify]: Simplify 0 into 0 1.671 * [backup-simplify]: Simplify 0 into 0 1.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.672 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.675 * [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 1.675 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.676 * [backup-simplify]: Simplify (+ 0 0) into 0 1.676 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.677 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.678 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.680 * [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 1.680 * [taylor]: Taking taylor expansion of 0 in k 1.680 * [backup-simplify]: Simplify 0 into 0 1.680 * [backup-simplify]: Simplify 0 into 0 1.681 * [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)))))) 1.681 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 1) 1.681 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.681 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.681 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.681 * [taylor]: Taking taylor expansion of 2.0 in n 1.681 * [backup-simplify]: Simplify 2.0 into 2.0 1.681 * [taylor]: Taking taylor expansion of (* n PI) in n 1.681 * [taylor]: Taking taylor expansion of n in n 1.681 * [backup-simplify]: Simplify 0 into 0 1.681 * [backup-simplify]: Simplify 1 into 1 1.681 * [taylor]: Taking taylor expansion of PI in n 1.681 * [backup-simplify]: Simplify PI into PI 1.681 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.681 * [taylor]: Taking taylor expansion of 2.0 in n 1.681 * [backup-simplify]: Simplify 2.0 into 2.0 1.681 * [taylor]: Taking taylor expansion of (* n PI) in n 1.681 * [taylor]: Taking taylor expansion of n in n 1.681 * [backup-simplify]: Simplify 0 into 0 1.682 * [backup-simplify]: Simplify 1 into 1 1.682 * [taylor]: Taking taylor expansion of PI in n 1.682 * [backup-simplify]: Simplify PI into PI 1.682 * [backup-simplify]: Simplify (* 0 PI) into 0 1.682 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.682 * [backup-simplify]: Simplify 0 into 0 1.683 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.684 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.684 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.685 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.685 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.685 * [backup-simplify]: Simplify 0 into 0 1.686 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.686 * [backup-simplify]: Simplify (+ (* 2.0 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 PI))))) into 0 1.688 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.688 * [backup-simplify]: Simplify 0 into 0 1.689 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.689 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.689 * [backup-simplify]: Simplify 0 into 0 1.690 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.691 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.691 * [backup-simplify]: Simplify 0 into 0 1.692 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.693 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.693 * [backup-simplify]: Simplify 0 into 0 1.693 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.694 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.694 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.694 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.694 * [taylor]: Taking taylor expansion of 2.0 in n 1.694 * [backup-simplify]: Simplify 2.0 into 2.0 1.694 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.694 * [taylor]: Taking taylor expansion of PI in n 1.694 * [backup-simplify]: Simplify PI into PI 1.694 * [taylor]: Taking taylor expansion of n in n 1.694 * [backup-simplify]: Simplify 0 into 0 1.694 * [backup-simplify]: Simplify 1 into 1 1.694 * [backup-simplify]: Simplify (/ PI 1) into PI 1.694 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.694 * [taylor]: Taking taylor expansion of 2.0 in n 1.694 * [backup-simplify]: Simplify 2.0 into 2.0 1.694 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.694 * [taylor]: Taking taylor expansion of PI in n 1.694 * [backup-simplify]: Simplify PI into PI 1.694 * [taylor]: Taking taylor expansion of n in n 1.694 * [backup-simplify]: Simplify 0 into 0 1.694 * [backup-simplify]: Simplify 1 into 1 1.695 * [backup-simplify]: Simplify (/ PI 1) into PI 1.695 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.695 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.696 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.696 * [backup-simplify]: Simplify (+ (* 2.0 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)))) into 0 1.697 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.697 * [backup-simplify]: Simplify 0 into 0 1.698 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.698 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.698 * [backup-simplify]: Simplify 0 into 0 1.699 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.700 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.700 * [backup-simplify]: Simplify 0 into 0 1.700 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.701 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 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)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.703 * [backup-simplify]: Simplify 0 into 0 1.703 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.703 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.703 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.703 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.703 * [taylor]: Taking taylor expansion of -2.0 in n 1.703 * [backup-simplify]: Simplify -2.0 into -2.0 1.703 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.703 * [taylor]: Taking taylor expansion of PI in n 1.703 * [backup-simplify]: Simplify PI into PI 1.703 * [taylor]: Taking taylor expansion of n in n 1.703 * [backup-simplify]: Simplify 0 into 0 1.703 * [backup-simplify]: Simplify 1 into 1 1.704 * [backup-simplify]: Simplify (/ PI 1) into PI 1.704 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.704 * [taylor]: Taking taylor expansion of -2.0 in n 1.704 * [backup-simplify]: Simplify -2.0 into -2.0 1.704 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.704 * [taylor]: Taking taylor expansion of PI in n 1.704 * [backup-simplify]: Simplify PI into PI 1.704 * [taylor]: Taking taylor expansion of n in n 1.704 * [backup-simplify]: Simplify 0 into 0 1.704 * [backup-simplify]: Simplify 1 into 1 1.704 * [backup-simplify]: Simplify (/ PI 1) into PI 1.704 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.705 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.705 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.706 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.706 * [backup-simplify]: Simplify 0 into 0 1.706 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.707 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.707 * [backup-simplify]: Simplify 0 into 0 1.707 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.708 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.708 * [backup-simplify]: Simplify 0 into 0 1.709 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.709 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.710 * [backup-simplify]: Simplify 0 into 0 1.710 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.711 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.711 * [backup-simplify]: Simplify 0 into 0 1.712 * [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 1.712 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.712 * [backup-simplify]: Simplify 0 into 0 1.713 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.713 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1) 1.713 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.713 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.713 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.713 * [taylor]: Taking taylor expansion of 2.0 in n 1.713 * [backup-simplify]: Simplify 2.0 into 2.0 1.713 * [taylor]: Taking taylor expansion of (* n PI) in n 1.713 * [taylor]: Taking taylor expansion of n in n 1.713 * [backup-simplify]: Simplify 0 into 0 1.713 * [backup-simplify]: Simplify 1 into 1 1.713 * [taylor]: Taking taylor expansion of PI in n 1.713 * [backup-simplify]: Simplify PI into PI 1.713 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.713 * [taylor]: Taking taylor expansion of 2.0 in n 1.713 * [backup-simplify]: Simplify 2.0 into 2.0 1.713 * [taylor]: Taking taylor expansion of (* n PI) in n 1.713 * [taylor]: Taking taylor expansion of n in n 1.713 * [backup-simplify]: Simplify 0 into 0 1.713 * [backup-simplify]: Simplify 1 into 1 1.713 * [taylor]: Taking taylor expansion of PI in n 1.713 * [backup-simplify]: Simplify PI into PI 1.714 * [backup-simplify]: Simplify (* 0 PI) into 0 1.714 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.714 * [backup-simplify]: Simplify 0 into 0 1.715 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.716 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.716 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.717 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.717 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.717 * [backup-simplify]: Simplify 0 into 0 1.718 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.718 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.718 * [backup-simplify]: Simplify 0 into 0 1.719 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.720 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.720 * [backup-simplify]: Simplify 0 into 0 1.721 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.721 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.721 * [backup-simplify]: Simplify 0 into 0 1.722 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.723 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.723 * [backup-simplify]: Simplify 0 into 0 1.724 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.725 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.725 * [backup-simplify]: Simplify 0 into 0 1.725 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.726 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.726 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.726 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.726 * [taylor]: Taking taylor expansion of 2.0 in n 1.726 * [backup-simplify]: Simplify 2.0 into 2.0 1.726 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.726 * [taylor]: Taking taylor expansion of PI in n 1.726 * [backup-simplify]: Simplify PI into PI 1.726 * [taylor]: Taking taylor expansion of n in n 1.726 * [backup-simplify]: Simplify 0 into 0 1.726 * [backup-simplify]: Simplify 1 into 1 1.726 * [backup-simplify]: Simplify (/ PI 1) into PI 1.726 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.726 * [taylor]: Taking taylor expansion of 2.0 in n 1.726 * [backup-simplify]: Simplify 2.0 into 2.0 1.726 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.726 * [taylor]: Taking taylor expansion of PI in n 1.726 * [backup-simplify]: Simplify PI into PI 1.726 * [taylor]: Taking taylor expansion of n in n 1.726 * [backup-simplify]: Simplify 0 into 0 1.726 * [backup-simplify]: Simplify 1 into 1 1.727 * [backup-simplify]: Simplify (/ PI 1) into PI 1.727 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.727 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.728 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.728 * [backup-simplify]: Simplify 0 into 0 1.729 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.729 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.729 * [backup-simplify]: Simplify 0 into 0 1.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.731 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.731 * [backup-simplify]: Simplify 0 into 0 1.731 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.732 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.732 * [backup-simplify]: Simplify 0 into 0 1.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.733 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.733 * [backup-simplify]: Simplify 0 into 0 1.734 * [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 1.735 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.735 * [backup-simplify]: Simplify 0 into 0 1.735 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.735 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.735 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.735 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.736 * [taylor]: Taking taylor expansion of -2.0 in n 1.736 * [backup-simplify]: Simplify -2.0 into -2.0 1.736 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.736 * [taylor]: Taking taylor expansion of PI in n 1.736 * [backup-simplify]: Simplify PI into PI 1.736 * [taylor]: Taking taylor expansion of n in n 1.736 * [backup-simplify]: Simplify 0 into 0 1.736 * [backup-simplify]: Simplify 1 into 1 1.736 * [backup-simplify]: Simplify (/ PI 1) into PI 1.736 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.736 * [taylor]: Taking taylor expansion of -2.0 in n 1.736 * [backup-simplify]: Simplify -2.0 into -2.0 1.736 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.736 * [taylor]: Taking taylor expansion of PI in n 1.736 * [backup-simplify]: Simplify PI into PI 1.736 * [taylor]: Taking taylor expansion of n in n 1.736 * [backup-simplify]: Simplify 0 into 0 1.736 * [backup-simplify]: Simplify 1 into 1 1.736 * [backup-simplify]: Simplify (/ PI 1) into PI 1.737 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.737 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.738 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.738 * [backup-simplify]: Simplify 0 into 0 1.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.739 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.739 * [backup-simplify]: Simplify 0 into 0 1.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.740 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.740 * [backup-simplify]: Simplify 0 into 0 1.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.741 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.741 * [backup-simplify]: Simplify 0 into 0 1.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.743 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.743 * [backup-simplify]: Simplify 0 into 0 1.743 * [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 1.744 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.744 * [backup-simplify]: Simplify 0 into 0 1.745 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.745 * * * [progress]: simplifying candidates 1.746 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.125 (* (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)) 1.747 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (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)) (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (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)) (expm1 (* (* h0 PI) h1)) (log1p (* (* h0 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) (expm1 (* (* h0 PI) h1)) (log1p (* (* h0 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)) 1.753 * * [simplify]: iteration 0 : 407 enodes (cost 832 ) 1.761 * * [simplify]: iteration 1 : 1658 enodes (cost 770 ) 1.793 * * [simplify]: iteration 2 : 5001 enodes (cost 732 ) 1.800 * * * [progress]: adding candidates to table 2.179 * * [progress]: iteration 3 / 4 2.180 * * * [progress]: picking best candidate 2.195 * * * * [pick]: Picked # 2.195 * * * [progress]: localizing error 2.223 * * * [progress]: generating rewritten candidates 2.223 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1) 2.334 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 2.358 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 1 2) 2.359 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1 1 2 2) 2.363 * * * [progress]: generating series expansions 2.363 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1) 2.364 * [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))) 2.364 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.364 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.364 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.364 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.364 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.364 * [taylor]: Taking taylor expansion of 0.5 in k 2.364 * [backup-simplify]: Simplify 0.5 into 0.5 2.364 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.364 * [taylor]: Taking taylor expansion of 1.0 in k 2.364 * [backup-simplify]: Simplify 1.0 into 1.0 2.364 * [taylor]: Taking taylor expansion of k in k 2.364 * [backup-simplify]: Simplify 0 into 0 2.364 * [backup-simplify]: Simplify 1 into 1 2.364 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.364 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.364 * [taylor]: Taking taylor expansion of 2.0 in k 2.364 * [backup-simplify]: Simplify 2.0 into 2.0 2.364 * [taylor]: Taking taylor expansion of (* n PI) in k 2.365 * [taylor]: Taking taylor expansion of n in k 2.365 * [backup-simplify]: Simplify n into n 2.365 * [taylor]: Taking taylor expansion of PI in k 2.365 * [backup-simplify]: Simplify PI into PI 2.365 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.365 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.365 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.365 * [backup-simplify]: Simplify (- 0) into 0 2.365 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.366 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.366 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.366 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.366 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.366 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.366 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.366 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.366 * [taylor]: Taking taylor expansion of 0.5 in n 2.366 * [backup-simplify]: Simplify 0.5 into 0.5 2.366 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.366 * [taylor]: Taking taylor expansion of 1.0 in n 2.366 * [backup-simplify]: Simplify 1.0 into 1.0 2.366 * [taylor]: Taking taylor expansion of k in n 2.366 * [backup-simplify]: Simplify k into k 2.366 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.366 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.366 * [taylor]: Taking taylor expansion of 2.0 in n 2.366 * [backup-simplify]: Simplify 2.0 into 2.0 2.366 * [taylor]: Taking taylor expansion of (* n PI) in n 2.366 * [taylor]: Taking taylor expansion of n in n 2.366 * [backup-simplify]: Simplify 0 into 0 2.366 * [backup-simplify]: Simplify 1 into 1 2.366 * [taylor]: Taking taylor expansion of PI in n 2.366 * [backup-simplify]: Simplify PI into PI 2.366 * [backup-simplify]: Simplify (* 0 PI) into 0 2.367 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.368 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.368 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.369 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.369 * [backup-simplify]: Simplify (- k) into (- k) 2.369 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.369 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.370 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.371 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.371 * [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))))) 2.371 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.371 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.371 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.371 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.371 * [taylor]: Taking taylor expansion of 0.5 in n 2.371 * [backup-simplify]: Simplify 0.5 into 0.5 2.371 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.371 * [taylor]: Taking taylor expansion of 1.0 in n 2.372 * [backup-simplify]: Simplify 1.0 into 1.0 2.372 * [taylor]: Taking taylor expansion of k in n 2.372 * [backup-simplify]: Simplify k into k 2.372 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.372 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.372 * [taylor]: Taking taylor expansion of 2.0 in n 2.372 * [backup-simplify]: Simplify 2.0 into 2.0 2.372 * [taylor]: Taking taylor expansion of (* n PI) in n 2.372 * [taylor]: Taking taylor expansion of n in n 2.372 * [backup-simplify]: Simplify 0 into 0 2.372 * [backup-simplify]: Simplify 1 into 1 2.372 * [taylor]: Taking taylor expansion of PI in n 2.372 * [backup-simplify]: Simplify PI into PI 2.372 * [backup-simplify]: Simplify (* 0 PI) into 0 2.372 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.373 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.374 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.375 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.375 * [backup-simplify]: Simplify (- k) into (- k) 2.375 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.375 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.376 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.376 * [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)))) 2.377 * [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))))) 2.377 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.377 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.377 * [taylor]: Taking taylor expansion of 0.5 in k 2.377 * [backup-simplify]: Simplify 0.5 into 0.5 2.377 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.377 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.377 * [taylor]: Taking taylor expansion of 1.0 in k 2.377 * [backup-simplify]: Simplify 1.0 into 1.0 2.377 * [taylor]: Taking taylor expansion of k in k 2.377 * [backup-simplify]: Simplify 0 into 0 2.377 * [backup-simplify]: Simplify 1 into 1 2.377 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.377 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.377 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.377 * [taylor]: Taking taylor expansion of 2.0 in k 2.377 * [backup-simplify]: Simplify 2.0 into 2.0 2.377 * [taylor]: Taking taylor expansion of PI in k 2.377 * [backup-simplify]: Simplify PI into PI 2.378 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.378 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.378 * [taylor]: Taking taylor expansion of (log n) in k 2.378 * [taylor]: Taking taylor expansion of n in k 2.378 * [backup-simplify]: Simplify n into n 2.378 * [backup-simplify]: Simplify (log n) into (log n) 2.379 * [backup-simplify]: Simplify (- 0) into 0 2.379 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.379 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.380 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.381 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 2.381 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.382 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.383 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.383 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.384 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.384 * [backup-simplify]: Simplify (- 0) into 0 2.385 * [backup-simplify]: Simplify (+ 0 0) into 0 2.385 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 2.386 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.386 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.387 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.387 * [taylor]: Taking taylor expansion of 0 in k 2.387 * [backup-simplify]: Simplify 0 into 0 2.387 * [backup-simplify]: Simplify 0 into 0 2.388 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.389 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.389 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.390 * [backup-simplify]: Simplify (+ 0 0) into 0 2.390 * [backup-simplify]: Simplify (- 1) into -1 2.390 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.391 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.392 * [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)))) 2.394 * [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)))))) 2.396 * [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)))))) 2.397 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.397 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.399 * [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 2.399 * [backup-simplify]: Simplify (- 0) into 0 2.399 * [backup-simplify]: Simplify (+ 0 0) into 0 2.400 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 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 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.403 * [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 2.403 * [taylor]: Taking taylor expansion of 0 in k 2.403 * [backup-simplify]: Simplify 0 into 0 2.403 * [backup-simplify]: Simplify 0 into 0 2.403 * [backup-simplify]: Simplify 0 into 0 2.404 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.405 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.406 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.407 * [backup-simplify]: Simplify (+ 0 0) into 0 2.407 * [backup-simplify]: Simplify (- 0) into 0 2.407 * [backup-simplify]: Simplify (+ 0 0) into 0 2.408 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.410 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.412 * [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)))))) 2.415 * [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)))))) 2.424 * [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)))))) 2.425 * [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)))) 2.425 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.425 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.425 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.425 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.425 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.425 * [taylor]: Taking taylor expansion of 0.5 in k 2.425 * [backup-simplify]: Simplify 0.5 into 0.5 2.425 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.425 * [taylor]: Taking taylor expansion of 1.0 in k 2.425 * [backup-simplify]: Simplify 1.0 into 1.0 2.425 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.425 * [taylor]: Taking taylor expansion of k in k 2.425 * [backup-simplify]: Simplify 0 into 0 2.425 * [backup-simplify]: Simplify 1 into 1 2.426 * [backup-simplify]: Simplify (/ 1 1) into 1 2.426 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.426 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.426 * [taylor]: Taking taylor expansion of 2.0 in k 2.426 * [backup-simplify]: Simplify 2.0 into 2.0 2.426 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.426 * [taylor]: Taking taylor expansion of PI in k 2.426 * [backup-simplify]: Simplify PI into PI 2.426 * [taylor]: Taking taylor expansion of n in k 2.426 * [backup-simplify]: Simplify n into n 2.426 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.426 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.426 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.426 * [backup-simplify]: Simplify (- 1) into -1 2.426 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.427 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.427 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.427 * [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))))) 2.427 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.427 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.427 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.427 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.427 * [taylor]: Taking taylor expansion of 0.5 in n 2.427 * [backup-simplify]: Simplify 0.5 into 0.5 2.427 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.427 * [taylor]: Taking taylor expansion of 1.0 in n 2.427 * [backup-simplify]: Simplify 1.0 into 1.0 2.427 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.427 * [taylor]: Taking taylor expansion of k in n 2.427 * [backup-simplify]: Simplify k into k 2.427 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.427 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.427 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.427 * [taylor]: Taking taylor expansion of 2.0 in n 2.427 * [backup-simplify]: Simplify 2.0 into 2.0 2.427 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.427 * [taylor]: Taking taylor expansion of PI in n 2.427 * [backup-simplify]: Simplify PI into PI 2.427 * [taylor]: Taking taylor expansion of n in n 2.428 * [backup-simplify]: Simplify 0 into 0 2.428 * [backup-simplify]: Simplify 1 into 1 2.428 * [backup-simplify]: Simplify (/ PI 1) into PI 2.428 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.429 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.429 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.429 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.429 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.430 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.430 * [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)))) 2.431 * [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))))) 2.431 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.431 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.431 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.431 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.431 * [taylor]: Taking taylor expansion of 0.5 in n 2.431 * [backup-simplify]: Simplify 0.5 into 0.5 2.431 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.431 * [taylor]: Taking taylor expansion of 1.0 in n 2.431 * [backup-simplify]: Simplify 1.0 into 1.0 2.431 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.431 * [taylor]: Taking taylor expansion of k in n 2.431 * [backup-simplify]: Simplify k into k 2.431 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.431 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.431 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.431 * [taylor]: Taking taylor expansion of 2.0 in n 2.431 * [backup-simplify]: Simplify 2.0 into 2.0 2.431 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.431 * [taylor]: Taking taylor expansion of PI in n 2.432 * [backup-simplify]: Simplify PI into PI 2.432 * [taylor]: Taking taylor expansion of n in n 2.432 * [backup-simplify]: Simplify 0 into 0 2.432 * [backup-simplify]: Simplify 1 into 1 2.432 * [backup-simplify]: Simplify (/ PI 1) into PI 2.432 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.433 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.433 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.433 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.433 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.434 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.434 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.435 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.435 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.435 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.435 * [taylor]: Taking taylor expansion of 0.5 in k 2.435 * [backup-simplify]: Simplify 0.5 into 0.5 2.435 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.435 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.435 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.435 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.435 * [taylor]: Taking taylor expansion of 2.0 in k 2.435 * [backup-simplify]: Simplify 2.0 into 2.0 2.435 * [taylor]: Taking taylor expansion of PI in k 2.435 * [backup-simplify]: Simplify PI into PI 2.436 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.436 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.436 * [taylor]: Taking taylor expansion of (log n) in k 2.436 * [taylor]: Taking taylor expansion of n in k 2.436 * [backup-simplify]: Simplify n into n 2.436 * [backup-simplify]: Simplify (log n) into (log n) 2.436 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.436 * [taylor]: Taking taylor expansion of 1.0 in k 2.436 * [backup-simplify]: Simplify 1.0 into 1.0 2.437 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.437 * [taylor]: Taking taylor expansion of k in k 2.437 * [backup-simplify]: Simplify 0 into 0 2.437 * [backup-simplify]: Simplify 1 into 1 2.437 * [backup-simplify]: Simplify (/ 1 1) into 1 2.437 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.437 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.438 * [backup-simplify]: Simplify (- 1) into -1 2.438 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.439 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.439 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.440 * [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))))) 2.441 * [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))))) 2.441 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.442 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.442 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.443 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.443 * [backup-simplify]: Simplify (- 0) into 0 2.443 * [backup-simplify]: Simplify (+ 0 0) into 0 2.443 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.444 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.445 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.446 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.446 * [taylor]: Taking taylor expansion of 0 in k 2.446 * [backup-simplify]: Simplify 0 into 0 2.446 * [backup-simplify]: Simplify 0 into 0 2.446 * [backup-simplify]: Simplify 0 into 0 2.447 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.447 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.449 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.449 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.450 * [backup-simplify]: Simplify (- 0) into 0 2.450 * [backup-simplify]: Simplify (+ 0 0) into 0 2.450 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.451 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.452 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.454 * [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 2.454 * [taylor]: Taking taylor expansion of 0 in k 2.454 * [backup-simplify]: Simplify 0 into 0 2.454 * [backup-simplify]: Simplify 0 into 0 2.454 * [backup-simplify]: Simplify 0 into 0 2.454 * [backup-simplify]: Simplify 0 into 0 2.454 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.455 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.458 * [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 2.458 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.458 * [backup-simplify]: Simplify (- 0) into 0 2.458 * [backup-simplify]: Simplify (+ 0 0) into 0 2.459 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.460 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.461 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.462 * [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 2.462 * [taylor]: Taking taylor expansion of 0 in k 2.463 * [backup-simplify]: Simplify 0 into 0 2.463 * [backup-simplify]: Simplify 0 into 0 2.463 * [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)))) 2.464 * [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))) 2.464 * [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 2.464 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.464 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in k 2.464 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in k 2.464 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.464 * [taylor]: Taking taylor expansion of 0.5 in k 2.464 * [backup-simplify]: Simplify 0.5 into 0.5 2.464 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.464 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.464 * [taylor]: Taking taylor expansion of k in k 2.464 * [backup-simplify]: Simplify 0 into 0 2.464 * [backup-simplify]: Simplify 1 into 1 2.465 * [backup-simplify]: Simplify (/ 1 1) into 1 2.465 * [taylor]: Taking taylor expansion of 1.0 in k 2.465 * [backup-simplify]: Simplify 1.0 into 1.0 2.465 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in k 2.465 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in k 2.465 * [taylor]: Taking taylor expansion of 2.0 in k 2.465 * [backup-simplify]: Simplify 2.0 into 2.0 2.465 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in k 2.465 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in k 2.465 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in k 2.465 * [taylor]: Taking taylor expansion of (cbrt -1) in k 2.465 * [taylor]: Taking taylor expansion of -1 in k 2.465 * [backup-simplify]: Simplify -1 into -1 2.465 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.466 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.466 * [taylor]: Taking taylor expansion of PI in k 2.466 * [backup-simplify]: Simplify PI into PI 2.466 * [taylor]: Taking taylor expansion of n in k 2.466 * [backup-simplify]: Simplify n into n 2.467 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 2.468 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 2.469 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 2.469 * [backup-simplify]: Simplify (/ (* -1 PI) n) into (* -1 (/ PI n)) 2.469 * [backup-simplify]: Simplify (* 2.0 (* -1 (/ PI n))) into (* -2.0 (/ PI n)) 2.469 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.469 * [backup-simplify]: Simplify (+ 1 0) into 1 2.470 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.470 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.471 * [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)))))) 2.471 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.471 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 2.471 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 2.471 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.471 * [taylor]: Taking taylor expansion of 0.5 in n 2.471 * [backup-simplify]: Simplify 0.5 into 0.5 2.471 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.471 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.471 * [taylor]: Taking taylor expansion of k in n 2.471 * [backup-simplify]: Simplify k into k 2.471 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.471 * [taylor]: Taking taylor expansion of 1.0 in n 2.471 * [backup-simplify]: Simplify 1.0 into 1.0 2.471 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 2.471 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 2.471 * [taylor]: Taking taylor expansion of 2.0 in n 2.471 * [backup-simplify]: Simplify 2.0 into 2.0 2.471 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 2.471 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 2.471 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 2.471 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.471 * [taylor]: Taking taylor expansion of -1 in n 2.471 * [backup-simplify]: Simplify -1 into -1 2.472 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.472 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.472 * [taylor]: Taking taylor expansion of PI in n 2.472 * [backup-simplify]: Simplify PI into PI 2.472 * [taylor]: Taking taylor expansion of n in n 2.472 * [backup-simplify]: Simplify 0 into 0 2.472 * [backup-simplify]: Simplify 1 into 1 2.473 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 2.474 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 2.475 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 2.476 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 2.476 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 2.477 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.477 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.477 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.478 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.479 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.479 * [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))))) 2.479 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.479 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 2.479 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 2.479 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.480 * [taylor]: Taking taylor expansion of 0.5 in n 2.480 * [backup-simplify]: Simplify 0.5 into 0.5 2.480 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.480 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.480 * [taylor]: Taking taylor expansion of k in n 2.480 * [backup-simplify]: Simplify k into k 2.480 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.480 * [taylor]: Taking taylor expansion of 1.0 in n 2.480 * [backup-simplify]: Simplify 1.0 into 1.0 2.480 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 2.480 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 2.480 * [taylor]: Taking taylor expansion of 2.0 in n 2.480 * [backup-simplify]: Simplify 2.0 into 2.0 2.480 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 2.480 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 2.480 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 2.480 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.480 * [taylor]: Taking taylor expansion of -1 in n 2.480 * [backup-simplify]: Simplify -1 into -1 2.480 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.480 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.480 * [taylor]: Taking taylor expansion of PI in n 2.481 * [backup-simplify]: Simplify PI into PI 2.481 * [taylor]: Taking taylor expansion of n in n 2.481 * [backup-simplify]: Simplify 0 into 0 2.481 * [backup-simplify]: Simplify 1 into 1 2.481 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 2.483 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 2.484 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 2.484 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 2.485 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 2.485 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.485 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.485 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.486 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.487 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.488 * [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))))) 2.488 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.488 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.488 * [taylor]: Taking taylor expansion of 0.5 in k 2.488 * [backup-simplify]: Simplify 0.5 into 0.5 2.488 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.488 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.488 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.488 * [taylor]: Taking taylor expansion of k in k 2.488 * [backup-simplify]: Simplify 0 into 0 2.488 * [backup-simplify]: Simplify 1 into 1 2.488 * [backup-simplify]: Simplify (/ 1 1) into 1 2.488 * [taylor]: Taking taylor expansion of 1.0 in k 2.488 * [backup-simplify]: Simplify 1.0 into 1.0 2.488 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.488 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.488 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.488 * [taylor]: Taking taylor expansion of -2.0 in k 2.488 * [backup-simplify]: Simplify -2.0 into -2.0 2.488 * [taylor]: Taking taylor expansion of PI in k 2.488 * [backup-simplify]: Simplify PI into PI 2.489 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.489 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.489 * [taylor]: Taking taylor expansion of (log n) in k 2.489 * [taylor]: Taking taylor expansion of n in k 2.489 * [backup-simplify]: Simplify n into n 2.489 * [backup-simplify]: Simplify (log n) into (log n) 2.490 * [backup-simplify]: Simplify (+ 1 0) into 1 2.490 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.490 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.491 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.492 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.492 * [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))))) 2.493 * [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))))) 2.493 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (cbrt -1))) into 0 2.494 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow (cbrt -1) 2))) into 0 2.495 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (* 0 PI)) into 0 2.495 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)))) into 0 2.496 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* -1 PI))) into 0 2.497 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.497 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.497 * [backup-simplify]: Simplify (+ 0 0) into 0 2.497 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.498 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.499 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.500 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.500 * [taylor]: Taking taylor expansion of 0 in k 2.500 * [backup-simplify]: Simplify 0 into 0 2.500 * [backup-simplify]: Simplify 0 into 0 2.500 * [backup-simplify]: Simplify 0 into 0 2.501 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.502 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (cbrt -1)))) into 0 2.502 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2)))) into 0 2.503 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (* 0 PI))) into 0 2.504 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.504 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* -1 PI)))) into 0 2.506 * [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 2.506 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.506 * [backup-simplify]: Simplify (+ 0 0) into 0 2.507 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.508 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.509 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.510 * [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 2.510 * [taylor]: Taking taylor expansion of 0 in k 2.510 * [backup-simplify]: Simplify 0 into 0 2.510 * [backup-simplify]: Simplify 0 into 0 2.510 * [backup-simplify]: Simplify 0 into 0 2.510 * [backup-simplify]: Simplify 0 into 0 2.511 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.512 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1))))) into 0 2.512 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2))))) into 0 2.513 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.517 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.518 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* -1 PI))))) into 0 2.522 * [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 2.522 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.522 * [backup-simplify]: Simplify (+ 0 0) into 0 2.523 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.524 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.525 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.527 * [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 2.527 * [taylor]: Taking taylor expansion of 0 in k 2.527 * [backup-simplify]: Simplify 0 into 0 2.527 * [backup-simplify]: Simplify 0 into 0 2.527 * [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)))))) 2.527 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 2.528 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 2.528 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.528 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.528 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.528 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.528 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.528 * [taylor]: Taking taylor expansion of 0.5 in k 2.528 * [backup-simplify]: Simplify 0.5 into 0.5 2.528 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.528 * [taylor]: Taking taylor expansion of 1.0 in k 2.528 * [backup-simplify]: Simplify 1.0 into 1.0 2.528 * [taylor]: Taking taylor expansion of k in k 2.528 * [backup-simplify]: Simplify 0 into 0 2.528 * [backup-simplify]: Simplify 1 into 1 2.528 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.528 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.528 * [taylor]: Taking taylor expansion of 2.0 in k 2.528 * [backup-simplify]: Simplify 2.0 into 2.0 2.528 * [taylor]: Taking taylor expansion of (* n PI) in k 2.528 * [taylor]: Taking taylor expansion of n in k 2.528 * [backup-simplify]: Simplify n into n 2.528 * [taylor]: Taking taylor expansion of PI in k 2.528 * [backup-simplify]: Simplify PI into PI 2.528 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.528 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.528 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.529 * [backup-simplify]: Simplify (- 0) into 0 2.529 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.529 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.529 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.529 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.529 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.529 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.529 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.529 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.529 * [taylor]: Taking taylor expansion of 0.5 in n 2.529 * [backup-simplify]: Simplify 0.5 into 0.5 2.529 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.529 * [taylor]: Taking taylor expansion of 1.0 in n 2.529 * [backup-simplify]: Simplify 1.0 into 1.0 2.530 * [taylor]: Taking taylor expansion of k in n 2.530 * [backup-simplify]: Simplify k into k 2.530 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.530 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.530 * [taylor]: Taking taylor expansion of 2.0 in n 2.530 * [backup-simplify]: Simplify 2.0 into 2.0 2.530 * [taylor]: Taking taylor expansion of (* n PI) in n 2.530 * [taylor]: Taking taylor expansion of n in n 2.530 * [backup-simplify]: Simplify 0 into 0 2.530 * [backup-simplify]: Simplify 1 into 1 2.530 * [taylor]: Taking taylor expansion of PI in n 2.530 * [backup-simplify]: Simplify PI into PI 2.530 * [backup-simplify]: Simplify (* 0 PI) into 0 2.530 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.531 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.532 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.532 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.533 * [backup-simplify]: Simplify (- k) into (- k) 2.533 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.533 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.533 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.534 * [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)))) 2.535 * [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))))) 2.535 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.535 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.535 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.535 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.535 * [taylor]: Taking taylor expansion of 0.5 in n 2.535 * [backup-simplify]: Simplify 0.5 into 0.5 2.535 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.535 * [taylor]: Taking taylor expansion of 1.0 in n 2.535 * [backup-simplify]: Simplify 1.0 into 1.0 2.535 * [taylor]: Taking taylor expansion of k in n 2.535 * [backup-simplify]: Simplify k into k 2.535 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.535 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.535 * [taylor]: Taking taylor expansion of 2.0 in n 2.535 * [backup-simplify]: Simplify 2.0 into 2.0 2.535 * [taylor]: Taking taylor expansion of (* n PI) in n 2.535 * [taylor]: Taking taylor expansion of n in n 2.535 * [backup-simplify]: Simplify 0 into 0 2.535 * [backup-simplify]: Simplify 1 into 1 2.535 * [taylor]: Taking taylor expansion of PI in n 2.535 * [backup-simplify]: Simplify PI into PI 2.535 * [backup-simplify]: Simplify (* 0 PI) into 0 2.536 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.537 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.537 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.538 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.538 * [backup-simplify]: Simplify (- k) into (- k) 2.538 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.538 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.539 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.540 * [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)))) 2.540 * [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))))) 2.540 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.540 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.540 * [taylor]: Taking taylor expansion of 0.5 in k 2.541 * [backup-simplify]: Simplify 0.5 into 0.5 2.541 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.541 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.541 * [taylor]: Taking taylor expansion of 1.0 in k 2.541 * [backup-simplify]: Simplify 1.0 into 1.0 2.541 * [taylor]: Taking taylor expansion of k in k 2.541 * [backup-simplify]: Simplify 0 into 0 2.541 * [backup-simplify]: Simplify 1 into 1 2.541 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.541 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.541 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.541 * [taylor]: Taking taylor expansion of 2.0 in k 2.541 * [backup-simplify]: Simplify 2.0 into 2.0 2.541 * [taylor]: Taking taylor expansion of PI in k 2.541 * [backup-simplify]: Simplify PI into PI 2.541 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.542 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.542 * [taylor]: Taking taylor expansion of (log n) in k 2.542 * [taylor]: Taking taylor expansion of n in k 2.542 * [backup-simplify]: Simplify n into n 2.542 * [backup-simplify]: Simplify (log n) into (log n) 2.542 * [backup-simplify]: Simplify (- 0) into 0 2.542 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.543 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.543 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.544 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 2.545 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.545 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.546 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.547 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.548 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.548 * [backup-simplify]: Simplify (- 0) into 0 2.548 * [backup-simplify]: Simplify (+ 0 0) into 0 2.548 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 2.549 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.550 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.551 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.551 * [taylor]: Taking taylor expansion of 0 in k 2.551 * [backup-simplify]: Simplify 0 into 0 2.551 * [backup-simplify]: Simplify 0 into 0 2.552 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.552 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.553 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.553 * [backup-simplify]: Simplify (+ 0 0) into 0 2.553 * [backup-simplify]: Simplify (- 1) into -1 2.554 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.555 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.556 * [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)))) 2.558 * [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)))))) 2.560 * [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)))))) 2.560 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.561 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.563 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.563 * [backup-simplify]: Simplify (- 0) into 0 2.563 * [backup-simplify]: Simplify (+ 0 0) into 0 2.564 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.564 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.565 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.567 * [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 2.567 * [taylor]: Taking taylor expansion of 0 in k 2.567 * [backup-simplify]: Simplify 0 into 0 2.567 * [backup-simplify]: Simplify 0 into 0 2.567 * [backup-simplify]: Simplify 0 into 0 2.567 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.569 * [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 2.570 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.570 * [backup-simplify]: Simplify (+ 0 0) into 0 2.570 * [backup-simplify]: Simplify (- 0) into 0 2.571 * [backup-simplify]: Simplify (+ 0 0) into 0 2.572 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.573 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.575 * [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)))))) 2.578 * [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)))))) 2.584 * [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)))))) 2.585 * [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)))) 2.585 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.585 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.585 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.585 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.585 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.585 * [taylor]: Taking taylor expansion of 0.5 in k 2.585 * [backup-simplify]: Simplify 0.5 into 0.5 2.585 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.585 * [taylor]: Taking taylor expansion of 1.0 in k 2.585 * [backup-simplify]: Simplify 1.0 into 1.0 2.585 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.585 * [taylor]: Taking taylor expansion of k in k 2.585 * [backup-simplify]: Simplify 0 into 0 2.585 * [backup-simplify]: Simplify 1 into 1 2.585 * [backup-simplify]: Simplify (/ 1 1) into 1 2.585 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.585 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.585 * [taylor]: Taking taylor expansion of 2.0 in k 2.585 * [backup-simplify]: Simplify 2.0 into 2.0 2.585 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.585 * [taylor]: Taking taylor expansion of PI in k 2.585 * [backup-simplify]: Simplify PI into PI 2.585 * [taylor]: Taking taylor expansion of n in k 2.585 * [backup-simplify]: Simplify n into n 2.585 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.585 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.586 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.586 * [backup-simplify]: Simplify (- 1) into -1 2.586 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.586 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.586 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.587 * [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))))) 2.587 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.587 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.587 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.587 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.587 * [taylor]: Taking taylor expansion of 0.5 in n 2.587 * [backup-simplify]: Simplify 0.5 into 0.5 2.587 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.587 * [taylor]: Taking taylor expansion of 1.0 in n 2.587 * [backup-simplify]: Simplify 1.0 into 1.0 2.587 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.587 * [taylor]: Taking taylor expansion of k in n 2.587 * [backup-simplify]: Simplify k into k 2.587 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.587 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.587 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.587 * [taylor]: Taking taylor expansion of 2.0 in n 2.587 * [backup-simplify]: Simplify 2.0 into 2.0 2.587 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.587 * [taylor]: Taking taylor expansion of PI in n 2.587 * [backup-simplify]: Simplify PI into PI 2.587 * [taylor]: Taking taylor expansion of n in n 2.587 * [backup-simplify]: Simplify 0 into 0 2.587 * [backup-simplify]: Simplify 1 into 1 2.587 * [backup-simplify]: Simplify (/ PI 1) into PI 2.587 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.588 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.588 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.588 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.588 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.589 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.590 * [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)))) 2.591 * [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))))) 2.591 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.591 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.591 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.591 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.591 * [taylor]: Taking taylor expansion of 0.5 in n 2.591 * [backup-simplify]: Simplify 0.5 into 0.5 2.591 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.591 * [taylor]: Taking taylor expansion of 1.0 in n 2.591 * [backup-simplify]: Simplify 1.0 into 1.0 2.591 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.591 * [taylor]: Taking taylor expansion of k in n 2.591 * [backup-simplify]: Simplify k into k 2.591 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.591 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.591 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.591 * [taylor]: Taking taylor expansion of 2.0 in n 2.591 * [backup-simplify]: Simplify 2.0 into 2.0 2.591 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.591 * [taylor]: Taking taylor expansion of PI in n 2.591 * [backup-simplify]: Simplify PI into PI 2.591 * [taylor]: Taking taylor expansion of n in n 2.591 * [backup-simplify]: Simplify 0 into 0 2.591 * [backup-simplify]: Simplify 1 into 1 2.591 * [backup-simplify]: Simplify (/ PI 1) into PI 2.591 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.592 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.592 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.592 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.592 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.593 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.594 * [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)))) 2.595 * [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))))) 2.595 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.595 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.595 * [taylor]: Taking taylor expansion of 0.5 in k 2.595 * [backup-simplify]: Simplify 0.5 into 0.5 2.595 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.595 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.595 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.595 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.595 * [taylor]: Taking taylor expansion of 2.0 in k 2.595 * [backup-simplify]: Simplify 2.0 into 2.0 2.595 * [taylor]: Taking taylor expansion of PI in k 2.595 * [backup-simplify]: Simplify PI into PI 2.595 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.596 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.596 * [taylor]: Taking taylor expansion of (log n) in k 2.596 * [taylor]: Taking taylor expansion of n in k 2.596 * [backup-simplify]: Simplify n into n 2.596 * [backup-simplify]: Simplify (log n) into (log n) 2.596 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.596 * [taylor]: Taking taylor expansion of 1.0 in k 2.596 * [backup-simplify]: Simplify 1.0 into 1.0 2.596 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.596 * [taylor]: Taking taylor expansion of k in k 2.596 * [backup-simplify]: Simplify 0 into 0 2.596 * [backup-simplify]: Simplify 1 into 1 2.596 * [backup-simplify]: Simplify (/ 1 1) into 1 2.596 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.597 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.597 * [backup-simplify]: Simplify (- 1) into -1 2.597 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.598 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.599 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.599 * [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))))) 2.600 * [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))))) 2.601 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.601 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.602 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.602 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.602 * [backup-simplify]: Simplify (- 0) into 0 2.603 * [backup-simplify]: Simplify (+ 0 0) into 0 2.603 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.604 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.604 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.606 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.606 * [taylor]: Taking taylor expansion of 0 in k 2.606 * [backup-simplify]: Simplify 0 into 0 2.606 * [backup-simplify]: Simplify 0 into 0 2.606 * [backup-simplify]: Simplify 0 into 0 2.606 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.607 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.612 * [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 2.612 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.612 * [backup-simplify]: Simplify (- 0) into 0 2.612 * [backup-simplify]: Simplify (+ 0 0) into 0 2.613 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.614 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.615 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.616 * [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 2.616 * [taylor]: Taking taylor expansion of 0 in k 2.616 * [backup-simplify]: Simplify 0 into 0 2.616 * [backup-simplify]: Simplify 0 into 0 2.616 * [backup-simplify]: Simplify 0 into 0 2.616 * [backup-simplify]: Simplify 0 into 0 2.617 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.617 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.620 * [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 2.620 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.621 * [backup-simplify]: Simplify (- 0) into 0 2.621 * [backup-simplify]: Simplify (+ 0 0) into 0 2.622 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.622 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.624 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.625 * [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 2.625 * [taylor]: Taking taylor expansion of 0 in k 2.625 * [backup-simplify]: Simplify 0 into 0 2.625 * [backup-simplify]: Simplify 0 into 0 2.626 * [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)))) 2.627 * [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))) 2.627 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.627 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.627 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.627 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.627 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.627 * [taylor]: Taking taylor expansion of 0.5 in k 2.627 * [backup-simplify]: Simplify 0.5 into 0.5 2.627 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.627 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.627 * [taylor]: Taking taylor expansion of k in k 2.627 * [backup-simplify]: Simplify 0 into 0 2.627 * [backup-simplify]: Simplify 1 into 1 2.627 * [backup-simplify]: Simplify (/ 1 1) into 1 2.627 * [taylor]: Taking taylor expansion of 1.0 in k 2.627 * [backup-simplify]: Simplify 1.0 into 1.0 2.627 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.627 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.627 * [taylor]: Taking taylor expansion of -2.0 in k 2.627 * [backup-simplify]: Simplify -2.0 into -2.0 2.627 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.627 * [taylor]: Taking taylor expansion of PI in k 2.627 * [backup-simplify]: Simplify PI into PI 2.627 * [taylor]: Taking taylor expansion of n in k 2.627 * [backup-simplify]: Simplify n into n 2.627 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.627 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.627 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.628 * [backup-simplify]: Simplify (+ 1 0) into 1 2.628 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.628 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.628 * [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)))))) 2.628 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.628 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.628 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.628 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.628 * [taylor]: Taking taylor expansion of 0.5 in n 2.628 * [backup-simplify]: Simplify 0.5 into 0.5 2.628 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.628 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.628 * [taylor]: Taking taylor expansion of k in n 2.628 * [backup-simplify]: Simplify k into k 2.628 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.628 * [taylor]: Taking taylor expansion of 1.0 in n 2.628 * [backup-simplify]: Simplify 1.0 into 1.0 2.628 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.628 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.628 * [taylor]: Taking taylor expansion of -2.0 in n 2.629 * [backup-simplify]: Simplify -2.0 into -2.0 2.629 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.629 * [taylor]: Taking taylor expansion of PI in n 2.629 * [backup-simplify]: Simplify PI into PI 2.629 * [taylor]: Taking taylor expansion of n in n 2.629 * [backup-simplify]: Simplify 0 into 0 2.629 * [backup-simplify]: Simplify 1 into 1 2.629 * [backup-simplify]: Simplify (/ PI 1) into PI 2.629 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.630 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.630 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.630 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.631 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.631 * [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)))) 2.632 * [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))))) 2.632 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.632 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.632 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.632 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.632 * [taylor]: Taking taylor expansion of 0.5 in n 2.632 * [backup-simplify]: Simplify 0.5 into 0.5 2.632 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.632 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.632 * [taylor]: Taking taylor expansion of k in n 2.632 * [backup-simplify]: Simplify k into k 2.632 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.632 * [taylor]: Taking taylor expansion of 1.0 in n 2.632 * [backup-simplify]: Simplify 1.0 into 1.0 2.632 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.632 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.632 * [taylor]: Taking taylor expansion of -2.0 in n 2.632 * [backup-simplify]: Simplify -2.0 into -2.0 2.632 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.633 * [taylor]: Taking taylor expansion of PI in n 2.633 * [backup-simplify]: Simplify PI into PI 2.633 * [taylor]: Taking taylor expansion of n in n 2.633 * [backup-simplify]: Simplify 0 into 0 2.633 * [backup-simplify]: Simplify 1 into 1 2.633 * [backup-simplify]: Simplify (/ PI 1) into PI 2.633 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.634 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.634 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.634 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.635 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.635 * [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)))) 2.636 * [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))))) 2.636 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.636 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.636 * [taylor]: Taking taylor expansion of 0.5 in k 2.636 * [backup-simplify]: Simplify 0.5 into 0.5 2.636 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.636 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.636 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.636 * [taylor]: Taking taylor expansion of k in k 2.636 * [backup-simplify]: Simplify 0 into 0 2.636 * [backup-simplify]: Simplify 1 into 1 2.637 * [backup-simplify]: Simplify (/ 1 1) into 1 2.637 * [taylor]: Taking taylor expansion of 1.0 in k 2.637 * [backup-simplify]: Simplify 1.0 into 1.0 2.637 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.637 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.637 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.637 * [taylor]: Taking taylor expansion of -2.0 in k 2.637 * [backup-simplify]: Simplify -2.0 into -2.0 2.637 * [taylor]: Taking taylor expansion of PI in k 2.637 * [backup-simplify]: Simplify PI into PI 2.637 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.638 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.638 * [taylor]: Taking taylor expansion of (log n) in k 2.638 * [taylor]: Taking taylor expansion of n in k 2.638 * [backup-simplify]: Simplify n into n 2.638 * [backup-simplify]: Simplify (log n) into (log n) 2.638 * [backup-simplify]: Simplify (+ 1 0) into 1 2.638 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.639 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.639 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.640 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.641 * [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))))) 2.641 * [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))))) 2.642 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.642 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.643 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.643 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.644 * [backup-simplify]: Simplify (+ 0 0) into 0 2.644 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.645 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.645 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.647 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.647 * [taylor]: Taking taylor expansion of 0 in k 2.647 * [backup-simplify]: Simplify 0 into 0 2.647 * [backup-simplify]: Simplify 0 into 0 2.647 * [backup-simplify]: Simplify 0 into 0 2.647 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.648 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.650 * [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 2.650 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.650 * [backup-simplify]: Simplify (+ 0 0) into 0 2.651 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.651 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.652 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.654 * [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 2.654 * [taylor]: Taking taylor expansion of 0 in k 2.654 * [backup-simplify]: Simplify 0 into 0 2.654 * [backup-simplify]: Simplify 0 into 0 2.654 * [backup-simplify]: Simplify 0 into 0 2.654 * [backup-simplify]: Simplify 0 into 0 2.654 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.655 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.658 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 2.658 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.659 * [backup-simplify]: Simplify (+ 0 0) into 0 2.659 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.661 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.663 * [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 2.663 * [taylor]: Taking taylor expansion of 0 in k 2.663 * [backup-simplify]: Simplify 0 into 0 2.663 * [backup-simplify]: Simplify 0 into 0 2.664 * [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)))))) 2.664 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 1 2) 2.664 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 2.664 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 2.664 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.664 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.664 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.664 * [taylor]: Taking taylor expansion of 1/3 in n 2.664 * [backup-simplify]: Simplify 1/3 into 1/3 2.664 * [taylor]: Taking taylor expansion of (log n) in n 2.664 * [taylor]: Taking taylor expansion of n in n 2.664 * [backup-simplify]: Simplify 0 into 0 2.664 * [backup-simplify]: Simplify 1 into 1 2.664 * [backup-simplify]: Simplify (log 1) into 0 2.664 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.664 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.665 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.665 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.665 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.665 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.665 * [taylor]: Taking taylor expansion of 1/3 in n 2.665 * [backup-simplify]: Simplify 1/3 into 1/3 2.665 * [taylor]: Taking taylor expansion of (log n) in n 2.665 * [taylor]: Taking taylor expansion of n in n 2.665 * [backup-simplify]: Simplify 0 into 0 2.665 * [backup-simplify]: Simplify 1 into 1 2.665 * [backup-simplify]: Simplify (log 1) into 0 2.665 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.665 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.665 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.665 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.666 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.666 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.667 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 2.667 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.667 * [backup-simplify]: Simplify 0 into 0 2.669 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.669 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.669 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 2.670 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.670 * [backup-simplify]: Simplify 0 into 0 2.672 * [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 2.673 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.673 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 2.674 * [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 2.674 * [backup-simplify]: Simplify 0 into 0 2.679 * [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 2.680 * [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 (log n)))))) into 0 2.682 * [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 2.682 * [backup-simplify]: Simplify 0 into 0 2.690 * [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 2.690 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.691 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 2.693 * [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 2.693 * [backup-simplify]: Simplify 0 into 0 2.710 * [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 2.711 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.713 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 2.715 * [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 2.715 * [backup-simplify]: Simplify 0 into 0 2.715 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.716 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 2.716 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 2.716 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.716 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.716 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.716 * [taylor]: Taking taylor expansion of 1/3 in n 2.716 * [backup-simplify]: Simplify 1/3 into 1/3 2.716 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.716 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.716 * [taylor]: Taking taylor expansion of n in n 2.716 * [backup-simplify]: Simplify 0 into 0 2.716 * [backup-simplify]: Simplify 1 into 1 2.716 * [backup-simplify]: Simplify (/ 1 1) into 1 2.716 * [backup-simplify]: Simplify (log 1) into 0 2.717 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.717 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.717 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.717 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.717 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.717 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.717 * [taylor]: Taking taylor expansion of 1/3 in n 2.717 * [backup-simplify]: Simplify 1/3 into 1/3 2.717 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.717 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.717 * [taylor]: Taking taylor expansion of n in n 2.717 * [backup-simplify]: Simplify 0 into 0 2.717 * [backup-simplify]: Simplify 1 into 1 2.717 * [backup-simplify]: Simplify (/ 1 1) into 1 2.717 * [backup-simplify]: Simplify (log 1) into 0 2.718 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.718 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.718 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.718 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 2.718 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.719 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.719 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.720 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 2.720 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.720 * [backup-simplify]: Simplify 0 into 0 2.720 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.722 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.722 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.723 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 2.723 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.723 * [backup-simplify]: Simplify 0 into 0 2.724 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.727 * [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 2.727 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.728 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 2.728 * [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 2.728 * [backup-simplify]: Simplify 0 into 0 2.729 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.734 * [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 2.734 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.735 * [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 into 0 2.737 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.745 * [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 2.745 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.746 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 2.748 * [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 2.748 * [backup-simplify]: Simplify 0 into 0 2.749 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.763 * [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 2.764 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.765 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 2.768 * [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 2.768 * [backup-simplify]: Simplify 0 into 0 2.768 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 2.768 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.768 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 2.768 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.768 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.768 * [taylor]: Taking taylor expansion of -1 in n 2.768 * [backup-simplify]: Simplify -1 into -1 2.769 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.769 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.769 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.769 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.769 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.769 * [taylor]: Taking taylor expansion of 1/3 in n 2.769 * [backup-simplify]: Simplify 1/3 into 1/3 2.769 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.769 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.769 * [taylor]: Taking taylor expansion of n in n 2.769 * [backup-simplify]: Simplify 0 into 0 2.769 * [backup-simplify]: Simplify 1 into 1 2.769 * [backup-simplify]: Simplify (/ 1 1) into 1 2.770 * [backup-simplify]: Simplify (log 1) into 0 2.770 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.770 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.770 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.770 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.770 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.770 * [taylor]: Taking taylor expansion of -1 in n 2.770 * [backup-simplify]: Simplify -1 into -1 2.770 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.771 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.771 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.771 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.771 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.771 * [taylor]: Taking taylor expansion of 1/3 in n 2.771 * [backup-simplify]: Simplify 1/3 into 1/3 2.771 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.771 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.771 * [taylor]: Taking taylor expansion of n in n 2.771 * [backup-simplify]: Simplify 0 into 0 2.771 * [backup-simplify]: Simplify 1 into 1 2.771 * [backup-simplify]: Simplify (/ 1 1) into 1 2.772 * [backup-simplify]: Simplify (log 1) into 0 2.772 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.772 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.772 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.772 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.776 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.776 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 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)) 2.778 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 2.778 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.779 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 2.779 * [backup-simplify]: Simplify 0 into 0 2.779 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.780 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.781 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.781 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 2.782 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.783 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.783 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 2.783 * [backup-simplify]: Simplify 0 into 0 2.784 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.786 * [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 2.787 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.787 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 2.788 * [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 2.789 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.790 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 2.790 * [backup-simplify]: Simplify 0 into 0 2.790 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.795 * [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 2.795 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.796 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 2.798 * [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 2.799 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.800 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 2.800 * [backup-simplify]: Simplify 0 into 0 2.800 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) 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 2.808 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.809 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 2.811 * [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 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.813 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 2.813 * [backup-simplify]: Simplify 0 into 0 2.814 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.827 * [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 2.828 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.829 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 2.832 * [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 2.833 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.835 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 2.835 * [backup-simplify]: Simplify 0 into 0 2.835 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 2.835 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1 1 2 2) 2.835 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 2.835 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 2.835 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.835 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.835 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.835 * [taylor]: Taking taylor expansion of 1/3 in n 2.835 * [backup-simplify]: Simplify 1/3 into 1/3 2.835 * [taylor]: Taking taylor expansion of (log n) in n 2.835 * [taylor]: Taking taylor expansion of n in n 2.835 * [backup-simplify]: Simplify 0 into 0 2.835 * [backup-simplify]: Simplify 1 into 1 2.836 * [backup-simplify]: Simplify (log 1) into 0 2.836 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.836 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.836 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.836 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.836 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.836 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.836 * [taylor]: Taking taylor expansion of 1/3 in n 2.836 * [backup-simplify]: Simplify 1/3 into 1/3 2.836 * [taylor]: Taking taylor expansion of (log n) in n 2.836 * [taylor]: Taking taylor expansion of n in n 2.836 * [backup-simplify]: Simplify 0 into 0 2.836 * [backup-simplify]: Simplify 1 into 1 2.836 * [backup-simplify]: Simplify (log 1) into 0 2.837 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.837 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 2.837 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 2.837 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.838 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.838 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.838 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 2.839 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.839 * [backup-simplify]: Simplify 0 into 0 2.840 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.840 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.841 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 2.841 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.841 * [backup-simplify]: Simplify 0 into 0 2.844 * [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 2.844 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.845 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 2.846 * [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 2.846 * [backup-simplify]: Simplify 0 into 0 2.851 * [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 2.851 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.855 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 2.857 * [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 2.857 * [backup-simplify]: Simplify 0 into 0 2.865 * [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 2.865 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.866 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 2.868 * [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 2.868 * [backup-simplify]: Simplify 0 into 0 2.882 * [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 2.882 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.884 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 2.886 * [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 2.886 * [backup-simplify]: Simplify 0 into 0 2.886 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 2.887 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 2.887 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 2.887 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.887 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.887 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.887 * [taylor]: Taking taylor expansion of 1/3 in n 2.887 * [backup-simplify]: Simplify 1/3 into 1/3 2.887 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.887 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.887 * [taylor]: Taking taylor expansion of n in n 2.887 * [backup-simplify]: Simplify 0 into 0 2.887 * [backup-simplify]: Simplify 1 into 1 2.887 * [backup-simplify]: Simplify (/ 1 1) into 1 2.887 * [backup-simplify]: Simplify (log 1) into 0 2.887 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.888 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.888 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.888 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.888 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.888 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.888 * [taylor]: Taking taylor expansion of 1/3 in n 2.888 * [backup-simplify]: Simplify 1/3 into 1/3 2.888 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.888 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.888 * [taylor]: Taking taylor expansion of n in n 2.888 * [backup-simplify]: Simplify 0 into 0 2.888 * [backup-simplify]: Simplify 1 into 1 2.888 * [backup-simplify]: Simplify (/ 1 1) into 1 2.888 * [backup-simplify]: Simplify (log 1) into 0 2.888 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.889 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.889 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.889 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 2.889 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.890 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.890 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.890 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 2.891 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.891 * [backup-simplify]: Simplify 0 into 0 2.891 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.893 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.893 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.894 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 2.894 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.894 * [backup-simplify]: Simplify 0 into 0 2.895 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.897 * [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 2.897 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.898 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 2.899 * [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 2.899 * [backup-simplify]: Simplify 0 into 0 2.900 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.904 * [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 2.905 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.906 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 2.907 * [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 2.907 * [backup-simplify]: Simplify 0 into 0 2.908 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.915 * [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 2.915 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.917 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 2.918 * [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 2.918 * [backup-simplify]: Simplify 0 into 0 2.919 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.936 * [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 2.937 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.938 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 2.941 * [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 2.941 * [backup-simplify]: Simplify 0 into 0 2.941 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 2.941 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.941 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 2.941 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.941 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.941 * [taylor]: Taking taylor expansion of -1 in n 2.941 * [backup-simplify]: Simplify -1 into -1 2.942 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.942 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.942 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.942 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.942 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.942 * [taylor]: Taking taylor expansion of 1/3 in n 2.942 * [backup-simplify]: Simplify 1/3 into 1/3 2.942 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.942 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.942 * [taylor]: Taking taylor expansion of n in n 2.942 * [backup-simplify]: Simplify 0 into 0 2.942 * [backup-simplify]: Simplify 1 into 1 2.942 * [backup-simplify]: Simplify (/ 1 1) into 1 2.943 * [backup-simplify]: Simplify (log 1) into 0 2.943 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.943 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.943 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.943 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.943 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.943 * [taylor]: Taking taylor expansion of -1 in n 2.943 * [backup-simplify]: Simplify -1 into -1 2.943 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 2.944 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 2.944 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.944 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.944 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.944 * [taylor]: Taking taylor expansion of 1/3 in n 2.944 * [backup-simplify]: Simplify 1/3 into 1/3 2.944 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.944 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.944 * [taylor]: Taking taylor expansion of n in n 2.944 * [backup-simplify]: Simplify 0 into 0 2.944 * [backup-simplify]: Simplify 1 into 1 2.944 * [backup-simplify]: Simplify (/ 1 1) into 1 2.944 * [backup-simplify]: Simplify (log 1) into 0 2.945 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.945 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 2.945 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 2.945 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.946 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 2.946 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.947 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.947 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.947 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 2.948 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.948 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 2.948 * [backup-simplify]: Simplify 0 into 0 2.949 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.950 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 2.951 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.951 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 2.952 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.953 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.954 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 2.954 * [backup-simplify]: Simplify 0 into 0 2.954 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.957 * [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 2.957 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.958 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 2.959 * [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 2.959 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.960 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 2.960 * [backup-simplify]: Simplify 0 into 0 2.961 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.965 * [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 2.966 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.967 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 2.968 * [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 2.969 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 2.970 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 2.970 * [backup-simplify]: Simplify 0 into 0 2.971 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.978 * [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 2.979 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 2.980 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 2.982 * [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 2.982 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 2.984 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 2.984 * [backup-simplify]: Simplify 0 into 0 2.984 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.998 * [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 2.998 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 3.000 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 3.003 * [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 3.004 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 3.005 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 3.005 * [backup-simplify]: Simplify 0 into 0 3.005 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 3.005 * * * [progress]: simplifying candidates 3.014 * [simplify]: Simplifying: (expm1 (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (+ (+ (+ (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)) (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (cbrt n)) (log1p (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)) (expm1 (cbrt n)) (log1p (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)) 3.014 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (log1p (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (* (+ (+ (+ (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)) (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (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)) (expm1 (cbrt h1)) (log1p (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)) (expm1 (cbrt h1)) (log1p (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)) 3.021 * * [simplify]: iteration 0 : 511 enodes (cost 996 ) 3.029 * * [simplify]: iteration 1 : 1634 enodes (cost 936 ) 3.057 * * [simplify]: iteration 2 : 5001 enodes (cost 729 ) 3.061 * * * [progress]: adding candidates to table 3.512 * * [progress]: iteration 4 / 4 3.512 * * * [progress]: picking best candidate 3.524 * * * * [pick]: Picked # 3.524 * * * [progress]: localizing error 3.540 * * * [progress]: generating rewritten candidates 3.540 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.566 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 3.592 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 3.611 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 3.650 * * * [progress]: generating series expansions 3.650 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.650 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 3.650 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.650 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.650 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.650 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.650 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.651 * [taylor]: Taking taylor expansion of 0.5 in k 3.651 * [backup-simplify]: Simplify 0.5 into 0.5 3.651 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.651 * [taylor]: Taking taylor expansion of 1.0 in k 3.651 * [backup-simplify]: Simplify 1.0 into 1.0 3.651 * [taylor]: Taking taylor expansion of k in k 3.651 * [backup-simplify]: Simplify 0 into 0 3.651 * [backup-simplify]: Simplify 1 into 1 3.651 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.651 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.651 * [taylor]: Taking taylor expansion of 2.0 in k 3.651 * [backup-simplify]: Simplify 2.0 into 2.0 3.651 * [taylor]: Taking taylor expansion of (* n PI) in k 3.651 * [taylor]: Taking taylor expansion of n in k 3.651 * [backup-simplify]: Simplify n into n 3.651 * [taylor]: Taking taylor expansion of PI in k 3.651 * [backup-simplify]: Simplify PI into PI 3.651 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.651 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.651 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.651 * [backup-simplify]: Simplify (- 0) into 0 3.651 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.652 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.652 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.652 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.652 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.652 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.652 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.652 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.652 * [taylor]: Taking taylor expansion of 0.5 in n 3.652 * [backup-simplify]: Simplify 0.5 into 0.5 3.652 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.652 * [taylor]: Taking taylor expansion of 1.0 in n 3.652 * [backup-simplify]: Simplify 1.0 into 1.0 3.652 * [taylor]: Taking taylor expansion of k in n 3.652 * [backup-simplify]: Simplify k into k 3.652 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.652 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.652 * [taylor]: Taking taylor expansion of 2.0 in n 3.652 * [backup-simplify]: Simplify 2.0 into 2.0 3.652 * [taylor]: Taking taylor expansion of (* n PI) in n 3.652 * [taylor]: Taking taylor expansion of n in n 3.652 * [backup-simplify]: Simplify 0 into 0 3.652 * [backup-simplify]: Simplify 1 into 1 3.652 * [taylor]: Taking taylor expansion of PI in n 3.652 * [backup-simplify]: Simplify PI into PI 3.653 * [backup-simplify]: Simplify (* 0 PI) into 0 3.653 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.654 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.655 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.655 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.655 * [backup-simplify]: Simplify (- k) into (- k) 3.655 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.655 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.656 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.657 * [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)))) 3.658 * [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))))) 3.658 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.658 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.658 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.658 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.658 * [taylor]: Taking taylor expansion of 0.5 in n 3.658 * [backup-simplify]: Simplify 0.5 into 0.5 3.658 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.658 * [taylor]: Taking taylor expansion of 1.0 in n 3.658 * [backup-simplify]: Simplify 1.0 into 1.0 3.658 * [taylor]: Taking taylor expansion of k in n 3.658 * [backup-simplify]: Simplify k into k 3.658 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.658 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.658 * [taylor]: Taking taylor expansion of 2.0 in n 3.658 * [backup-simplify]: Simplify 2.0 into 2.0 3.658 * [taylor]: Taking taylor expansion of (* n PI) in n 3.658 * [taylor]: Taking taylor expansion of n in n 3.658 * [backup-simplify]: Simplify 0 into 0 3.658 * [backup-simplify]: Simplify 1 into 1 3.658 * [taylor]: Taking taylor expansion of PI in n 3.658 * [backup-simplify]: Simplify PI into PI 3.658 * [backup-simplify]: Simplify (* 0 PI) into 0 3.659 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.659 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.660 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.661 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.661 * [backup-simplify]: Simplify (- k) into (- k) 3.661 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.661 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.662 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.663 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.663 * [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))))) 3.663 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.663 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.664 * [taylor]: Taking taylor expansion of 0.5 in k 3.664 * [backup-simplify]: Simplify 0.5 into 0.5 3.664 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.664 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.664 * [taylor]: Taking taylor expansion of 1.0 in k 3.664 * [backup-simplify]: Simplify 1.0 into 1.0 3.664 * [taylor]: Taking taylor expansion of k in k 3.664 * [backup-simplify]: Simplify 0 into 0 3.664 * [backup-simplify]: Simplify 1 into 1 3.664 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.664 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.664 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.664 * [taylor]: Taking taylor expansion of 2.0 in k 3.664 * [backup-simplify]: Simplify 2.0 into 2.0 3.664 * [taylor]: Taking taylor expansion of PI in k 3.664 * [backup-simplify]: Simplify PI into PI 3.664 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.665 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.665 * [taylor]: Taking taylor expansion of (log n) in k 3.665 * [taylor]: Taking taylor expansion of n in k 3.665 * [backup-simplify]: Simplify n into n 3.665 * [backup-simplify]: Simplify (log n) into (log n) 3.665 * [backup-simplify]: Simplify (- 0) into 0 3.665 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.666 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.667 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.667 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 3.668 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.669 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.669 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.670 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.671 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.671 * [backup-simplify]: Simplify (- 0) into 0 3.671 * [backup-simplify]: Simplify (+ 0 0) into 0 3.671 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.672 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.673 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.674 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.674 * [taylor]: Taking taylor expansion of 0 in k 3.674 * [backup-simplify]: Simplify 0 into 0 3.674 * [backup-simplify]: Simplify 0 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 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.676 * [backup-simplify]: Simplify (+ 0 0) into 0 3.683 * [backup-simplify]: Simplify (- 1) into -1 3.683 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.684 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.686 * [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)))) 3.688 * [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)))))) 3.689 * [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)))))) 3.690 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.691 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.692 * [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 3.692 * [backup-simplify]: Simplify (- 0) into 0 3.693 * [backup-simplify]: Simplify (+ 0 0) into 0 3.693 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.694 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.695 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.696 * [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 3.696 * [taylor]: Taking taylor expansion of 0 in k 3.696 * [backup-simplify]: Simplify 0 into 0 3.696 * [backup-simplify]: Simplify 0 into 0 3.696 * [backup-simplify]: Simplify 0 into 0 3.697 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.699 * [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 3.700 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.700 * [backup-simplify]: Simplify (+ 0 0) into 0 3.700 * [backup-simplify]: Simplify (- 0) into 0 3.700 * [backup-simplify]: Simplify (+ 0 0) into 0 3.701 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.703 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 3.705 * [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)))))) 3.708 * [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)))))) 3.714 * [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)))))) 3.715 * [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)))) 3.715 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.715 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.715 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.715 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.715 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.715 * [taylor]: Taking taylor expansion of 0.5 in k 3.715 * [backup-simplify]: Simplify 0.5 into 0.5 3.715 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.715 * [taylor]: Taking taylor expansion of 1.0 in k 3.715 * [backup-simplify]: Simplify 1.0 into 1.0 3.715 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.715 * [taylor]: Taking taylor expansion of k in k 3.715 * [backup-simplify]: Simplify 0 into 0 3.715 * [backup-simplify]: Simplify 1 into 1 3.715 * [backup-simplify]: Simplify (/ 1 1) into 1 3.715 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.715 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.715 * [taylor]: Taking taylor expansion of 2.0 in k 3.715 * [backup-simplify]: Simplify 2.0 into 2.0 3.715 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.715 * [taylor]: Taking taylor expansion of PI in k 3.715 * [backup-simplify]: Simplify PI into PI 3.715 * [taylor]: Taking taylor expansion of n in k 3.715 * [backup-simplify]: Simplify n into n 3.715 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.715 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.715 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.716 * [backup-simplify]: Simplify (- 1) into -1 3.716 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.716 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.716 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.716 * [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))))) 3.716 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.716 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.716 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.716 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.716 * [taylor]: Taking taylor expansion of 0.5 in n 3.717 * [backup-simplify]: Simplify 0.5 into 0.5 3.717 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.717 * [taylor]: Taking taylor expansion of 1.0 in n 3.717 * [backup-simplify]: Simplify 1.0 into 1.0 3.717 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.717 * [taylor]: Taking taylor expansion of k in n 3.717 * [backup-simplify]: Simplify k into k 3.717 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.717 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.717 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.717 * [taylor]: Taking taylor expansion of 2.0 in n 3.717 * [backup-simplify]: Simplify 2.0 into 2.0 3.717 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.717 * [taylor]: Taking taylor expansion of PI in n 3.717 * [backup-simplify]: Simplify PI into PI 3.717 * [taylor]: Taking taylor expansion of n in n 3.717 * [backup-simplify]: Simplify 0 into 0 3.717 * [backup-simplify]: Simplify 1 into 1 3.717 * [backup-simplify]: Simplify (/ PI 1) into PI 3.717 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.718 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.718 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.718 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.718 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.719 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.720 * [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)))) 3.720 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 3.720 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.720 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.720 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.720 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.720 * [taylor]: Taking taylor expansion of 0.5 in n 3.720 * [backup-simplify]: Simplify 0.5 into 0.5 3.721 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.721 * [taylor]: Taking taylor expansion of 1.0 in n 3.721 * [backup-simplify]: Simplify 1.0 into 1.0 3.721 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.721 * [taylor]: Taking taylor expansion of k in n 3.721 * [backup-simplify]: Simplify k into k 3.721 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.721 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.721 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.721 * [taylor]: Taking taylor expansion of 2.0 in n 3.721 * [backup-simplify]: Simplify 2.0 into 2.0 3.721 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.721 * [taylor]: Taking taylor expansion of PI in n 3.721 * [backup-simplify]: Simplify PI into PI 3.721 * [taylor]: Taking taylor expansion of n in n 3.721 * [backup-simplify]: Simplify 0 into 0 3.721 * [backup-simplify]: Simplify 1 into 1 3.721 * [backup-simplify]: Simplify (/ PI 1) into PI 3.721 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.722 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.722 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.722 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.722 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.723 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.724 * [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)))) 3.724 * [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))))) 3.725 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.725 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.725 * [taylor]: Taking taylor expansion of 0.5 in k 3.725 * [backup-simplify]: Simplify 0.5 into 0.5 3.725 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.725 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.725 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.725 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.725 * [taylor]: Taking taylor expansion of 2.0 in k 3.725 * [backup-simplify]: Simplify 2.0 into 2.0 3.725 * [taylor]: Taking taylor expansion of PI in k 3.725 * [backup-simplify]: Simplify PI into PI 3.725 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.726 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.726 * [taylor]: Taking taylor expansion of (log n) in k 3.726 * [taylor]: Taking taylor expansion of n in k 3.726 * [backup-simplify]: Simplify n into n 3.726 * [backup-simplify]: Simplify (log n) into (log n) 3.726 * [taylor]: Taking taylor expansion of (- 1.0 (/ 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 (/ 1 k) in k 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 3.727 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.727 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 3.727 * [backup-simplify]: Simplify (- 1) into -1 3.728 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.728 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 3.729 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 3.730 * [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))))) 3.730 * [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))))) 3.731 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.731 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.732 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.732 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.733 * [backup-simplify]: Simplify (- 0) into 0 3.733 * [backup-simplify]: Simplify (+ 0 0) into 0 3.733 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.734 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.735 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.736 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.736 * [taylor]: Taking taylor expansion of 0 in k 3.736 * [backup-simplify]: Simplify 0 into 0 3.736 * [backup-simplify]: Simplify 0 into 0 3.736 * [backup-simplify]: Simplify 0 into 0 3.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.737 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.739 * [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 3.739 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.739 * [backup-simplify]: Simplify (- 0) into 0 3.739 * [backup-simplify]: Simplify (+ 0 0) into 0 3.740 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 3.741 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.741 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 3.743 * [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 3.743 * [taylor]: Taking taylor expansion of 0 in k 3.743 * [backup-simplify]: Simplify 0 into 0 3.743 * [backup-simplify]: Simplify 0 into 0 3.743 * [backup-simplify]: Simplify 0 into 0 3.743 * [backup-simplify]: Simplify 0 into 0 3.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.747 * [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 3.747 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.747 * [backup-simplify]: Simplify (- 0) into 0 3.748 * [backup-simplify]: Simplify (+ 0 0) into 0 3.748 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 3.749 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.750 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 3.752 * [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 3.752 * [taylor]: Taking taylor expansion of 0 in k 3.752 * [backup-simplify]: Simplify 0 into 0 3.752 * [backup-simplify]: Simplify 0 into 0 3.753 * [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)))) 3.753 * [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))) 3.753 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.753 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.753 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.753 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.753 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.753 * [taylor]: Taking taylor expansion of 0.5 in k 3.753 * [backup-simplify]: Simplify 0.5 into 0.5 3.753 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.753 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.753 * [taylor]: Taking taylor expansion of k in k 3.753 * [backup-simplify]: Simplify 0 into 0 3.753 * [backup-simplify]: Simplify 1 into 1 3.753 * [backup-simplify]: Simplify (/ 1 1) into 1 3.754 * [taylor]: Taking taylor expansion of 1.0 in k 3.754 * [backup-simplify]: Simplify 1.0 into 1.0 3.754 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.754 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.754 * [taylor]: Taking taylor expansion of -2.0 in k 3.754 * [backup-simplify]: Simplify -2.0 into -2.0 3.754 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.754 * [taylor]: Taking taylor expansion of PI in k 3.754 * [backup-simplify]: Simplify PI into PI 3.754 * [taylor]: Taking taylor expansion of n in k 3.754 * [backup-simplify]: Simplify n into n 3.754 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.754 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.754 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.754 * [backup-simplify]: Simplify (+ 1 0) into 1 3.754 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.754 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.755 * [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)))))) 3.755 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.755 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.755 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.755 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.755 * [taylor]: Taking taylor expansion of 0.5 in n 3.755 * [backup-simplify]: Simplify 0.5 into 0.5 3.755 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.755 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.755 * [taylor]: Taking taylor expansion of k in n 3.755 * [backup-simplify]: Simplify k into k 3.755 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.755 * [taylor]: Taking taylor expansion of 1.0 in n 3.755 * [backup-simplify]: Simplify 1.0 into 1.0 3.755 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.755 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.755 * [taylor]: Taking taylor expansion of -2.0 in n 3.755 * [backup-simplify]: Simplify -2.0 into -2.0 3.755 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.755 * [taylor]: Taking taylor expansion of PI in n 3.755 * [backup-simplify]: Simplify PI into PI 3.755 * [taylor]: Taking taylor expansion of n in n 3.755 * [backup-simplify]: Simplify 0 into 0 3.755 * [backup-simplify]: Simplify 1 into 1 3.755 * [backup-simplify]: Simplify (/ PI 1) into PI 3.756 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.756 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.756 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.756 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.757 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.758 * [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)))) 3.759 * [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))))) 3.759 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.759 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.759 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.759 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.759 * [taylor]: Taking taylor expansion of 0.5 in n 3.759 * [backup-simplify]: Simplify 0.5 into 0.5 3.759 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.759 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.759 * [taylor]: Taking taylor expansion of k in n 3.759 * [backup-simplify]: Simplify k into k 3.759 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.759 * [taylor]: Taking taylor expansion of 1.0 in n 3.759 * [backup-simplify]: Simplify 1.0 into 1.0 3.759 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.759 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.759 * [taylor]: Taking taylor expansion of -2.0 in n 3.759 * [backup-simplify]: Simplify -2.0 into -2.0 3.759 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.759 * [taylor]: Taking taylor expansion of PI in n 3.759 * [backup-simplify]: Simplify PI into PI 3.759 * [taylor]: Taking taylor expansion of n in n 3.759 * [backup-simplify]: Simplify 0 into 0 3.759 * [backup-simplify]: Simplify 1 into 1 3.759 * [backup-simplify]: Simplify (/ PI 1) into PI 3.760 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.760 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.760 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.760 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.761 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.762 * [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)))) 3.763 * [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))))) 3.763 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 3.763 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 3.763 * [taylor]: Taking taylor expansion of 0.5 in k 3.763 * [backup-simplify]: Simplify 0.5 into 0.5 3.763 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 3.763 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.763 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.763 * [taylor]: Taking taylor expansion of k in k 3.763 * [backup-simplify]: Simplify 0 into 0 3.763 * [backup-simplify]: Simplify 1 into 1 3.763 * [backup-simplify]: Simplify (/ 1 1) into 1 3.763 * [taylor]: Taking taylor expansion of 1.0 in k 3.763 * [backup-simplify]: Simplify 1.0 into 1.0 3.763 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.763 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.763 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.763 * [taylor]: Taking taylor expansion of -2.0 in k 3.763 * [backup-simplify]: Simplify -2.0 into -2.0 3.763 * [taylor]: Taking taylor expansion of PI in k 3.763 * [backup-simplify]: Simplify PI into PI 3.764 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.764 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.764 * [taylor]: Taking taylor expansion of (log n) in k 3.764 * [taylor]: Taking taylor expansion of n in k 3.764 * [backup-simplify]: Simplify n into n 3.764 * [backup-simplify]: Simplify (log n) into (log n) 3.765 * [backup-simplify]: Simplify (+ 1 0) into 1 3.765 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.765 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 3.766 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 3.767 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 3.767 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 3.768 * [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))))) 3.768 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.769 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.770 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.770 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.770 * [backup-simplify]: Simplify (+ 0 0) into 0 3.770 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.771 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.772 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.778 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.778 * [taylor]: Taking taylor expansion of 0 in k 3.778 * [backup-simplify]: Simplify 0 into 0 3.778 * [backup-simplify]: Simplify 0 into 0 3.778 * [backup-simplify]: Simplify 0 into 0 3.779 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.779 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.781 * [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 3.781 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.781 * [backup-simplify]: Simplify (+ 0 0) into 0 3.782 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 3.783 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.784 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 3.785 * [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 3.785 * [taylor]: Taking taylor expansion of 0 in k 3.785 * [backup-simplify]: Simplify 0 into 0 3.785 * [backup-simplify]: Simplify 0 into 0 3.785 * [backup-simplify]: Simplify 0 into 0 3.785 * [backup-simplify]: Simplify 0 into 0 3.786 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.786 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.789 * [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 3.789 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.790 * [backup-simplify]: Simplify (+ 0 0) into 0 3.790 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 3.791 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.792 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 3.794 * [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 3.794 * [taylor]: Taking taylor expansion of 0 in k 3.794 * [backup-simplify]: Simplify 0 into 0 3.794 * [backup-simplify]: Simplify 0 into 0 3.794 * [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)))))) 3.795 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 3.795 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k))) 3.795 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.795 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.795 * [taylor]: Taking taylor expansion of 1.0 in k 3.795 * [backup-simplify]: Simplify 1.0 into 1.0 3.795 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.795 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.795 * [taylor]: Taking taylor expansion of k in k 3.795 * [backup-simplify]: Simplify 0 into 0 3.795 * [backup-simplify]: Simplify 1 into 1 3.795 * [backup-simplify]: Simplify (/ 1 1) into 1 3.795 * [backup-simplify]: Simplify (sqrt 0) into 0 3.796 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.796 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.796 * [taylor]: Taking taylor expansion of 1.0 in k 3.796 * [backup-simplify]: Simplify 1.0 into 1.0 3.796 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.796 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.796 * [taylor]: Taking taylor expansion of k in k 3.796 * [backup-simplify]: Simplify 0 into 0 3.796 * [backup-simplify]: Simplify 1 into 1 3.796 * [backup-simplify]: Simplify (/ 1 1) into 1 3.797 * [backup-simplify]: Simplify (sqrt 0) into 0 3.797 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.798 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.798 * [backup-simplify]: Simplify 0 into 0 3.799 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.799 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.799 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.801 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.802 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.802 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.803 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.805 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.806 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.806 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.807 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 3.807 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k)) 3.807 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.807 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.807 * [taylor]: Taking taylor expansion of 1.0 in k 3.807 * [backup-simplify]: Simplify 1.0 into 1.0 3.807 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.807 * [taylor]: Taking taylor expansion of k in k 3.807 * [backup-simplify]: Simplify 0 into 0 3.807 * [backup-simplify]: Simplify 1 into 1 3.807 * [backup-simplify]: Simplify (sqrt 0) into 0 3.808 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.808 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.808 * [taylor]: Taking taylor expansion of 1.0 in k 3.808 * [backup-simplify]: Simplify 1.0 into 1.0 3.808 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.808 * [taylor]: Taking taylor expansion of k in k 3.808 * [backup-simplify]: Simplify 0 into 0 3.808 * [backup-simplify]: Simplify 1 into 1 3.808 * [backup-simplify]: Simplify (sqrt 0) into 0 3.809 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.809 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.809 * [backup-simplify]: Simplify 0 into 0 3.810 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.810 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.812 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.813 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.814 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.816 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.817 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.817 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.818 * [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)))))))) 3.818 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k))) 3.818 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.818 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.818 * [taylor]: Taking taylor expansion of 1.0 in k 3.818 * [backup-simplify]: Simplify 1.0 into 1.0 3.818 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.818 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.818 * [taylor]: Taking taylor expansion of -1 in k 3.818 * [backup-simplify]: Simplify -1 into -1 3.818 * [taylor]: Taking taylor expansion of k in k 3.818 * [backup-simplify]: Simplify 0 into 0 3.818 * [backup-simplify]: Simplify 1 into 1 3.819 * [backup-simplify]: Simplify (/ -1 1) into -1 3.819 * [backup-simplify]: Simplify (sqrt 0) into 0 3.820 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.820 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.820 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.820 * [taylor]: Taking taylor expansion of 1.0 in k 3.820 * [backup-simplify]: Simplify 1.0 into 1.0 3.820 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.820 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.820 * [taylor]: Taking taylor expansion of -1 in k 3.820 * [backup-simplify]: Simplify -1 into -1 3.820 * [taylor]: Taking taylor expansion of k in k 3.820 * [backup-simplify]: Simplify 0 into 0 3.820 * [backup-simplify]: Simplify 1 into 1 3.820 * [backup-simplify]: Simplify (/ -1 1) into -1 3.821 * [backup-simplify]: Simplify (sqrt 0) into 0 3.821 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.822 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.822 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.822 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.824 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.826 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.826 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.826 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.828 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.831 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 3.831 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.832 * [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))))) 3.832 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 3.832 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.832 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.832 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.832 * [taylor]: Taking taylor expansion of 2.0 in n 3.832 * [backup-simplify]: Simplify 2.0 into 2.0 3.832 * [taylor]: Taking taylor expansion of (* n PI) in n 3.832 * [taylor]: Taking taylor expansion of n in n 3.832 * [backup-simplify]: Simplify 0 into 0 3.832 * [backup-simplify]: Simplify 1 into 1 3.832 * [taylor]: Taking taylor expansion of PI in n 3.832 * [backup-simplify]: Simplify PI into PI 3.832 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.832 * [taylor]: Taking taylor expansion of 2.0 in n 3.832 * [backup-simplify]: Simplify 2.0 into 2.0 3.832 * [taylor]: Taking taylor expansion of (* n PI) in n 3.833 * [taylor]: Taking taylor expansion of n in n 3.833 * [backup-simplify]: Simplify 0 into 0 3.833 * [backup-simplify]: Simplify 1 into 1 3.833 * [taylor]: Taking taylor expansion of PI in n 3.833 * [backup-simplify]: Simplify PI into PI 3.833 * [backup-simplify]: Simplify (* 0 PI) into 0 3.833 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.833 * [backup-simplify]: Simplify 0 into 0 3.834 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.835 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.836 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.836 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.837 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.837 * [backup-simplify]: Simplify 0 into 0 3.837 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.838 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.838 * [backup-simplify]: Simplify 0 into 0 3.839 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.839 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.839 * [backup-simplify]: Simplify 0 into 0 3.840 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.841 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 3.841 * [backup-simplify]: Simplify 0 into 0 3.842 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.843 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 3.843 * [backup-simplify]: Simplify 0 into 0 3.844 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 3.845 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 3.845 * [backup-simplify]: Simplify 0 into 0 3.845 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.845 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 3.845 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.845 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.845 * [taylor]: Taking taylor expansion of 2.0 in n 3.845 * [backup-simplify]: Simplify 2.0 into 2.0 3.845 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.845 * [taylor]: Taking taylor expansion of PI in n 3.845 * [backup-simplify]: Simplify PI into PI 3.845 * [taylor]: Taking taylor expansion of n in n 3.845 * [backup-simplify]: Simplify 0 into 0 3.845 * [backup-simplify]: Simplify 1 into 1 3.846 * [backup-simplify]: Simplify (/ PI 1) into PI 3.846 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.846 * [taylor]: Taking taylor expansion of 2.0 in n 3.846 * [backup-simplify]: Simplify 2.0 into 2.0 3.846 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.846 * [taylor]: Taking taylor expansion of PI in n 3.846 * [backup-simplify]: Simplify PI into PI 3.846 * [taylor]: Taking taylor expansion of n in n 3.846 * [backup-simplify]: Simplify 0 into 0 3.846 * [backup-simplify]: Simplify 1 into 1 3.846 * [backup-simplify]: Simplify (/ PI 1) into PI 3.847 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.847 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.847 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.848 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.848 * [backup-simplify]: Simplify 0 into 0 3.848 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.849 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.849 * [backup-simplify]: Simplify 0 into 0 3.849 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.850 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.850 * [backup-simplify]: Simplify 0 into 0 3.851 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.851 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.851 * [backup-simplify]: Simplify 0 into 0 3.852 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.853 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.853 * [backup-simplify]: Simplify 0 into 0 3.853 * [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 3.854 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.854 * [backup-simplify]: Simplify 0 into 0 3.854 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 3.855 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 3.855 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.855 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.855 * [taylor]: Taking taylor expansion of -2.0 in n 3.855 * [backup-simplify]: Simplify -2.0 into -2.0 3.855 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.855 * [taylor]: Taking taylor expansion of PI in n 3.855 * [backup-simplify]: Simplify PI into PI 3.855 * [taylor]: Taking taylor expansion of n in n 3.855 * [backup-simplify]: Simplify 0 into 0 3.855 * [backup-simplify]: Simplify 1 into 1 3.855 * [backup-simplify]: Simplify (/ PI 1) into PI 3.855 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.855 * [taylor]: Taking taylor expansion of -2.0 in n 3.855 * [backup-simplify]: Simplify -2.0 into -2.0 3.855 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.855 * [taylor]: Taking taylor expansion of PI in n 3.855 * [backup-simplify]: Simplify PI into PI 3.855 * [taylor]: Taking taylor expansion of n in n 3.855 * [backup-simplify]: Simplify 0 into 0 3.855 * [backup-simplify]: Simplify 1 into 1 3.856 * [backup-simplify]: Simplify (/ PI 1) into PI 3.856 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.856 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.857 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.857 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.857 * [backup-simplify]: Simplify 0 into 0 3.858 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.858 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.858 * [backup-simplify]: Simplify 0 into 0 3.859 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.860 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.860 * [backup-simplify]: Simplify 0 into 0 3.860 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.861 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.861 * [backup-simplify]: Simplify 0 into 0 3.861 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.862 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.862 * [backup-simplify]: Simplify 0 into 0 3.863 * [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 3.869 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.869 * [backup-simplify]: Simplify 0 into 0 3.870 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 3.870 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 3.870 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4)) 3.870 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 3.870 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 3.870 * [taylor]: Taking taylor expansion of 1.0 in k 3.870 * [backup-simplify]: Simplify 1.0 into 1.0 3.870 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 3.870 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 3.870 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 3.870 * [taylor]: Taking taylor expansion of 1/4 in k 3.870 * [backup-simplify]: Simplify 1/4 into 1/4 3.870 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.870 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.870 * [taylor]: Taking taylor expansion of k in k 3.870 * [backup-simplify]: Simplify 0 into 0 3.870 * [backup-simplify]: Simplify 1 into 1 3.870 * [backup-simplify]: Simplify (/ 1 1) into 1 3.871 * [backup-simplify]: Simplify (log 1) into 0 3.871 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.871 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 3.871 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 3.871 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 3.871 * [taylor]: Taking taylor expansion of 1.0 in k 3.871 * [backup-simplify]: Simplify 1.0 into 1.0 3.871 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 3.871 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 3.871 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 3.871 * [taylor]: Taking taylor expansion of 1/4 in k 3.871 * [backup-simplify]: Simplify 1/4 into 1/4 3.871 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.871 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.871 * [taylor]: Taking taylor expansion of k in k 3.871 * [backup-simplify]: Simplify 0 into 0 3.871 * [backup-simplify]: Simplify 1 into 1 3.872 * [backup-simplify]: Simplify (/ 1 1) into 1 3.872 * [backup-simplify]: Simplify (log 1) into 0 3.872 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.872 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 3.872 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 3.872 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 3.872 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 3.873 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.874 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.874 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.874 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 3.875 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 3.875 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0 3.875 * [backup-simplify]: Simplify 0 into 0 3.876 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.877 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 3.877 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.878 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 3.878 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.879 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0 3.879 * [backup-simplify]: Simplify 0 into 0 3.880 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.882 * [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 3.882 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.883 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 3.884 * [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 3.884 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0 3.884 * [backup-simplify]: Simplify 0 into 0 3.885 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.890 * [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 3.890 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.891 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 3.892 * [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 3.893 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0 3.893 * [backup-simplify]: Simplify 0 into 0 3.894 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.902 * [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 3.902 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.903 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 3.905 * [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 3.906 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0 3.906 * [backup-simplify]: Simplify 0 into 0 3.907 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.921 * [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 3.921 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 3.922 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 3.925 * [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 3.927 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0 3.927 * [backup-simplify]: Simplify 0 into 0 3.927 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 3.927 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4)) 3.927 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 3.927 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 3.927 * [taylor]: Taking taylor expansion of 1.0 in k 3.927 * [backup-simplify]: Simplify 1.0 into 1.0 3.927 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 3.927 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 3.928 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 3.928 * [taylor]: Taking taylor expansion of 1/4 in k 3.928 * [backup-simplify]: Simplify 1/4 into 1/4 3.928 * [taylor]: Taking taylor expansion of (log k) in k 3.928 * [taylor]: Taking taylor expansion of k in k 3.928 * [backup-simplify]: Simplify 0 into 0 3.928 * [backup-simplify]: Simplify 1 into 1 3.928 * [backup-simplify]: Simplify (log 1) into 0 3.928 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.928 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 3.928 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 3.928 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 3.928 * [taylor]: Taking taylor expansion of 1.0 in k 3.928 * [backup-simplify]: Simplify 1.0 into 1.0 3.928 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 3.928 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 3.928 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 3.928 * [taylor]: Taking taylor expansion of 1/4 in k 3.928 * [backup-simplify]: Simplify 1/4 into 1/4 3.928 * [taylor]: Taking taylor expansion of (log k) in k 3.928 * [taylor]: Taking taylor expansion of k in k 3.928 * [backup-simplify]: Simplify 0 into 0 3.928 * [backup-simplify]: Simplify 1 into 1 3.929 * [backup-simplify]: Simplify (log 1) into 0 3.929 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.929 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 3.929 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 3.929 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 3.929 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 3.930 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.930 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.931 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 3.931 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 3.932 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0 3.932 * [backup-simplify]: Simplify 0 into 0 3.933 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 3.933 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.934 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 3.935 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.935 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 3.935 * [backup-simplify]: Simplify 0 into 0 3.938 * [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 3.938 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.939 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 3.939 * [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 3.940 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 3.940 * [backup-simplify]: Simplify 0 into 0 3.945 * [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 3.945 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.952 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 3.953 * [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 3.954 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0 3.954 * [backup-simplify]: Simplify 0 into 0 3.962 * [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 3.962 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.964 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 3.965 * [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 3.967 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0 3.967 * [backup-simplify]: Simplify 0 into 0 3.981 * [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 3.981 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 3.982 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 3.985 * [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 3.986 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0 3.986 * [backup-simplify]: Simplify 0 into 0 3.987 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 3.987 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) 3.987 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 3.987 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 3.987 * [taylor]: Taking taylor expansion of 1.0 in k 3.987 * [backup-simplify]: Simplify 1.0 into 1.0 3.987 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 3.987 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 3.987 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.987 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.987 * [taylor]: Taking taylor expansion of -1 in k 3.987 * [backup-simplify]: Simplify -1 into -1 3.987 * [taylor]: Taking taylor expansion of k in k 3.987 * [backup-simplify]: Simplify 0 into 0 3.987 * [backup-simplify]: Simplify 1 into 1 3.987 * [backup-simplify]: Simplify (/ -1 1) into -1 3.987 * [backup-simplify]: Simplify (sqrt 0) into 0 3.988 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.989 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 3.989 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 3.989 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.991 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.992 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.993 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 3.993 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 3.993 * [taylor]: Taking taylor expansion of 1.0 in k 3.993 * [backup-simplify]: Simplify 1.0 into 1.0 3.993 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 3.993 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 3.993 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.993 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.993 * [taylor]: Taking taylor expansion of -1 in k 3.993 * [backup-simplify]: Simplify -1 into -1 3.993 * [taylor]: Taking taylor expansion of k in k 3.993 * [backup-simplify]: Simplify 0 into 0 3.993 * [backup-simplify]: Simplify 1 into 1 3.993 * [backup-simplify]: Simplify (/ -1 1) into -1 3.994 * [backup-simplify]: Simplify (sqrt 0) into 0 3.994 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.995 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 3.995 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 3.995 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.997 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.998 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.999 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 4.000 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 4.000 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 4.002 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 4.003 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 4.004 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.006 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.008 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.011 * [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))) 4.017 * [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)))))) 4.022 * [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)))))) 4.035 * [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))))))))) 4.035 * * * [progress]: simplifying candidates 4.043 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 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(sqrt h3)) (/ (cbrt h2) (cbrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (cbrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt (cbrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (cbrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (cbrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (cbrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt (cbrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ (sqrt h2) (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ h2 (cbrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (cbrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt (cbrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt (sqrt h3))))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ h2 (sqrt (sqrt h3)))) (/ (sqrt (sqrt h3)) (/ 1 (sqrt (sqrt h3)))) (* (sqrt (sqrt h3)) (sqrt (sqrt h3))) (expm1 (* (* h0 PI) h1)) (log1p (* (* h0 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) (expm1 (/ h2 (sqrt (sqrt h3)))) (log1p (/ h2 (sqrt (sqrt h3)))) (- (log h2) (log (sqrt (sqrt h3)))) (log (/ h2 (sqrt (sqrt h3)))) (exp (/ h2 (sqrt (sqrt h3)))) (/ (* (* h2 h2) h2) (* (* (sqrt (sqrt h3)) (sqrt (sqrt h3))) (sqrt (sqrt h3)))) (* (cbrt (/ h2 (sqrt (sqrt h3)))) (cbrt (/ h2 (sqrt (sqrt h3))))) (cbrt (/ h2 (sqrt (sqrt h3)))) (* (* (/ h2 (sqrt (sqrt h3))) (/ h2 (sqrt (sqrt h3)))) (/ h2 (sqrt (sqrt h3)))) (sqrt (/ h2 (sqrt (sqrt h3)))) (sqrt (/ h2 (sqrt (sqrt h3)))) (- h2) (- (sqrt (sqrt h3))) (/ (* (cbrt h2) (cbrt h2)) (* (cbrt (sqrt (sqrt h3))) (cbrt (sqrt (sqrt h3))))) (/ (cbrt h2) (cbrt (sqrt (sqrt h3)))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (* (cbrt (sqrt h3)) (cbrt (sqrt h3))))) (/ (cbrt h2) (sqrt (cbrt (sqrt h3)))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt (* (cbrt h3) (cbrt h3))))) (/ (cbrt h2) (sqrt (sqrt (cbrt h3)))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt (sqrt h3)))) (/ (cbrt h2) (sqrt (sqrt (sqrt h3)))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt 1))) (/ (cbrt h2) (sqrt (sqrt h3))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt (sqrt h3)))) (/ (cbrt h2) (sqrt (sqrt (sqrt h3)))) (/ (* (cbrt h2) (cbrt h2)) (sqrt 1)) (/ (cbrt h2) (sqrt (sqrt h3))) (/ (* (cbrt h2) (cbrt h2)) (sqrt (sqrt (sqrt h3)))) (/ (cbrt h2) (sqrt (sqrt (sqrt h3)))) (/ (* (cbrt h2) (cbrt h2)) 1) (/ (cbrt h2) (sqrt (sqrt h3))) (/ (sqrt h2) (* (cbrt (sqrt (sqrt h3))) (cbrt (sqrt (sqrt h3))))) (/ (sqrt h2) (cbrt (sqrt (sqrt h3)))) (/ (sqrt h2) (sqrt (* (cbrt (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))))))))) 4.063 * * [simplify]: iteration 0 : 1355 enodes (cost 5833 ) 4.085 * * [simplify]: iteration 1 : 5001 enodes (cost 5050 ) 4.106 * * * [progress]: adding candidates to table 4.864 * [progress]: [Phase 3 of 3] Extracting. 4.864 * * [regime]: Finding splitpoints for: (# # # # # # #) 4.866 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 4.866 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 4.900 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 4.933 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 4.966 * * * [regime]: Found split indices: #