11.660 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.079 * * * [progress]: [2/2] Setting up program. 0.082 * [progress]: [Phase 2 of 3] Improving. 0.082 * [simplify]: Simplifying using # : (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.084 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.086 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.087 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.090 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.096 * * [simplify]: iteration 4 : 1034 enodes (cost 8 ) 0.119 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.119 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.119 * * [progress]: iteration 1 / 4 0.119 * * * [progress]: picking best candidate 0.121 * * * * [pick]: Picked # 0.122 * * * [progress]: localizing error 0.134 * * * [progress]: generating rewritten candidates 0.134 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.144 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.150 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.153 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.179 * * * [progress]: generating series expansions 0.180 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.180 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.180 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.180 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.180 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.180 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.180 * [taylor]: Taking taylor expansion of 0.5 in k 0.181 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.181 * [taylor]: Taking taylor expansion of 1.0 in k 0.181 * [taylor]: Taking taylor expansion of k in k 0.181 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.181 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.181 * [taylor]: Taking taylor expansion of 2.0 in k 0.181 * [taylor]: Taking taylor expansion of (* n PI) in k 0.181 * [taylor]: Taking taylor expansion of n in k 0.181 * [taylor]: Taking taylor expansion of PI in k 0.182 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.182 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.182 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.182 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.182 * [taylor]: Taking taylor expansion of 0.5 in n 0.182 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.182 * [taylor]: Taking taylor expansion of 1.0 in n 0.182 * [taylor]: Taking taylor expansion of k in n 0.182 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.182 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.182 * [taylor]: Taking taylor expansion of 2.0 in n 0.182 * [taylor]: Taking taylor expansion of (* n PI) in n 0.182 * [taylor]: Taking taylor expansion of n in n 0.182 * [taylor]: Taking taylor expansion of PI in n 0.188 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.188 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.188 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.188 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.188 * [taylor]: Taking taylor expansion of 0.5 in n 0.188 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.188 * [taylor]: Taking taylor expansion of 1.0 in n 0.188 * [taylor]: Taking taylor expansion of k in n 0.188 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.188 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.188 * [taylor]: Taking taylor expansion of 2.0 in n 0.188 * [taylor]: Taking taylor expansion of (* n PI) in n 0.188 * [taylor]: Taking taylor expansion of n in n 0.188 * [taylor]: Taking taylor expansion of PI in n 0.193 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.193 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.193 * [taylor]: Taking taylor expansion of 0.5 in k 0.193 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.193 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.193 * [taylor]: Taking taylor expansion of 1.0 in k 0.193 * [taylor]: Taking taylor expansion of k in k 0.193 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.193 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.193 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.193 * [taylor]: Taking taylor expansion of 2.0 in k 0.193 * [taylor]: Taking taylor expansion of PI in k 0.194 * [taylor]: Taking taylor expansion of (log n) in k 0.194 * [taylor]: Taking taylor expansion of n in k 0.204 * [taylor]: Taking taylor expansion of 0 in k 0.220 * [taylor]: Taking taylor expansion of 0 in k 0.239 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.239 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.239 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.239 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.239 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.239 * [taylor]: Taking taylor expansion of 0.5 in k 0.239 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.239 * [taylor]: Taking taylor expansion of 1.0 in k 0.239 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.239 * [taylor]: Taking taylor expansion of k in k 0.240 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.240 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.240 * [taylor]: Taking taylor expansion of 2.0 in k 0.240 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.240 * [taylor]: Taking taylor expansion of PI in k 0.240 * [taylor]: Taking taylor expansion of n in k 0.241 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.241 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.241 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.241 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.241 * [taylor]: Taking taylor expansion of 0.5 in n 0.241 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.241 * [taylor]: Taking taylor expansion of 1.0 in n 0.241 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.241 * [taylor]: Taking taylor expansion of k in n 0.241 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.241 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.241 * [taylor]: Taking taylor expansion of 2.0 in n 0.241 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.241 * [taylor]: Taking taylor expansion of PI in n 0.241 * [taylor]: Taking taylor expansion of n in n 0.245 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.245 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.245 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.245 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.245 * [taylor]: Taking taylor expansion of 0.5 in n 0.245 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.245 * [taylor]: Taking taylor expansion of 1.0 in n 0.245 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.245 * [taylor]: Taking taylor expansion of k in n 0.245 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.245 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.245 * [taylor]: Taking taylor expansion of 2.0 in n 0.245 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.245 * [taylor]: Taking taylor expansion of PI in n 0.245 * [taylor]: Taking taylor expansion of n in n 0.255 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.255 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.255 * [taylor]: Taking taylor expansion of 0.5 in k 0.255 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.255 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.255 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.255 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.255 * [taylor]: Taking taylor expansion of 2.0 in k 0.255 * [taylor]: Taking taylor expansion of PI in k 0.256 * [taylor]: Taking taylor expansion of (log n) in k 0.256 * [taylor]: Taking taylor expansion of n in k 0.256 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.256 * [taylor]: Taking taylor expansion of 1.0 in k 0.256 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.256 * [taylor]: Taking taylor expansion of k in k 0.266 * [taylor]: Taking taylor expansion of 0 in k 0.273 * [taylor]: Taking taylor expansion of 0 in k 0.283 * [taylor]: Taking taylor expansion of 0 in k 0.284 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.284 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.284 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.284 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.284 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.284 * [taylor]: Taking taylor expansion of 0.5 in k 0.284 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.284 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.284 * [taylor]: Taking taylor expansion of k in k 0.285 * [taylor]: Taking taylor expansion of 1.0 in k 0.285 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.285 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.285 * [taylor]: Taking taylor expansion of -2.0 in k 0.285 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.285 * [taylor]: Taking taylor expansion of PI in k 0.285 * [taylor]: Taking taylor expansion of n in k 0.285 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.286 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.286 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.286 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.286 * [taylor]: Taking taylor expansion of 0.5 in n 0.286 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.286 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.286 * [taylor]: Taking taylor expansion of k in n 0.286 * [taylor]: Taking taylor expansion of 1.0 in n 0.286 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.286 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.286 * [taylor]: Taking taylor expansion of -2.0 in n 0.286 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.286 * [taylor]: Taking taylor expansion of PI in n 0.286 * [taylor]: Taking taylor expansion of n in n 0.289 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.290 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.290 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.290 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.290 * [taylor]: Taking taylor expansion of 0.5 in n 0.290 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.290 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.290 * [taylor]: Taking taylor expansion of k in n 0.290 * [taylor]: Taking taylor expansion of 1.0 in n 0.290 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.290 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.290 * [taylor]: Taking taylor expansion of -2.0 in n 0.290 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.290 * [taylor]: Taking taylor expansion of PI in n 0.290 * [taylor]: Taking taylor expansion of n in n 0.293 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.293 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.294 * [taylor]: Taking taylor expansion of 0.5 in k 0.294 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.294 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.294 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.294 * [taylor]: Taking taylor expansion of k in k 0.294 * [taylor]: Taking taylor expansion of 1.0 in k 0.294 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.294 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.294 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.294 * [taylor]: Taking taylor expansion of -2.0 in k 0.294 * [taylor]: Taking taylor expansion of PI in k 0.295 * [taylor]: Taking taylor expansion of (log n) in k 0.295 * [taylor]: Taking taylor expansion of n in k 0.304 * [taylor]: Taking taylor expansion of 0 in k 0.311 * [taylor]: Taking taylor expansion of 0 in k 0.320 * [taylor]: Taking taylor expansion of 0 in k 0.321 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.322 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.322 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.322 * [taylor]: Taking taylor expansion of 2.0 in n 0.322 * [taylor]: Taking taylor expansion of (* n PI) in n 0.322 * [taylor]: Taking taylor expansion of n in n 0.322 * [taylor]: Taking taylor expansion of PI in n 0.322 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.322 * [taylor]: Taking taylor expansion of 2.0 in n 0.322 * [taylor]: Taking taylor expansion of (* n PI) in n 0.322 * [taylor]: Taking taylor expansion of n in n 0.322 * [taylor]: Taking taylor expansion of PI in n 0.335 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.335 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.335 * [taylor]: Taking taylor expansion of 2.0 in n 0.335 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.336 * [taylor]: Taking taylor expansion of PI in n 0.336 * [taylor]: Taking taylor expansion of n in n 0.336 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.336 * [taylor]: Taking taylor expansion of 2.0 in n 0.336 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.336 * [taylor]: Taking taylor expansion of PI in n 0.336 * [taylor]: Taking taylor expansion of n in n 0.352 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.352 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.352 * [taylor]: Taking taylor expansion of -2.0 in n 0.352 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.352 * [taylor]: Taking taylor expansion of PI in n 0.352 * [taylor]: Taking taylor expansion of n in n 0.352 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.352 * [taylor]: Taking taylor expansion of -2.0 in n 0.352 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.352 * [taylor]: Taking taylor expansion of PI in n 0.352 * [taylor]: Taking taylor expansion of n in n 0.361 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.361 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.361 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.361 * [taylor]: Taking taylor expansion of 1.0 in k 0.361 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.361 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.361 * [taylor]: Taking taylor expansion of k in k 0.363 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.363 * [taylor]: Taking taylor expansion of 1.0 in k 0.363 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.363 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.363 * [taylor]: Taking taylor expansion of k in k 0.374 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.374 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.374 * [taylor]: Taking taylor expansion of 1.0 in k 0.374 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.374 * [taylor]: Taking taylor expansion of k in k 0.375 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.375 * [taylor]: Taking taylor expansion of 1.0 in k 0.375 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.375 * [taylor]: Taking taylor expansion of k in k 0.386 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.386 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.386 * [taylor]: Taking taylor expansion of 1.0 in k 0.386 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.386 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.386 * [taylor]: Taking taylor expansion of -1 in k 0.386 * [taylor]: Taking taylor expansion of k in k 0.388 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.388 * [taylor]: Taking taylor expansion of 1.0 in k 0.388 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.388 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.388 * [taylor]: Taking taylor expansion of -1 in k 0.388 * [taylor]: Taking taylor expansion of k in k 0.400 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.400 * [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 0.400 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.400 * [taylor]: Taking taylor expansion of 1.0 in n 0.400 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.400 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.400 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.400 * [taylor]: Taking taylor expansion of k in n 0.401 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.401 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.401 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.401 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.401 * [taylor]: Taking taylor expansion of 0.5 in n 0.401 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.401 * [taylor]: Taking taylor expansion of 1.0 in n 0.401 * [taylor]: Taking taylor expansion of k in n 0.401 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.401 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.401 * [taylor]: Taking taylor expansion of 2.0 in n 0.401 * [taylor]: Taking taylor expansion of (* n PI) in n 0.401 * [taylor]: Taking taylor expansion of n in n 0.401 * [taylor]: Taking taylor expansion of PI in n 0.406 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.406 * [taylor]: Taking taylor expansion of 1.0 in k 0.406 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.406 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.406 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.406 * [taylor]: Taking taylor expansion of k in k 0.408 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.408 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.408 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.408 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.408 * [taylor]: Taking taylor expansion of 0.5 in k 0.408 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.408 * [taylor]: Taking taylor expansion of 1.0 in k 0.408 * [taylor]: Taking taylor expansion of k in k 0.408 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.408 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.408 * [taylor]: Taking taylor expansion of 2.0 in k 0.408 * [taylor]: Taking taylor expansion of (* n PI) in k 0.408 * [taylor]: Taking taylor expansion of n in k 0.408 * [taylor]: Taking taylor expansion of PI in k 0.409 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.409 * [taylor]: Taking taylor expansion of 1.0 in k 0.409 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.409 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.409 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.409 * [taylor]: Taking taylor expansion of k in k 0.410 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.410 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.410 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.410 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.410 * [taylor]: Taking taylor expansion of 0.5 in k 0.410 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.410 * [taylor]: Taking taylor expansion of 1.0 in k 0.410 * [taylor]: Taking taylor expansion of k in k 0.410 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.410 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.410 * [taylor]: Taking taylor expansion of 2.0 in k 0.410 * [taylor]: Taking taylor expansion of (* n PI) in k 0.410 * [taylor]: Taking taylor expansion of n in k 0.410 * [taylor]: Taking taylor expansion of PI in k 0.412 * [taylor]: Taking taylor expansion of 0 in n 0.417 * [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 0.417 * [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 0.417 * [taylor]: Taking taylor expansion of +nan.0 in n 0.417 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.417 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.417 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.417 * [taylor]: Taking taylor expansion of 0.5 in n 0.417 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.417 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.417 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.417 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.417 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.417 * [taylor]: Taking taylor expansion of 1.0 in n 0.417 * [taylor]: Taking taylor expansion of (log PI) in n 0.417 * [taylor]: Taking taylor expansion of PI in n 0.419 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.419 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.419 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.419 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.419 * [taylor]: Taking taylor expansion of 1.0 in n 0.419 * [taylor]: Taking taylor expansion of (log n) in n 0.419 * [taylor]: Taking taylor expansion of n in n 0.420 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.420 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.420 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.420 * [taylor]: Taking taylor expansion of 1.0 in n 0.420 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.420 * [taylor]: Taking taylor expansion of 2.0 in n 0.446 * [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 0.447 * [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 0.447 * [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 0.447 * [taylor]: Taking taylor expansion of +nan.0 in n 0.447 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.447 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.447 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.447 * [taylor]: Taking taylor expansion of 0.5 in n 0.447 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.447 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.447 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.447 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.447 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.447 * [taylor]: Taking taylor expansion of 1.0 in n 0.447 * [taylor]: Taking taylor expansion of (log PI) in n 0.447 * [taylor]: Taking taylor expansion of PI in n 0.449 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.449 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.449 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.449 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.449 * [taylor]: Taking taylor expansion of 1.0 in n 0.449 * [taylor]: Taking taylor expansion of (log n) in n 0.449 * [taylor]: Taking taylor expansion of n in n 0.449 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.449 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.450 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.450 * [taylor]: Taking taylor expansion of 1.0 in n 0.450 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.450 * [taylor]: Taking taylor expansion of 2.0 in n 0.455 * [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 0.455 * [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 0.455 * [taylor]: Taking taylor expansion of +nan.0 in n 0.455 * [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 0.455 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.455 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.455 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.455 * [taylor]: Taking taylor expansion of 0.5 in n 0.455 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.455 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.455 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.455 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.455 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.455 * [taylor]: Taking taylor expansion of 1.0 in n 0.455 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.455 * [taylor]: Taking taylor expansion of 2.0 in n 0.457 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.457 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.457 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.457 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.457 * [taylor]: Taking taylor expansion of 1.0 in n 0.457 * [taylor]: Taking taylor expansion of (log PI) in n 0.457 * [taylor]: Taking taylor expansion of PI in n 0.459 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.459 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.459 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.459 * [taylor]: Taking taylor expansion of 1.0 in n 0.459 * [taylor]: Taking taylor expansion of (log n) in n 0.459 * [taylor]: Taking taylor expansion of n in n 0.463 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.464 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.464 * [taylor]: Taking taylor expansion of 2.0 in n 0.464 * [taylor]: Taking taylor expansion of (* n PI) in n 0.464 * [taylor]: Taking taylor expansion of n in n 0.464 * [taylor]: Taking taylor expansion of PI in n 0.514 * [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 0.514 * [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 0.514 * [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 0.514 * [taylor]: Taking taylor expansion of +nan.0 in n 0.514 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.514 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.514 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.514 * [taylor]: Taking taylor expansion of 0.5 in n 0.514 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.515 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.515 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.515 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.515 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.515 * [taylor]: Taking taylor expansion of 1.0 in n 0.515 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.515 * [taylor]: Taking taylor expansion of 2.0 in n 0.516 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.516 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.516 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.516 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.516 * [taylor]: Taking taylor expansion of 1.0 in n 0.517 * [taylor]: Taking taylor expansion of (log n) in n 0.517 * [taylor]: Taking taylor expansion of n in n 0.517 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.517 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.517 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.517 * [taylor]: Taking taylor expansion of 1.0 in n 0.517 * [taylor]: Taking taylor expansion of (log PI) in n 0.517 * [taylor]: Taking taylor expansion of PI in n 0.528 * [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 0.528 * [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 0.528 * [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 0.528 * [taylor]: Taking taylor expansion of +nan.0 in n 0.528 * [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 0.528 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.528 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.528 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.528 * [taylor]: Taking taylor expansion of 0.5 in n 0.528 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.528 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.529 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.529 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.529 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.529 * [taylor]: Taking taylor expansion of 1.0 in n 0.529 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.529 * [taylor]: Taking taylor expansion of 2.0 in n 0.530 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.530 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.530 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.530 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.530 * [taylor]: Taking taylor expansion of 1.0 in n 0.530 * [taylor]: Taking taylor expansion of (log PI) in n 0.530 * [taylor]: Taking taylor expansion of PI in n 0.532 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.532 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.532 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.532 * [taylor]: Taking taylor expansion of 1.0 in n 0.532 * [taylor]: Taking taylor expansion of (log n) in n 0.532 * [taylor]: Taking taylor expansion of n in n 0.537 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.537 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.537 * [taylor]: Taking taylor expansion of 2.0 in n 0.537 * [taylor]: Taking taylor expansion of (* n PI) in n 0.537 * [taylor]: Taking taylor expansion of n in n 0.537 * [taylor]: Taking taylor expansion of PI in n 0.540 * [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 0.540 * [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 0.540 * [taylor]: Taking taylor expansion of +nan.0 in n 0.540 * [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 0.540 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.540 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.540 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.540 * [taylor]: Taking taylor expansion of 0.5 in n 0.540 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.540 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.540 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.540 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.540 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.540 * [taylor]: Taking taylor expansion of 1.0 in n 0.540 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.540 * [taylor]: Taking taylor expansion of 2.0 in n 0.542 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.542 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.543 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.543 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.543 * [taylor]: Taking taylor expansion of 1.0 in n 0.543 * [taylor]: Taking taylor expansion of (log PI) in n 0.543 * [taylor]: Taking taylor expansion of PI in n 0.544 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.544 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.545 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.545 * [taylor]: Taking taylor expansion of 1.0 in n 0.545 * [taylor]: Taking taylor expansion of (log n) in n 0.545 * [taylor]: Taking taylor expansion of n in n 0.549 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.549 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.549 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.549 * [taylor]: Taking taylor expansion of 2.0 in n 0.549 * [taylor]: Taking taylor expansion of (* n PI) in n 0.549 * [taylor]: Taking taylor expansion of n in n 0.549 * [taylor]: Taking taylor expansion of PI in n 0.628 * [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 0.628 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.629 * [taylor]: Taking taylor expansion of 1.0 in n 0.629 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.629 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.629 * [taylor]: Taking taylor expansion of k in n 0.629 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.629 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.629 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.629 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.629 * [taylor]: Taking taylor expansion of 0.5 in n 0.629 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.629 * [taylor]: Taking taylor expansion of 1.0 in n 0.629 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.629 * [taylor]: Taking taylor expansion of k in n 0.629 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.629 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.629 * [taylor]: Taking taylor expansion of 2.0 in n 0.629 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.629 * [taylor]: Taking taylor expansion of PI in n 0.629 * [taylor]: Taking taylor expansion of n in n 0.633 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.633 * [taylor]: Taking taylor expansion of 1.0 in k 0.633 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.633 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.633 * [taylor]: Taking taylor expansion of k in k 0.634 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.634 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.634 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.634 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.634 * [taylor]: Taking taylor expansion of 0.5 in k 0.634 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.634 * [taylor]: Taking taylor expansion of 1.0 in k 0.634 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.634 * [taylor]: Taking taylor expansion of k in k 0.635 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.635 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.635 * [taylor]: Taking taylor expansion of 2.0 in k 0.635 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.635 * [taylor]: Taking taylor expansion of PI in k 0.635 * [taylor]: Taking taylor expansion of n in k 0.636 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.636 * [taylor]: Taking taylor expansion of 1.0 in k 0.636 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.636 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.636 * [taylor]: Taking taylor expansion of k in k 0.637 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.637 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.637 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.637 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.637 * [taylor]: Taking taylor expansion of 0.5 in k 0.637 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.637 * [taylor]: Taking taylor expansion of 1.0 in k 0.637 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.637 * [taylor]: Taking taylor expansion of k in k 0.637 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.637 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.637 * [taylor]: Taking taylor expansion of 2.0 in k 0.637 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.637 * [taylor]: Taking taylor expansion of PI in k 0.637 * [taylor]: Taking taylor expansion of n in k 0.639 * [taylor]: Taking taylor expansion of 0 in n 0.640 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.640 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.640 * [taylor]: Taking taylor expansion of +nan.0 in n 0.640 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.640 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.640 * [taylor]: Taking taylor expansion of 0.5 in n 0.640 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.640 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.640 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.640 * [taylor]: Taking taylor expansion of 2.0 in n 0.640 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.640 * [taylor]: Taking taylor expansion of PI in n 0.640 * [taylor]: Taking taylor expansion of n in n 0.641 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.641 * [taylor]: Taking taylor expansion of 1.0 in n 0.641 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.641 * [taylor]: Taking taylor expansion of k in n 0.650 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.650 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.650 * [taylor]: Taking taylor expansion of +nan.0 in n 0.650 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.650 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.650 * [taylor]: Taking taylor expansion of 0.5 in n 0.650 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.650 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.650 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.650 * [taylor]: Taking taylor expansion of 2.0 in n 0.650 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.650 * [taylor]: Taking taylor expansion of PI in n 0.650 * [taylor]: Taking taylor expansion of n in n 0.652 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.652 * [taylor]: Taking taylor expansion of 1.0 in n 0.652 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.652 * [taylor]: Taking taylor expansion of k in n 0.668 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.668 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.668 * [taylor]: Taking taylor expansion of +nan.0 in n 0.668 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.668 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.668 * [taylor]: Taking taylor expansion of 0.5 in n 0.668 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.669 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.669 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.669 * [taylor]: Taking taylor expansion of 2.0 in n 0.669 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.669 * [taylor]: Taking taylor expansion of PI in n 0.669 * [taylor]: Taking taylor expansion of n in n 0.670 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.670 * [taylor]: Taking taylor expansion of 1.0 in n 0.670 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.670 * [taylor]: Taking taylor expansion of k in n 0.679 * [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 0.679 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.679 * [taylor]: Taking taylor expansion of 1.0 in n 0.679 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.679 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.679 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.679 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.679 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.679 * [taylor]: Taking taylor expansion of 0.5 in n 0.679 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.679 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.679 * [taylor]: Taking taylor expansion of k in n 0.679 * [taylor]: Taking taylor expansion of 1.0 in n 0.679 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.679 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.679 * [taylor]: Taking taylor expansion of -2.0 in n 0.679 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.679 * [taylor]: Taking taylor expansion of PI in n 0.679 * [taylor]: Taking taylor expansion of n in n 0.683 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.683 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.683 * [taylor]: Taking taylor expansion of -1 in n 0.683 * [taylor]: Taking taylor expansion of k in n 0.684 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.684 * [taylor]: Taking taylor expansion of 1.0 in k 0.684 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.684 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.684 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.684 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.684 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.684 * [taylor]: Taking taylor expansion of 0.5 in k 0.684 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.684 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.684 * [taylor]: Taking taylor expansion of k in k 0.684 * [taylor]: Taking taylor expansion of 1.0 in k 0.684 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.684 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.684 * [taylor]: Taking taylor expansion of -2.0 in k 0.684 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.684 * [taylor]: Taking taylor expansion of PI in k 0.684 * [taylor]: Taking taylor expansion of n in k 0.685 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.685 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.685 * [taylor]: Taking taylor expansion of -1 in k 0.685 * [taylor]: Taking taylor expansion of k in k 0.687 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.687 * [taylor]: Taking taylor expansion of 1.0 in k 0.687 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.687 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.687 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.687 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.687 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.687 * [taylor]: Taking taylor expansion of 0.5 in k 0.687 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.687 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.687 * [taylor]: Taking taylor expansion of k in k 0.687 * [taylor]: Taking taylor expansion of 1.0 in k 0.687 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.687 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.687 * [taylor]: Taking taylor expansion of -2.0 in k 0.687 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.687 * [taylor]: Taking taylor expansion of PI in k 0.687 * [taylor]: Taking taylor expansion of n in k 0.688 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.688 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.688 * [taylor]: Taking taylor expansion of -1 in k 0.688 * [taylor]: Taking taylor expansion of k in k 0.690 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.690 * [taylor]: Taking taylor expansion of +nan.0 in n 0.690 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.690 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.690 * [taylor]: Taking taylor expansion of 0.5 in n 0.690 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.690 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.690 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.690 * [taylor]: Taking taylor expansion of k in n 0.690 * [taylor]: Taking taylor expansion of 1.0 in n 0.690 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.690 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.690 * [taylor]: Taking taylor expansion of -2.0 in n 0.690 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.690 * [taylor]: Taking taylor expansion of PI in n 0.690 * [taylor]: Taking taylor expansion of n in n 0.700 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.700 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.700 * [taylor]: Taking taylor expansion of +nan.0 in n 0.700 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.700 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.700 * [taylor]: Taking taylor expansion of 0.5 in n 0.700 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.700 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.700 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.700 * [taylor]: Taking taylor expansion of k in n 0.700 * [taylor]: Taking taylor expansion of 1.0 in n 0.700 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.700 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.700 * [taylor]: Taking taylor expansion of -2.0 in n 0.700 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.700 * [taylor]: Taking taylor expansion of PI in n 0.700 * [taylor]: Taking taylor expansion of n in n 0.723 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.723 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.723 * [taylor]: Taking taylor expansion of +nan.0 in n 0.723 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.723 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.723 * [taylor]: Taking taylor expansion of 0.5 in n 0.724 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.724 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.724 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.724 * [taylor]: Taking taylor expansion of k in n 0.724 * [taylor]: Taking taylor expansion of 1.0 in n 0.724 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.724 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.724 * [taylor]: Taking taylor expansion of -2.0 in n 0.724 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.724 * [taylor]: Taking taylor expansion of PI in n 0.724 * [taylor]: Taking taylor expansion of n in n 0.733 * * * [progress]: simplifying candidates 0.737 * [simplify]: Simplifying using # : (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (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) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 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))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 0.747 * * [simplify]: iteration 0 : 950 enodes (cost 1461 ) 0.764 * * [simplify]: iteration 1 : 3924 enodes (cost 1358 ) 0.826 * * [simplify]: iteration 2 : 5002 enodes (cost 1344 ) 0.832 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) 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)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 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))) (* (* 2.0 PI) n) (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))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (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 (* (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 1/2) (pow (* (* 2.0 PI) n) 1/2) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (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) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (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)) (/ (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)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (* (fabs (cbrt k)) 1)) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (* (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)))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (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) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 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))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 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 (exp 0.5) (log (* (* 2.0 PI) n))) (pow (log (* 2.0 PI)) 2)) (* (pow (log n) 2) (pow (exp 0.5) (log (* (* 2.0 PI) n)))))) (pow (* (* 2.0 PI) n) 0.5)) (* (* (* (* (log n) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log (* 2.0 PI))) (pow k 2)) 0.25)) (* (* (* k (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log n)) 0.5)) (* (* (* k (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) 0.5)) (pow (* (* 2.0 PI) n) (* 0.5 (- 1.0 k))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (- (* +nan.0 k)) (- (* +nan.0 (pow k 2)) +nan.0)) (+ (* +nan.0 (- (/ 1 k) (/ 1 (pow k 3)))) (/ (- +nan.0) (pow k 2))) (+ (- (* +nan.0 (/ 1 k)) +nan.0) (/ (- +nan.0) (pow k 2))) (+ (- (* +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)))) k) (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))))) (+ (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)))) 0.833 * * * [progress]: adding candidates to table 1.234 * * [progress]: iteration 2 / 4 1.234 * * * [progress]: picking best candidate 1.260 * * * * [pick]: Picked # 1.261 * * * [progress]: localizing error 1.275 * * * [progress]: generating rewritten candidates 1.275 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.285 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 1.301 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 1.307 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 1.345 * * * [progress]: generating series expansions 1.345 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.346 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.346 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.346 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.346 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.346 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.346 * [taylor]: Taking taylor expansion of 0.5 in k 1.346 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.346 * [taylor]: Taking taylor expansion of 1.0 in k 1.346 * [taylor]: Taking taylor expansion of k in k 1.346 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.346 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.346 * [taylor]: Taking taylor expansion of 2.0 in k 1.346 * [taylor]: Taking taylor expansion of (* n PI) in k 1.346 * [taylor]: Taking taylor expansion of n in k 1.346 * [taylor]: Taking taylor expansion of PI in k 1.347 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.347 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.347 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.347 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.347 * [taylor]: Taking taylor expansion of 0.5 in n 1.347 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.347 * [taylor]: Taking taylor expansion of 1.0 in n 1.347 * [taylor]: Taking taylor expansion of k in n 1.347 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.347 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.347 * [taylor]: Taking taylor expansion of 2.0 in n 1.347 * [taylor]: Taking taylor expansion of (* n PI) in n 1.347 * [taylor]: Taking taylor expansion of n in n 1.347 * [taylor]: Taking taylor expansion of PI in n 1.353 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.353 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.353 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.353 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.353 * [taylor]: Taking taylor expansion of 0.5 in n 1.353 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.353 * [taylor]: Taking taylor expansion of 1.0 in n 1.353 * [taylor]: Taking taylor expansion of k in n 1.353 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.353 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.353 * [taylor]: Taking taylor expansion of 2.0 in n 1.353 * [taylor]: Taking taylor expansion of (* n PI) in n 1.353 * [taylor]: Taking taylor expansion of n in n 1.353 * [taylor]: Taking taylor expansion of PI in n 1.359 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.359 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.359 * [taylor]: Taking taylor expansion of 0.5 in k 1.359 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.359 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.359 * [taylor]: Taking taylor expansion of 1.0 in k 1.359 * [taylor]: Taking taylor expansion of k in k 1.359 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.359 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.359 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.359 * [taylor]: Taking taylor expansion of 2.0 in k 1.359 * [taylor]: Taking taylor expansion of PI in k 1.360 * [taylor]: Taking taylor expansion of (log n) in k 1.360 * [taylor]: Taking taylor expansion of n in k 1.369 * [taylor]: Taking taylor expansion of 0 in k 1.385 * [taylor]: Taking taylor expansion of 0 in k 1.411 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.411 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.411 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.411 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.411 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.411 * [taylor]: Taking taylor expansion of 0.5 in k 1.411 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.411 * [taylor]: Taking taylor expansion of 1.0 in k 1.411 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.412 * [taylor]: Taking taylor expansion of k in k 1.412 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.412 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.412 * [taylor]: Taking taylor expansion of 2.0 in k 1.412 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.412 * [taylor]: Taking taylor expansion of PI in k 1.412 * [taylor]: Taking taylor expansion of n in k 1.413 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.413 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.413 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.413 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.413 * [taylor]: Taking taylor expansion of 0.5 in n 1.413 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.413 * [taylor]: Taking taylor expansion of 1.0 in n 1.413 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.413 * [taylor]: Taking taylor expansion of k in n 1.413 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.413 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.413 * [taylor]: Taking taylor expansion of 2.0 in n 1.413 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.413 * [taylor]: Taking taylor expansion of PI in n 1.413 * [taylor]: Taking taylor expansion of n in n 1.417 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.417 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.417 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.417 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.417 * [taylor]: Taking taylor expansion of 0.5 in n 1.417 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.417 * [taylor]: Taking taylor expansion of 1.0 in n 1.417 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.417 * [taylor]: Taking taylor expansion of k in n 1.417 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.417 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.417 * [taylor]: Taking taylor expansion of 2.0 in n 1.417 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.417 * [taylor]: Taking taylor expansion of PI in n 1.417 * [taylor]: Taking taylor expansion of n in n 1.421 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.421 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.421 * [taylor]: Taking taylor expansion of 0.5 in k 1.421 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.421 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.421 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.421 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.421 * [taylor]: Taking taylor expansion of 2.0 in k 1.421 * [taylor]: Taking taylor expansion of PI in k 1.422 * [taylor]: Taking taylor expansion of (log n) in k 1.422 * [taylor]: Taking taylor expansion of n in k 1.422 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.422 * [taylor]: Taking taylor expansion of 1.0 in k 1.422 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.422 * [taylor]: Taking taylor expansion of k in k 1.432 * [taylor]: Taking taylor expansion of 0 in k 1.440 * [taylor]: Taking taylor expansion of 0 in k 1.449 * [taylor]: Taking taylor expansion of 0 in k 1.450 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.450 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.450 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.450 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.450 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.450 * [taylor]: Taking taylor expansion of 0.5 in k 1.450 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.450 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.450 * [taylor]: Taking taylor expansion of k in k 1.451 * [taylor]: Taking taylor expansion of 1.0 in k 1.451 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.451 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.451 * [taylor]: Taking taylor expansion of -2.0 in k 1.451 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.451 * [taylor]: Taking taylor expansion of PI in k 1.451 * [taylor]: Taking taylor expansion of n in k 1.451 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.452 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.452 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.452 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.452 * [taylor]: Taking taylor expansion of 0.5 in n 1.452 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.452 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.452 * [taylor]: Taking taylor expansion of k in n 1.452 * [taylor]: Taking taylor expansion of 1.0 in n 1.452 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.452 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.452 * [taylor]: Taking taylor expansion of -2.0 in n 1.452 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.452 * [taylor]: Taking taylor expansion of PI in n 1.452 * [taylor]: Taking taylor expansion of n in n 1.455 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.455 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.455 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.455 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.456 * [taylor]: Taking taylor expansion of 0.5 in n 1.456 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.456 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.456 * [taylor]: Taking taylor expansion of k in n 1.456 * [taylor]: Taking taylor expansion of 1.0 in n 1.456 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.456 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.456 * [taylor]: Taking taylor expansion of -2.0 in n 1.456 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.456 * [taylor]: Taking taylor expansion of PI in n 1.456 * [taylor]: Taking taylor expansion of n in n 1.459 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.459 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.460 * [taylor]: Taking taylor expansion of 0.5 in k 1.460 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.460 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.460 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.460 * [taylor]: Taking taylor expansion of k in k 1.460 * [taylor]: Taking taylor expansion of 1.0 in k 1.460 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.460 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.460 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.460 * [taylor]: Taking taylor expansion of -2.0 in k 1.460 * [taylor]: Taking taylor expansion of PI in k 1.461 * [taylor]: Taking taylor expansion of (log n) in k 1.461 * [taylor]: Taking taylor expansion of n in k 1.470 * [taylor]: Taking taylor expansion of 0 in k 1.477 * [taylor]: Taking taylor expansion of 0 in k 1.487 * [taylor]: Taking taylor expansion of 0 in k 1.487 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 1.488 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.488 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.488 * [taylor]: Taking taylor expansion of 1.0 in k 1.488 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.488 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.488 * [taylor]: Taking taylor expansion of k in k 1.489 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.489 * [taylor]: Taking taylor expansion of 1.0 in k 1.489 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.489 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.489 * [taylor]: Taking taylor expansion of k in k 1.507 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.507 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.507 * [taylor]: Taking taylor expansion of 1.0 in k 1.507 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.507 * [taylor]: Taking taylor expansion of k in k 1.508 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.508 * [taylor]: Taking taylor expansion of 1.0 in k 1.508 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.508 * [taylor]: Taking taylor expansion of k in k 1.518 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.518 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.518 * [taylor]: Taking taylor expansion of 1.0 in k 1.518 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.519 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.519 * [taylor]: Taking taylor expansion of -1 in k 1.519 * [taylor]: Taking taylor expansion of k in k 1.520 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.520 * [taylor]: Taking taylor expansion of 1.0 in k 1.520 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.520 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.520 * [taylor]: Taking taylor expansion of -1 in k 1.520 * [taylor]: Taking taylor expansion of k in k 1.533 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 1.533 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.533 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.533 * [taylor]: Taking taylor expansion of 2.0 in n 1.533 * [taylor]: Taking taylor expansion of (* n PI) in n 1.533 * [taylor]: Taking taylor expansion of n in n 1.533 * [taylor]: Taking taylor expansion of PI in n 1.533 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.533 * [taylor]: Taking taylor expansion of 2.0 in n 1.533 * [taylor]: Taking taylor expansion of (* n PI) in n 1.533 * [taylor]: Taking taylor expansion of n in n 1.533 * [taylor]: Taking taylor expansion of PI in n 1.546 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.546 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.546 * [taylor]: Taking taylor expansion of 2.0 in n 1.546 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.546 * [taylor]: Taking taylor expansion of PI in n 1.546 * [taylor]: Taking taylor expansion of n in n 1.546 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.546 * [taylor]: Taking taylor expansion of 2.0 in n 1.546 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.546 * [taylor]: Taking taylor expansion of PI in n 1.546 * [taylor]: Taking taylor expansion of n in n 1.555 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.555 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.556 * [taylor]: Taking taylor expansion of -2.0 in n 1.556 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.556 * [taylor]: Taking taylor expansion of PI in n 1.556 * [taylor]: Taking taylor expansion of n in n 1.556 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.556 * [taylor]: Taking taylor expansion of -2.0 in n 1.556 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.556 * [taylor]: Taking taylor expansion of PI in n 1.556 * [taylor]: Taking taylor expansion of n in n 1.565 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 1.565 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 1.565 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 1.565 * [taylor]: Taking taylor expansion of 1.0 in k 1.565 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1.565 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1.565 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1.565 * [taylor]: Taking taylor expansion of 1/4 in k 1.565 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 1.565 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.565 * [taylor]: Taking taylor expansion of k in k 1.566 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 1.566 * [taylor]: Taking taylor expansion of 1.0 in k 1.566 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1.566 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1.566 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1.566 * [taylor]: Taking taylor expansion of 1/4 in k 1.566 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 1.566 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.566 * [taylor]: Taking taylor expansion of k in k 1.630 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 1.630 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 1.630 * [taylor]: Taking taylor expansion of 1.0 in k 1.630 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 1.630 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1.630 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 1.630 * [taylor]: Taking taylor expansion of 1/4 in k 1.630 * [taylor]: Taking taylor expansion of (log k) in k 1.630 * [taylor]: Taking taylor expansion of k in k 1.630 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 1.630 * [taylor]: Taking taylor expansion of 1.0 in k 1.630 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 1.631 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1.631 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 1.631 * [taylor]: Taking taylor expansion of 1/4 in k 1.631 * [taylor]: Taking taylor expansion of (log k) in k 1.631 * [taylor]: Taking taylor expansion of k in k 1.691 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 1.691 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 1.691 * [taylor]: Taking taylor expansion of 1.0 in k 1.691 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 1.691 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1.691 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.691 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.691 * [taylor]: Taking taylor expansion of -1 in k 1.692 * [taylor]: Taking taylor expansion of k in k 1.698 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 1.698 * [taylor]: Taking taylor expansion of 1.0 in k 1.698 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 1.698 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1.698 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.698 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.698 * [taylor]: Taking taylor expansion of -1 in k 1.698 * [taylor]: Taking taylor expansion of k in k 1.737 * * * [progress]: simplifying candidates 1.755 * [simplify]: Simplifying using # : (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (- (- (log 1.0) (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (- (log (/ 1.0 (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (log (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (exp (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (/ 1.0 (sqrt (sqrt k)))) (- (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt 1)) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) 1) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt 1)) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) 1) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) 1) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1)) (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1) (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt 1)) (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1) (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt 1))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt 1)) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) 1) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) 1) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt 1))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt 1))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt 1))) (sqrt (sqrt 1))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt 1))) (sqrt 1)) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt 1))) 1) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) 1) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt 1)) (sqrt (sqrt 1))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt 1)) (sqrt 1)) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt 1)) 1) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) 1) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) 1) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) 1) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) 1) (sqrt (sqrt 1))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) 1) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) 1) (sqrt 1)) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) 1) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) 1) 1) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1)) (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1) (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt 1)) (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1) (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) 1) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) 1) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt 1))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt 1))) 1) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) 1) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt 1)) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt 1)) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt 1)) 1) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) 1) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 1) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 1) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 1) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 1) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 1) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 1) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 1) 1) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 1) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt 1))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt 1)) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 1) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) 1) (/ (sqrt (sqrt k)) (cbrt (/ 1.0 (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (sqrt (/ 1.0 (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt k)))) (* (sqrt (sqrt k)) (sqrt (sqrt k))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt (sqrt k)))) (log (/ 1.0 (sqrt (sqrt k)))) (exp (/ 1.0 (sqrt (sqrt k)))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (cbrt (/ 1.0 (sqrt (sqrt k)))) (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (- 1.0) (- (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt 1))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (cbrt (sqrt (sqrt k)))) (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1.0 (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1.0 (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt 1))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1 1) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) 1.0) (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt 1))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1.0 1) (/ (sqrt (sqrt k)) (cbrt 1.0)) (/ (sqrt (sqrt k)) (sqrt 1.0)) (/ (sqrt (sqrt k)) 1.0) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (- (* 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))))))))) 1.774 * * [simplify]: iteration 0 : 1334 enodes (cost 5795 ) 1.795 * * [simplify]: iteration 1 : 5001 enodes (cost 5011 ) 1.814 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) 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)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 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))) (* (* 2.0 PI) n) (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))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (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 (* (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (- (log 1.0) (log (sqrt k))) (- (log 1.0) (log (sqrt k))) (- (log 1.0) (log (sqrt k))) (exp (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (pow (/ 1.0 (sqrt k)) 3) (pow (/ 1.0 (sqrt k)) 3) (* (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (/ 1.0 (sqrt (sqrt k)))) (- (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (/ (fabs (cbrt (sqrt k))) (cbrt (/ 1.0 (sqrt (sqrt k)))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (fabs (cbrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (fabs (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (fabs (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (cbrt 1.0) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt 1.0))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (sqrt (sqrt (* (cbrt k) (cbrt k)))) (fabs (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (/ (fabs (cbrt (sqrt k))) (cbrt 1.0))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (/ (fabs (cbrt (sqrt k))) (cbrt 1.0))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (/ (fabs (cbrt (sqrt k))) (cbrt 1.0))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (sqrt (sqrt (* (cbrt k) (cbrt k)))) (fabs (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (cbrt 1.0) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt (sqrt k))) (cbrt 1.0))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt (sqrt k))) (cbrt 1.0))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt (sqrt k))) (cbrt 1.0))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (* (fabs (cbrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* (fabs (cbrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (* (sqrt (sqrt (* (cbrt k) (cbrt k)))) (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (* 1 (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (* 1 (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (* 1 (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* (sqrt (sqrt (* (cbrt k) (cbrt k)))) (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* 1 (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* 1 (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* 1 (fabs (cbrt (sqrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1 (* (fabs (cbrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1 (* (fabs (cbrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ 1.0 (cbrt (sqrt k))) (/ 1 (* (sqrt (sqrt (* (cbrt k) (cbrt k)))) (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))) (/ 1 (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ 1 (* 1 (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1 (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ 1 (* 1 (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1 (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ 1 (* 1 (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k)))) (/ 1 (* (sqrt (sqrt (* (cbrt k) (cbrt k)))) (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ 1 (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1 (* 1 (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ 1 (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1 (* 1 (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ 1 (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1 (* 1 (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1 (* 1 (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1.0 (fabs (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1.0 (/ 1 (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1.0 (/ 1 (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1.0 (/ 1 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ (sqrt k) 1.0) (/ (/ 1.0 (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (* (fabs (cbrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (cbrt (/ 1.0 (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (sqrt (/ 1.0 (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt k) 1.0) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt k) 1.0) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt k) 1.0) (/ (sqrt k) 1.0) (sqrt k) (sqrt k) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 1/2) (pow (* (* 2.0 PI) n) 1/2) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (log (/ 1.0 (sqrt (sqrt k)))) (log (/ 1.0 (sqrt (sqrt k)))) (exp (/ 1.0 (sqrt (sqrt k)))) (pow (/ 1.0 (sqrt (sqrt k))) 3) (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (cbrt (/ 1.0 (sqrt (sqrt k)))) (pow (/ 1.0 (sqrt (sqrt k))) 3) (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (- 1.0) (- (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (/ (fabs (cbrt (sqrt k))) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* 1 (fabs (cbrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (cbrt (sqrt (sqrt k)))) (/ 1 (* 1 (fabs (cbrt (sqrt k))))) (/ 1.0 (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1.0 (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) 1.0) (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (fabs (cbrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ (sqrt (sqrt k)) (cbrt 1.0)) (/ (sqrt (sqrt k)) (sqrt 1.0)) (/ (sqrt (sqrt k)) 1.0) (- (- (+ (+ (* (* 0.125 (pow k 2)) (+ (* (pow (exp 0.5) (log (* (* 2.0 PI) n))) (pow (log (* 2.0 PI)) 2)) (* (pow (log n) 2) (pow (exp 0.5) (log (* (* 2.0 PI) n)))))) (pow (* (* 2.0 PI) n) 0.5)) (* (* (* (* (log n) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log (* 2.0 PI))) (pow k 2)) 0.25)) (* (* (* k (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log n)) 0.5)) (* (* (* k (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) 0.5)) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (+ (- (* +nan.0 k)) (- (* +nan.0 (pow k 2)) +nan.0)) (+ (- (* +nan.0 (/ 1 (pow k 2)))) (- (* +nan.0 (/ 1 k)) (* +nan.0 (/ 1 (pow k 3))))) (+ (- (* +nan.0 (/ 1 (pow k 2)))) (- (* +nan.0 (/ 1 k)) +nan.0)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (+ (- (* 1.0 (sqrt +nan.0)) (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))) (* +nan.0 (- (/ 1 (* (sqrt +nan.0) k)) (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))))) 1.817 * * * [progress]: adding candidates to table 2.562 * * [progress]: iteration 3 / 4 2.562 * * * [progress]: picking best candidate 2.585 * * * * [pick]: Picked # 2.586 * * * [progress]: localizing error 2.601 * * * [progress]: generating rewritten candidates 2.601 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 2.610 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 2.617 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 2.619 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 2.626 * * * [progress]: generating series expansions 2.626 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 2.627 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.627 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.627 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.627 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.627 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.627 * [taylor]: Taking taylor expansion of 0.5 in k 2.627 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.627 * [taylor]: Taking taylor expansion of 1.0 in k 2.627 * [taylor]: Taking taylor expansion of k in k 2.627 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.627 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.627 * [taylor]: Taking taylor expansion of 2.0 in k 2.627 * [taylor]: Taking taylor expansion of (* n PI) in k 2.627 * [taylor]: Taking taylor expansion of n in k 2.627 * [taylor]: Taking taylor expansion of PI in k 2.629 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.629 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.629 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.629 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.629 * [taylor]: Taking taylor expansion of 0.5 in n 2.629 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.629 * [taylor]: Taking taylor expansion of 1.0 in n 2.629 * [taylor]: Taking taylor expansion of k in n 2.629 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.629 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.629 * [taylor]: Taking taylor expansion of 2.0 in n 2.629 * [taylor]: Taking taylor expansion of (* n PI) in n 2.629 * [taylor]: Taking taylor expansion of n in n 2.629 * [taylor]: Taking taylor expansion of PI in n 2.634 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.634 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.634 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.634 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.634 * [taylor]: Taking taylor expansion of 0.5 in n 2.634 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.634 * [taylor]: Taking taylor expansion of 1.0 in n 2.635 * [taylor]: Taking taylor expansion of k in n 2.635 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.635 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.635 * [taylor]: Taking taylor expansion of 2.0 in n 2.635 * [taylor]: Taking taylor expansion of (* n PI) in n 2.635 * [taylor]: Taking taylor expansion of n in n 2.635 * [taylor]: Taking taylor expansion of PI in n 2.640 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.640 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.640 * [taylor]: Taking taylor expansion of 0.5 in k 2.640 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.640 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.640 * [taylor]: Taking taylor expansion of 1.0 in k 2.640 * [taylor]: Taking taylor expansion of k in k 2.640 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.640 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.640 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.640 * [taylor]: Taking taylor expansion of 2.0 in k 2.640 * [taylor]: Taking taylor expansion of PI in k 2.641 * [taylor]: Taking taylor expansion of (log n) in k 2.641 * [taylor]: Taking taylor expansion of n in k 2.651 * [taylor]: Taking taylor expansion of 0 in k 2.672 * [taylor]: Taking taylor expansion of 0 in k 2.691 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.692 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.692 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.692 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.692 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.692 * [taylor]: Taking taylor expansion of 0.5 in k 2.692 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.692 * [taylor]: Taking taylor expansion of 1.0 in k 2.692 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.692 * [taylor]: Taking taylor expansion of k in k 2.692 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.692 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.692 * [taylor]: Taking taylor expansion of 2.0 in k 2.692 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.692 * [taylor]: Taking taylor expansion of PI in k 2.692 * [taylor]: Taking taylor expansion of n in k 2.693 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.693 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.693 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.693 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.693 * [taylor]: Taking taylor expansion of 0.5 in n 2.693 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.693 * [taylor]: Taking taylor expansion of 1.0 in n 2.693 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.693 * [taylor]: Taking taylor expansion of k in n 2.693 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.693 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.693 * [taylor]: Taking taylor expansion of 2.0 in n 2.693 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.693 * [taylor]: Taking taylor expansion of PI in n 2.693 * [taylor]: Taking taylor expansion of n in n 2.697 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.697 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.698 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.698 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.698 * [taylor]: Taking taylor expansion of 0.5 in n 2.698 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.698 * [taylor]: Taking taylor expansion of 1.0 in n 2.698 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.698 * [taylor]: Taking taylor expansion of k in n 2.698 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.698 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.698 * [taylor]: Taking taylor expansion of 2.0 in n 2.698 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.698 * [taylor]: Taking taylor expansion of PI in n 2.698 * [taylor]: Taking taylor expansion of n in n 2.702 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.702 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.702 * [taylor]: Taking taylor expansion of 0.5 in k 2.702 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.702 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.702 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.702 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.702 * [taylor]: Taking taylor expansion of 2.0 in k 2.702 * [taylor]: Taking taylor expansion of PI in k 2.703 * [taylor]: Taking taylor expansion of (log n) in k 2.703 * [taylor]: Taking taylor expansion of n in k 2.703 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.703 * [taylor]: Taking taylor expansion of 1.0 in k 2.703 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.703 * [taylor]: Taking taylor expansion of k in k 2.713 * [taylor]: Taking taylor expansion of 0 in k 2.720 * [taylor]: Taking taylor expansion of 0 in k 2.729 * [taylor]: Taking taylor expansion of 0 in k 2.731 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.731 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.731 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.731 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.731 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.731 * [taylor]: Taking taylor expansion of 0.5 in k 2.731 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.731 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.731 * [taylor]: Taking taylor expansion of k in k 2.731 * [taylor]: Taking taylor expansion of 1.0 in k 2.731 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.731 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.731 * [taylor]: Taking taylor expansion of -2.0 in k 2.731 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.731 * [taylor]: Taking taylor expansion of PI in k 2.731 * [taylor]: Taking taylor expansion of n in k 2.732 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.732 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.732 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.732 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.732 * [taylor]: Taking taylor expansion of 0.5 in n 2.732 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.732 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.732 * [taylor]: Taking taylor expansion of k in n 2.732 * [taylor]: Taking taylor expansion of 1.0 in n 2.732 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.732 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.732 * [taylor]: Taking taylor expansion of -2.0 in n 2.732 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.732 * [taylor]: Taking taylor expansion of PI in n 2.732 * [taylor]: Taking taylor expansion of n in n 2.736 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.736 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.736 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.736 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.736 * [taylor]: Taking taylor expansion of 0.5 in n 2.736 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.736 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.736 * [taylor]: Taking taylor expansion of k in n 2.736 * [taylor]: Taking taylor expansion of 1.0 in n 2.736 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.736 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.736 * [taylor]: Taking taylor expansion of -2.0 in n 2.736 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.736 * [taylor]: Taking taylor expansion of PI in n 2.736 * [taylor]: Taking taylor expansion of n in n 2.740 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.740 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.740 * [taylor]: Taking taylor expansion of 0.5 in k 2.740 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.740 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.740 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.740 * [taylor]: Taking taylor expansion of k in k 2.740 * [taylor]: Taking taylor expansion of 1.0 in k 2.740 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.740 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.740 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.740 * [taylor]: Taking taylor expansion of -2.0 in k 2.740 * [taylor]: Taking taylor expansion of PI in k 2.747 * [taylor]: Taking taylor expansion of (log n) in k 2.747 * [taylor]: Taking taylor expansion of n in k 2.757 * [taylor]: Taking taylor expansion of 0 in k 2.764 * [taylor]: Taking taylor expansion of 0 in k 2.773 * [taylor]: Taking taylor expansion of 0 in k 2.774 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 2.774 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.774 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.774 * [taylor]: Taking taylor expansion of 2.0 in n 2.774 * [taylor]: Taking taylor expansion of (* n PI) in n 2.774 * [taylor]: Taking taylor expansion of n in n 2.774 * [taylor]: Taking taylor expansion of PI in n 2.774 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.774 * [taylor]: Taking taylor expansion of 2.0 in n 2.774 * [taylor]: Taking taylor expansion of (* n PI) in n 2.774 * [taylor]: Taking taylor expansion of n in n 2.774 * [taylor]: Taking taylor expansion of PI in n 2.787 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.787 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.787 * [taylor]: Taking taylor expansion of 2.0 in n 2.787 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.787 * [taylor]: Taking taylor expansion of PI in n 2.787 * [taylor]: Taking taylor expansion of n in n 2.787 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.787 * [taylor]: Taking taylor expansion of 2.0 in n 2.787 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.787 * [taylor]: Taking taylor expansion of PI in n 2.787 * [taylor]: Taking taylor expansion of n in n 2.796 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.797 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.797 * [taylor]: Taking taylor expansion of -2.0 in n 2.797 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.797 * [taylor]: Taking taylor expansion of PI in n 2.797 * [taylor]: Taking taylor expansion of n in n 2.797 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.797 * [taylor]: Taking taylor expansion of -2.0 in n 2.797 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.797 * [taylor]: Taking taylor expansion of PI in n 2.797 * [taylor]: Taking taylor expansion of n in n 2.806 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 2.806 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.806 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.806 * [taylor]: Taking taylor expansion of 1.0 in k 2.806 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.806 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.806 * [taylor]: Taking taylor expansion of k in k 2.808 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.808 * [taylor]: Taking taylor expansion of 1.0 in k 2.808 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.808 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.808 * [taylor]: Taking taylor expansion of k in k 2.820 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.820 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.820 * [taylor]: Taking taylor expansion of 1.0 in k 2.820 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.820 * [taylor]: Taking taylor expansion of k in k 2.821 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.821 * [taylor]: Taking taylor expansion of 1.0 in k 2.821 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.821 * [taylor]: Taking taylor expansion of k in k 2.838 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.838 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.838 * [taylor]: Taking taylor expansion of 1.0 in k 2.838 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.838 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.838 * [taylor]: Taking taylor expansion of -1 in k 2.838 * [taylor]: Taking taylor expansion of k in k 2.839 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.839 * [taylor]: Taking taylor expansion of 1.0 in k 2.839 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.839 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.839 * [taylor]: Taking taylor expansion of -1 in k 2.839 * [taylor]: Taking taylor expansion of k in k 2.852 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 2.852 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.852 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.852 * [taylor]: Taking taylor expansion of 1.0 in k 2.852 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.852 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.852 * [taylor]: Taking taylor expansion of k in k 2.853 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.853 * [taylor]: Taking taylor expansion of 1.0 in k 2.853 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.853 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.853 * [taylor]: Taking taylor expansion of k in k 2.865 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.865 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.865 * [taylor]: Taking taylor expansion of 1.0 in k 2.865 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.865 * [taylor]: Taking taylor expansion of k in k 2.866 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.866 * [taylor]: Taking taylor expansion of 1.0 in k 2.866 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.866 * [taylor]: Taking taylor expansion of k in k 2.876 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.876 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.876 * [taylor]: Taking taylor expansion of 1.0 in k 2.876 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.876 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.876 * [taylor]: Taking taylor expansion of -1 in k 2.876 * [taylor]: Taking taylor expansion of k in k 2.878 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.878 * [taylor]: Taking taylor expansion of 1.0 in k 2.878 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.878 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.878 * [taylor]: Taking taylor expansion of -1 in k 2.878 * [taylor]: Taking taylor expansion of k in k 2.890 * * * [progress]: simplifying candidates 2.893 * [simplify]: Simplifying using # : (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (+ (* 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 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 2.900 * * [simplify]: iteration 0 : 563 enodes (cost 883 ) 2.910 * * [simplify]: iteration 1 : 2197 enodes (cost 815 ) 2.947 * * [simplify]: iteration 2 : 5001 enodes (cost 791 ) 2.952 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) 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)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 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))) (* (* 2.0 PI) n) (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))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (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 (* (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 1/2) (pow (* (* 2.0 PI) n) 1/2) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (pow k 1/2)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (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)) (/ (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)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (* (fabs (cbrt k)) 1)) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (pow k 1/2)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (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)) (/ (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)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (* (fabs (cbrt k)) 1)) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (- (+ (+ (* (* 0.125 (pow k 2)) (+ (* (pow (exp 0.5) (log (* (* 2.0 PI) n))) (pow (log (* 2.0 PI)) 2)) (* (pow (log n) 2) (pow (exp 0.5) (log (* (* 2.0 PI) n)))))) (pow (* (* 2.0 PI) n) 0.5)) (* (* (* (* (log n) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log (* 2.0 PI))) (pow k 2)) 0.25)) (* (* (* k (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log n)) 0.5)) (* (* (* k (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) 0.5)) (pow (* (* 2.0 PI) n) (* 0.5 (- 1.0 k))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (- (* +nan.0 k)) (- (* +nan.0 (pow k 2)) +nan.0)) (+ (* +nan.0 (- (/ 1 k) (/ 1 (pow k 3)))) (/ (- +nan.0) (pow k 2))) (+ (- (* +nan.0 (/ 1 k)) +nan.0) (/ (- +nan.0) (pow k 2))) (+ (- (* +nan.0 k)) (- (* +nan.0 (pow k 2)) +nan.0)) (+ (* +nan.0 (- (/ 1 k) (/ 1 (pow k 3)))) (/ (- +nan.0) (pow k 2))) (+ (- (* +nan.0 (/ 1 k)) +nan.0) (/ (- +nan.0) (pow k 2))) 2.953 * * * [progress]: adding candidates to table 3.368 * * [progress]: iteration 4 / 4 3.368 * * * [progress]: picking best candidate 3.386 * * * * [pick]: Picked # 3.386 * * * [progress]: localizing error 3.409 * * * [progress]: generating rewritten candidates 3.409 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.419 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2 1 1) 3.419 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1 2 1 1 2) 3.420 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1 2 1 1 1) 3.422 * * * [progress]: generating series expansions 3.422 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.423 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.423 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.423 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.423 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.423 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.423 * [taylor]: Taking taylor expansion of 0.5 in k 3.423 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.423 * [taylor]: Taking taylor expansion of 1.0 in k 3.423 * [taylor]: Taking taylor expansion of k in k 3.423 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.423 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.423 * [taylor]: Taking taylor expansion of 2.0 in k 3.423 * [taylor]: Taking taylor expansion of (* n PI) in k 3.423 * [taylor]: Taking taylor expansion of n in k 3.423 * [taylor]: Taking taylor expansion of PI in k 3.424 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.424 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.424 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.424 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.425 * [taylor]: Taking taylor expansion of 0.5 in n 3.425 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.425 * [taylor]: Taking taylor expansion of 1.0 in n 3.425 * [taylor]: Taking taylor expansion of k in n 3.425 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.425 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.425 * [taylor]: Taking taylor expansion of 2.0 in n 3.425 * [taylor]: Taking taylor expansion of (* n PI) in n 3.425 * [taylor]: Taking taylor expansion of n in n 3.425 * [taylor]: Taking taylor expansion of PI in n 3.430 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.430 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.430 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.430 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.430 * [taylor]: Taking taylor expansion of 0.5 in n 3.430 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.430 * [taylor]: Taking taylor expansion of 1.0 in n 3.430 * [taylor]: Taking taylor expansion of k in n 3.430 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.430 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.431 * [taylor]: Taking taylor expansion of 2.0 in n 3.431 * [taylor]: Taking taylor expansion of (* n PI) in n 3.431 * [taylor]: Taking taylor expansion of n in n 3.431 * [taylor]: Taking taylor expansion of PI in n 3.436 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.436 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.436 * [taylor]: Taking taylor expansion of 0.5 in k 3.436 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.436 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.436 * [taylor]: Taking taylor expansion of 1.0 in k 3.436 * [taylor]: Taking taylor expansion of k in k 3.436 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.436 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.436 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.436 * [taylor]: Taking taylor expansion of 2.0 in k 3.436 * [taylor]: Taking taylor expansion of PI in k 3.442 * [taylor]: Taking taylor expansion of (log n) in k 3.442 * [taylor]: Taking taylor expansion of n in k 3.451 * [taylor]: Taking taylor expansion of 0 in k 3.468 * [taylor]: Taking taylor expansion of 0 in k 3.488 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.488 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.488 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.488 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.488 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.488 * [taylor]: Taking taylor expansion of 0.5 in k 3.488 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.488 * [taylor]: Taking taylor expansion of 1.0 in k 3.488 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.488 * [taylor]: Taking taylor expansion of k in k 3.488 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.488 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.488 * [taylor]: Taking taylor expansion of 2.0 in k 3.488 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.488 * [taylor]: Taking taylor expansion of PI in k 3.488 * [taylor]: Taking taylor expansion of n in k 3.489 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.489 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.489 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.489 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.489 * [taylor]: Taking taylor expansion of 0.5 in n 3.489 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.489 * [taylor]: Taking taylor expansion of 1.0 in n 3.489 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.489 * [taylor]: Taking taylor expansion of k in n 3.489 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.489 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.490 * [taylor]: Taking taylor expansion of 2.0 in n 3.490 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.490 * [taylor]: Taking taylor expansion of PI in n 3.490 * [taylor]: Taking taylor expansion of n in n 3.493 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.493 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.493 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.493 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.493 * [taylor]: Taking taylor expansion of 0.5 in n 3.493 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.493 * [taylor]: Taking taylor expansion of 1.0 in n 3.493 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.493 * [taylor]: Taking taylor expansion of k in n 3.493 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.493 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.493 * [taylor]: Taking taylor expansion of 2.0 in n 3.494 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.494 * [taylor]: Taking taylor expansion of PI in n 3.494 * [taylor]: Taking taylor expansion of n in n 3.497 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.497 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.497 * [taylor]: Taking taylor expansion of 0.5 in k 3.497 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.497 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.497 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.497 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.497 * [taylor]: Taking taylor expansion of 2.0 in k 3.497 * [taylor]: Taking taylor expansion of PI in k 3.498 * [taylor]: Taking taylor expansion of (log n) in k 3.498 * [taylor]: Taking taylor expansion of n in k 3.498 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.499 * [taylor]: Taking taylor expansion of 1.0 in k 3.499 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.499 * [taylor]: Taking taylor expansion of k in k 3.508 * [taylor]: Taking taylor expansion of 0 in k 3.516 * [taylor]: Taking taylor expansion of 0 in k 3.531 * [taylor]: Taking taylor expansion of 0 in k 3.533 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.533 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.533 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.533 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.533 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.533 * [taylor]: Taking taylor expansion of 0.5 in k 3.533 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.533 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.533 * [taylor]: Taking taylor expansion of k in k 3.533 * [taylor]: Taking taylor expansion of 1.0 in k 3.533 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.533 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.533 * [taylor]: Taking taylor expansion of -2.0 in k 3.533 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.533 * [taylor]: Taking taylor expansion of PI in k 3.533 * [taylor]: Taking taylor expansion of n in k 3.534 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.534 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.534 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.534 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.534 * [taylor]: Taking taylor expansion of 0.5 in n 3.534 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.534 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.534 * [taylor]: Taking taylor expansion of k in n 3.534 * [taylor]: Taking taylor expansion of 1.0 in n 3.534 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.534 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.534 * [taylor]: Taking taylor expansion of -2.0 in n 3.534 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.534 * [taylor]: Taking taylor expansion of PI in n 3.534 * [taylor]: Taking taylor expansion of n in n 3.538 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.538 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.538 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.538 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.538 * [taylor]: Taking taylor expansion of 0.5 in n 3.538 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.538 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.538 * [taylor]: Taking taylor expansion of k in n 3.538 * [taylor]: Taking taylor expansion of 1.0 in n 3.538 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.538 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.538 * [taylor]: Taking taylor expansion of -2.0 in n 3.538 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.538 * [taylor]: Taking taylor expansion of PI in n 3.538 * [taylor]: Taking taylor expansion of n in n 3.542 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 3.542 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 3.542 * [taylor]: Taking taylor expansion of 0.5 in k 3.542 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 3.542 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.542 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.542 * [taylor]: Taking taylor expansion of k in k 3.543 * [taylor]: Taking taylor expansion of 1.0 in k 3.543 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.543 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.543 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.543 * [taylor]: Taking taylor expansion of -2.0 in k 3.543 * [taylor]: Taking taylor expansion of PI in k 3.544 * [taylor]: Taking taylor expansion of (log n) in k 3.544 * [taylor]: Taking taylor expansion of n in k 3.553 * [taylor]: Taking taylor expansion of 0 in k 3.560 * [taylor]: Taking taylor expansion of 0 in k 3.569 * [taylor]: Taking taylor expansion of 0 in k 3.570 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2 1 1) 3.570 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 3.570 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 3.570 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 3.570 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 3.570 * [taylor]: Taking taylor expansion of 1/3 in k 3.570 * [taylor]: Taking taylor expansion of (log k) in k 3.570 * [taylor]: Taking taylor expansion of k in k 3.571 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 3.571 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 3.571 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 3.571 * [taylor]: Taking taylor expansion of 1/3 in k 3.571 * [taylor]: Taking taylor expansion of (log k) in k 3.571 * [taylor]: Taking taylor expansion of k in k 3.626 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 3.626 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.626 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.626 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.626 * [taylor]: Taking taylor expansion of 1/3 in k 3.626 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.626 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.626 * [taylor]: Taking taylor expansion of k in k 3.627 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.627 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.627 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.627 * [taylor]: Taking taylor expansion of 1/3 in k 3.627 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.627 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.627 * [taylor]: Taking taylor expansion of k in k 3.680 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in (k) around 0 3.680 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 3.680 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.680 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.680 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.680 * [taylor]: Taking taylor expansion of 1/3 in k 3.680 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.680 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.680 * [taylor]: Taking taylor expansion of k in k 3.681 * [taylor]: Taking taylor expansion of (cbrt -1) in k 3.681 * [taylor]: Taking taylor expansion of -1 in k 3.682 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 3.682 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.682 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.682 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.682 * [taylor]: Taking taylor expansion of 1/3 in k 3.682 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.682 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.682 * [taylor]: Taking taylor expansion of k in k 3.683 * [taylor]: Taking taylor expansion of (cbrt -1) in k 3.683 * [taylor]: Taking taylor expansion of -1 in k 3.751 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1 2 1 1 2) 3.751 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 3.751 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 3.751 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 3.751 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 3.751 * [taylor]: Taking taylor expansion of 1/3 in k 3.751 * [taylor]: Taking taylor expansion of (log k) in k 3.751 * [taylor]: Taking taylor expansion of k in k 3.752 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 3.752 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 3.752 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 3.752 * [taylor]: Taking taylor expansion of 1/3 in k 3.752 * [taylor]: Taking taylor expansion of (log k) in k 3.752 * [taylor]: Taking taylor expansion of k in k 3.808 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 3.808 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.808 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.808 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.808 * [taylor]: Taking taylor expansion of 1/3 in k 3.808 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.809 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.809 * [taylor]: Taking taylor expansion of k in k 3.809 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.809 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.809 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.809 * [taylor]: Taking taylor expansion of 1/3 in k 3.810 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.810 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.810 * [taylor]: Taking taylor expansion of k in k 3.868 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in (k) around 0 3.868 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 3.868 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.868 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.868 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.868 * [taylor]: Taking taylor expansion of 1/3 in k 3.868 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.868 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.868 * [taylor]: Taking taylor expansion of k in k 3.869 * [taylor]: Taking taylor expansion of (cbrt -1) in k 3.869 * [taylor]: Taking taylor expansion of -1 in k 3.870 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 3.870 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.870 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.870 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.870 * [taylor]: Taking taylor expansion of 1/3 in k 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 3.871 * [taylor]: Taking taylor expansion of (cbrt -1) in k 3.871 * [taylor]: Taking taylor expansion of -1 in k 3.938 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1 2 1 1 1) 3.938 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 3.938 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 3.938 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 3.938 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 3.938 * [taylor]: Taking taylor expansion of 1/3 in k 3.938 * [taylor]: Taking taylor expansion of (log k) in k 3.939 * [taylor]: Taking taylor expansion of k in k 3.939 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 3.939 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 3.939 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 3.939 * [taylor]: Taking taylor expansion of 1/3 in k 3.939 * [taylor]: Taking taylor expansion of (log k) in k 3.939 * [taylor]: Taking taylor expansion of k in k 3.989 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 3.989 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.989 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.989 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.989 * [taylor]: Taking taylor expansion of 1/3 in k 3.989 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.989 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.989 * [taylor]: Taking taylor expansion of k in k 3.990 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.990 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.990 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.990 * [taylor]: Taking taylor expansion of 1/3 in k 3.990 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.990 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.990 * [taylor]: Taking taylor expansion of k in k 4.049 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in (k) around 0 4.049 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 4.049 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.049 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.049 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.049 * [taylor]: Taking taylor expansion of 1/3 in k 4.049 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.049 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.049 * [taylor]: Taking taylor expansion of k in k 4.050 * [taylor]: Taking taylor expansion of (cbrt -1) in k 4.050 * [taylor]: Taking taylor expansion of -1 in k 4.051 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 4.051 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.051 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.051 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.051 * [taylor]: Taking taylor expansion of 1/3 in k 4.051 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.051 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.051 * [taylor]: Taking taylor expansion of k in k 4.052 * [taylor]: Taking taylor expansion of (cbrt -1) in k 4.052 * [taylor]: Taking taylor expansion of -1 in k 4.121 * * * [progress]: simplifying candidates 4.123 * [simplify]: Simplifying using # : (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (log (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (cbrt k) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) (* (* (cbrt k) (cbrt k)) (cbrt k)) (sqrt (cbrt k)) (sqrt (cbrt k)) (log (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (cbrt k) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) (* (* (cbrt k) (cbrt k)) (cbrt k)) (sqrt (cbrt k)) (sqrt (cbrt k)) (log (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (cbrt k) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) (* (* (cbrt k) (cbrt k)) (cbrt k)) (sqrt (cbrt k)) (sqrt (cbrt k)) (- (+ (* 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 k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) 4.128 * * [simplify]: iteration 0 : 356 enodes (cost 444 ) 4.133 * * [simplify]: iteration 1 : 1211 enodes (cost 420 ) 4.157 * * [simplify]: iteration 2 : 5001 enodes (cost 392 ) 4.159 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) 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)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 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))) (* (* 2.0 PI) n) (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))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (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 (* (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (log (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (pow k 1/3) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) k (sqrt (cbrt k)) (sqrt (cbrt k)) (log (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (pow k 1/3) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) k (sqrt (cbrt k)) (sqrt (cbrt k)) (log (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (pow k 1/3) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) k (sqrt (cbrt k)) (sqrt (cbrt k)) (+ (* (pow k 2) (+ (* (* (* (log (* 2.0 PI)) (log n)) (pow (* (* 2.0 PI) n) 0.5)) 0.25) (* (* (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (log n)) 0.125))) (- (* (+ (* (* 0.125 (pow k 2)) (pow (log (* 2.0 PI)) 2)) 1) (pow (* (* 2.0 PI) n) 0.5)) (* (* (* 0.5 k) (pow (* (* 2.0 PI) n) 0.5)) (log (* (* 2.0 PI) n))))) (pow (* (* 2.0 PI) n) (* 0.5 (- 1.0 k))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) 4.159 * * * [progress]: adding candidates to table 4.534 * [progress]: [Phase 3 of 3] Extracting. 4.534 * * [regime]: Finding splitpoints for: (# # # # # # #) 4.536 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 4.536 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 4.570 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 4.603 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 4.632 * * * [regime]: Found split indices: #