13.279 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.078 * * * [progress]: [2/2] Setting up program. 0.080 * [progress]: [Phase 2 of 3] Improving. 0.080 * [simplify]: Simplifying using # : (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.083 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.084 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.086 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.088 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.094 * * [simplify]: iteration 4 : 1044 enodes (cost 8 ) 0.118 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.118 * [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 # 0.121 * * * [progress]: localizing error 0.138 * * * [progress]: generating rewritten candidates 0.138 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.148 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.155 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.158 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.182 * * * [progress]: generating series expansions 0.182 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.183 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.183 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.183 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.183 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.183 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.183 * [taylor]: Taking taylor expansion of 0.5 in k 0.183 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.183 * [taylor]: Taking taylor expansion of 1.0 in k 0.183 * [taylor]: Taking taylor expansion of k in k 0.183 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.183 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.183 * [taylor]: Taking taylor expansion of 2.0 in k 0.183 * [taylor]: Taking taylor expansion of (* n PI) in k 0.183 * [taylor]: Taking taylor expansion of n in k 0.183 * [taylor]: Taking taylor expansion of PI in k 0.185 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.185 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.185 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.185 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.185 * [taylor]: Taking taylor expansion of 0.5 in n 0.185 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.185 * [taylor]: Taking taylor expansion of 1.0 in n 0.185 * [taylor]: Taking taylor expansion of k in n 0.185 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.185 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.185 * [taylor]: Taking taylor expansion of 2.0 in n 0.185 * [taylor]: Taking taylor expansion of (* n PI) in n 0.185 * [taylor]: Taking taylor expansion of n in n 0.185 * [taylor]: Taking taylor expansion of PI in n 0.191 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.191 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.191 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.191 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.191 * [taylor]: Taking taylor expansion of 0.5 in n 0.191 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.191 * [taylor]: Taking taylor expansion of 1.0 in n 0.191 * [taylor]: Taking taylor expansion of k in n 0.191 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.191 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.191 * [taylor]: Taking taylor expansion of 2.0 in n 0.191 * [taylor]: Taking taylor expansion of (* n PI) in n 0.191 * [taylor]: Taking taylor expansion of n in n 0.191 * [taylor]: Taking taylor expansion of PI in n 0.197 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.197 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.197 * [taylor]: Taking taylor expansion of 0.5 in k 0.197 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.197 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.197 * [taylor]: Taking taylor expansion of 1.0 in k 0.197 * [taylor]: Taking taylor expansion of k in k 0.197 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.197 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.197 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.197 * [taylor]: Taking taylor expansion of 2.0 in k 0.197 * [taylor]: Taking taylor expansion of PI in k 0.198 * [taylor]: Taking taylor expansion of (log n) in k 0.198 * [taylor]: Taking taylor expansion of n in k 0.208 * [taylor]: Taking taylor expansion of 0 in k 0.231 * [taylor]: Taking taylor expansion of 0 in k 0.250 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.250 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.250 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.250 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.250 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.250 * [taylor]: Taking taylor expansion of 0.5 in k 0.250 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.250 * [taylor]: Taking taylor expansion of 1.0 in k 0.250 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.250 * [taylor]: Taking taylor expansion of k in k 0.250 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.250 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.250 * [taylor]: Taking taylor expansion of 2.0 in k 0.250 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.250 * [taylor]: Taking taylor expansion of PI in k 0.250 * [taylor]: Taking taylor expansion of n in k 0.252 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.252 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.252 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.252 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.252 * [taylor]: Taking taylor expansion of 0.5 in n 0.252 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.252 * [taylor]: Taking taylor expansion of 1.0 in n 0.252 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.252 * [taylor]: Taking taylor expansion of k in n 0.252 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.252 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.252 * [taylor]: Taking taylor expansion of 2.0 in n 0.252 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.252 * [taylor]: Taking taylor expansion of PI in n 0.252 * [taylor]: Taking taylor expansion of n in n 0.256 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.256 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.256 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.256 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.256 * [taylor]: Taking taylor expansion of 0.5 in n 0.256 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.256 * [taylor]: Taking taylor expansion of 1.0 in n 0.256 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.256 * [taylor]: Taking taylor expansion of k in n 0.256 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.256 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.256 * [taylor]: Taking taylor expansion of 2.0 in n 0.256 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.256 * [taylor]: Taking taylor expansion of PI in n 0.256 * [taylor]: Taking taylor expansion of n in n 0.260 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.260 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.260 * [taylor]: Taking taylor expansion of 0.5 in k 0.260 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.260 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.260 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.260 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.260 * [taylor]: Taking taylor expansion of 2.0 in k 0.260 * [taylor]: Taking taylor expansion of PI in k 0.261 * [taylor]: Taking taylor expansion of (log n) in k 0.261 * [taylor]: Taking taylor expansion of n in k 0.261 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.261 * [taylor]: Taking taylor expansion of 1.0 in k 0.261 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.261 * [taylor]: Taking taylor expansion of k in k 0.271 * [taylor]: Taking taylor expansion of 0 in k 0.278 * [taylor]: Taking taylor expansion of 0 in k 0.288 * [taylor]: Taking taylor expansion of 0 in k 0.290 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.290 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.290 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.290 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.290 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.290 * [taylor]: Taking taylor expansion of 0.5 in k 0.290 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.290 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.290 * [taylor]: Taking taylor expansion of k in k 0.290 * [taylor]: Taking taylor expansion of 1.0 in k 0.290 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.290 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.290 * [taylor]: Taking taylor expansion of -2.0 in k 0.290 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.290 * [taylor]: Taking taylor expansion of PI in k 0.290 * [taylor]: Taking taylor expansion of n in k 0.291 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.291 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.291 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.291 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.291 * [taylor]: Taking taylor expansion of 0.5 in n 0.291 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.291 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.291 * [taylor]: Taking taylor expansion of k in n 0.291 * [taylor]: Taking taylor expansion of 1.0 in n 0.291 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.291 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.291 * [taylor]: Taking taylor expansion of -2.0 in n 0.291 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.291 * [taylor]: Taking taylor expansion of PI in n 0.291 * [taylor]: Taking taylor expansion of n in n 0.295 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.295 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.295 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.295 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.295 * [taylor]: Taking taylor expansion of 0.5 in n 0.295 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.295 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.295 * [taylor]: Taking taylor expansion of k in n 0.295 * [taylor]: Taking taylor expansion of 1.0 in n 0.295 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.295 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.295 * [taylor]: Taking taylor expansion of -2.0 in n 0.295 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.295 * [taylor]: Taking taylor expansion of PI in n 0.295 * [taylor]: Taking taylor expansion of n in n 0.299 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.299 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.299 * [taylor]: Taking taylor expansion of 0.5 in k 0.299 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.299 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.299 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.299 * [taylor]: Taking taylor expansion of k in k 0.300 * [taylor]: Taking taylor expansion of 1.0 in k 0.300 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.300 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.300 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.300 * [taylor]: Taking taylor expansion of -2.0 in k 0.300 * [taylor]: Taking taylor expansion of PI in k 0.301 * [taylor]: Taking taylor expansion of (log n) in k 0.301 * [taylor]: Taking taylor expansion of n in k 0.316 * [taylor]: Taking taylor expansion of 0 in k 0.324 * [taylor]: Taking taylor expansion of 0 in k 0.333 * [taylor]: Taking taylor expansion of 0 in k 0.334 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.334 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.334 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.334 * [taylor]: Taking taylor expansion of 2.0 in n 0.334 * [taylor]: Taking taylor expansion of (* n PI) in n 0.334 * [taylor]: Taking taylor expansion of n in n 0.334 * [taylor]: Taking taylor expansion of PI in n 0.334 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.334 * [taylor]: Taking taylor expansion of 2.0 in n 0.334 * [taylor]: Taking taylor expansion of (* n PI) in n 0.334 * [taylor]: Taking taylor expansion of n in n 0.334 * [taylor]: Taking taylor expansion of PI in n 0.347 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.347 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.347 * [taylor]: Taking taylor expansion of 2.0 in n 0.347 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.347 * [taylor]: Taking taylor expansion of PI in n 0.347 * [taylor]: Taking taylor expansion of n in n 0.347 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.347 * [taylor]: Taking taylor expansion of 2.0 in n 0.347 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.347 * [taylor]: Taking taylor expansion of PI in n 0.348 * [taylor]: Taking taylor expansion of n in n 0.357 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.357 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.357 * [taylor]: Taking taylor expansion of -2.0 in n 0.357 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.357 * [taylor]: Taking taylor expansion of PI in n 0.357 * [taylor]: Taking taylor expansion of n in n 0.357 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.357 * [taylor]: Taking taylor expansion of -2.0 in n 0.357 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.357 * [taylor]: Taking taylor expansion of PI in n 0.357 * [taylor]: Taking taylor expansion of n in n 0.366 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.366 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.366 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.366 * [taylor]: Taking taylor expansion of 1.0 in k 0.366 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.366 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.366 * [taylor]: Taking taylor expansion of k in k 0.368 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.368 * [taylor]: Taking taylor expansion of 1.0 in k 0.368 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.368 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.368 * [taylor]: Taking taylor expansion of k in k 0.380 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.380 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.380 * [taylor]: Taking taylor expansion of 1.0 in k 0.380 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.380 * [taylor]: Taking taylor expansion of k in k 0.381 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.381 * [taylor]: Taking taylor expansion of 1.0 in k 0.381 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.381 * [taylor]: Taking taylor expansion of k in k 0.399 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.399 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.399 * [taylor]: Taking taylor expansion of 1.0 in k 0.399 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.399 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.399 * [taylor]: Taking taylor expansion of -1 in k 0.399 * [taylor]: Taking taylor expansion of k in k 0.400 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.400 * [taylor]: Taking taylor expansion of 1.0 in k 0.400 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.400 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.400 * [taylor]: Taking taylor expansion of -1 in k 0.400 * [taylor]: Taking taylor expansion of k in k 0.412 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.413 * [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 0.413 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.413 * [taylor]: Taking taylor expansion of 1.0 in n 0.413 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.413 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.413 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.413 * [taylor]: Taking taylor expansion of k in n 0.413 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.413 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.413 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.413 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.413 * [taylor]: Taking taylor expansion of 0.5 in n 0.413 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.413 * [taylor]: Taking taylor expansion of 1.0 in n 0.413 * [taylor]: Taking taylor expansion of k in n 0.414 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.414 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.414 * [taylor]: Taking taylor expansion of 2.0 in n 0.414 * [taylor]: Taking taylor expansion of (* n PI) in n 0.414 * [taylor]: Taking taylor expansion of n in n 0.414 * [taylor]: Taking taylor expansion of PI in n 0.419 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.419 * [taylor]: Taking taylor expansion of 1.0 in k 0.419 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.419 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.419 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.419 * [taylor]: Taking taylor expansion of k in k 0.420 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.421 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.421 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.421 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.421 * [taylor]: Taking taylor expansion of 0.5 in k 0.421 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.421 * [taylor]: Taking taylor expansion of 1.0 in k 0.421 * [taylor]: Taking taylor expansion of k in k 0.421 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.421 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.421 * [taylor]: Taking taylor expansion of 2.0 in k 0.421 * [taylor]: Taking taylor expansion of (* n PI) in k 0.421 * [taylor]: Taking taylor expansion of n in k 0.421 * [taylor]: Taking taylor expansion of PI in k 0.422 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.422 * [taylor]: Taking taylor expansion of 1.0 in k 0.422 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.422 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.422 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.422 * [taylor]: Taking taylor expansion of k in k 0.423 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.423 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.423 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.423 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.423 * [taylor]: Taking taylor expansion of 0.5 in k 0.423 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.423 * [taylor]: Taking taylor expansion of 1.0 in k 0.423 * [taylor]: Taking taylor expansion of k in k 0.423 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.423 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.423 * [taylor]: Taking taylor expansion of 2.0 in k 0.423 * [taylor]: Taking taylor expansion of (* n PI) in k 0.423 * [taylor]: Taking taylor expansion of n in k 0.423 * [taylor]: Taking taylor expansion of PI in k 0.425 * [taylor]: Taking taylor expansion of 0 in n 0.431 * [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 0.431 * [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 0.431 * [taylor]: Taking taylor expansion of +nan.0 in n 0.431 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.431 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.431 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.431 * [taylor]: Taking taylor expansion of 0.5 in n 0.431 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.431 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.431 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.431 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.431 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.431 * [taylor]: Taking taylor expansion of 1.0 in n 0.431 * [taylor]: Taking taylor expansion of (log PI) in n 0.431 * [taylor]: Taking taylor expansion of PI in n 0.433 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.433 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.433 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.433 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.433 * [taylor]: Taking taylor expansion of 1.0 in n 0.433 * [taylor]: Taking taylor expansion of (log n) in n 0.433 * [taylor]: Taking taylor expansion of n in n 0.433 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.433 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.433 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.433 * [taylor]: Taking taylor expansion of 1.0 in n 0.434 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.434 * [taylor]: Taking taylor expansion of 2.0 in n 0.453 * [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 0.453 * [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 0.453 * [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 0.453 * [taylor]: Taking taylor expansion of +nan.0 in n 0.453 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.453 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.453 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.453 * [taylor]: Taking taylor expansion of 0.5 in n 0.453 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.453 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.453 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.453 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.453 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.453 * [taylor]: Taking taylor expansion of 1.0 in n 0.453 * [taylor]: Taking taylor expansion of (log PI) in n 0.454 * [taylor]: Taking taylor expansion of PI in n 0.455 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.455 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.455 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.455 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.455 * [taylor]: Taking taylor expansion of 1.0 in n 0.455 * [taylor]: Taking taylor expansion of (log n) in n 0.456 * [taylor]: Taking taylor expansion of n in n 0.456 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.456 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.456 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.456 * [taylor]: Taking taylor expansion of 1.0 in n 0.456 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.456 * [taylor]: Taking taylor expansion of 2.0 in n 0.462 * [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 0.462 * [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 0.462 * [taylor]: Taking taylor expansion of +nan.0 in n 0.462 * [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 0.462 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.462 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.462 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.462 * [taylor]: Taking taylor expansion of 0.5 in n 0.462 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.462 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.462 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.462 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.462 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.462 * [taylor]: Taking taylor expansion of 1.0 in n 0.462 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.462 * [taylor]: Taking taylor expansion of 2.0 in n 0.464 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.464 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.464 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.464 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.464 * [taylor]: Taking taylor expansion of 1.0 in n 0.464 * [taylor]: Taking taylor expansion of (log PI) in n 0.464 * [taylor]: Taking taylor expansion of PI in n 0.466 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.466 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.466 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.466 * [taylor]: Taking taylor expansion of 1.0 in n 0.466 * [taylor]: Taking taylor expansion of (log n) in n 0.466 * [taylor]: Taking taylor expansion of n in n 0.470 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.470 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.470 * [taylor]: Taking taylor expansion of 2.0 in n 0.470 * [taylor]: Taking taylor expansion of (* n PI) in n 0.470 * [taylor]: Taking taylor expansion of n in n 0.470 * [taylor]: Taking taylor expansion of PI in n 0.528 * [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 0.528 * [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 0.528 * [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 0.528 * [taylor]: Taking taylor expansion of +nan.0 in n 0.528 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.528 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.528 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 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 n 1.0) (pow PI 1.0)))) in n 0.528 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.528 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.528 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.528 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.528 * [taylor]: Taking taylor expansion of 1.0 in n 0.528 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.528 * [taylor]: Taking taylor expansion of 2.0 in n 0.530 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.530 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.530 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.530 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.530 * [taylor]: Taking taylor expansion of 1.0 in n 0.530 * [taylor]: Taking taylor expansion of (log n) in n 0.530 * [taylor]: Taking taylor expansion of n in n 0.531 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.531 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.531 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.531 * [taylor]: Taking taylor expansion of 1.0 in n 0.531 * [taylor]: Taking taylor expansion of (log PI) in n 0.531 * [taylor]: Taking taylor expansion of PI in n 0.536 * [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 0.536 * [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 0.537 * [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 0.537 * [taylor]: Taking taylor expansion of +nan.0 in n 0.537 * [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 0.537 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.537 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.537 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.537 * [taylor]: Taking taylor expansion of 0.5 in n 0.537 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.537 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.537 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.537 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.537 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.537 * [taylor]: Taking taylor expansion of 1.0 in n 0.537 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.537 * [taylor]: Taking taylor expansion of 2.0 in n 0.539 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.539 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.539 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.539 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.539 * [taylor]: Taking taylor expansion of 1.0 in n 0.539 * [taylor]: Taking taylor expansion of (log PI) in n 0.539 * [taylor]: Taking taylor expansion of PI in n 0.541 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.541 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.541 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.541 * [taylor]: Taking taylor expansion of 1.0 in n 0.541 * [taylor]: Taking taylor expansion of (log n) in n 0.541 * [taylor]: Taking taylor expansion of n in n 0.545 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.545 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.545 * [taylor]: Taking taylor expansion of 2.0 in n 0.545 * [taylor]: Taking taylor expansion of (* n PI) in n 0.545 * [taylor]: Taking taylor expansion of n in n 0.545 * [taylor]: Taking taylor expansion of PI in n 0.548 * [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 0.548 * [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 0.548 * [taylor]: Taking taylor expansion of +nan.0 in n 0.548 * [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 0.548 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.548 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.548 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.548 * [taylor]: Taking taylor expansion of 0.5 in n 0.548 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.548 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.548 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.548 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.548 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.548 * [taylor]: Taking taylor expansion of 1.0 in n 0.549 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.549 * [taylor]: Taking taylor expansion of 2.0 in n 0.550 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.550 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.550 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.550 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.550 * [taylor]: Taking taylor expansion of 1.0 in n 0.550 * [taylor]: Taking taylor expansion of (log PI) in n 0.550 * [taylor]: Taking taylor expansion of PI in n 0.552 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.552 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.552 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.552 * [taylor]: Taking taylor expansion of 1.0 in n 0.552 * [taylor]: Taking taylor expansion of (log n) in n 0.552 * [taylor]: Taking taylor expansion of n in n 0.557 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.557 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.557 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.557 * [taylor]: Taking taylor expansion of 2.0 in n 0.557 * [taylor]: Taking taylor expansion of (* n PI) in n 0.557 * [taylor]: Taking taylor expansion of n in n 0.557 * [taylor]: Taking taylor expansion of PI in n 0.638 * [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 0.638 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.638 * [taylor]: Taking taylor expansion of 1.0 in n 0.638 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.638 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.638 * [taylor]: Taking taylor expansion of k in n 0.638 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.638 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.638 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.638 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.638 * [taylor]: Taking taylor expansion of 0.5 in n 0.638 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.638 * [taylor]: Taking taylor expansion of 1.0 in n 0.638 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.638 * [taylor]: Taking taylor expansion of k in n 0.638 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.638 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.638 * [taylor]: Taking taylor expansion of 2.0 in n 0.638 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.638 * [taylor]: Taking taylor expansion of PI in n 0.638 * [taylor]: Taking taylor expansion of n in n 0.642 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.642 * [taylor]: Taking taylor expansion of 1.0 in k 0.642 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.642 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.642 * [taylor]: Taking taylor expansion of k in k 0.643 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.644 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.644 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.644 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.644 * [taylor]: Taking taylor expansion of 0.5 in k 0.644 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.644 * [taylor]: Taking taylor expansion of 1.0 in k 0.644 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.644 * [taylor]: Taking taylor expansion of k in k 0.644 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.644 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.644 * [taylor]: Taking taylor expansion of 2.0 in k 0.644 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.644 * [taylor]: Taking taylor expansion of PI in k 0.644 * [taylor]: Taking taylor expansion of n in k 0.645 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.645 * [taylor]: Taking taylor expansion of 1.0 in k 0.645 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.645 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.645 * [taylor]: Taking taylor expansion of k in k 0.646 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.646 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.646 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.646 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.646 * [taylor]: Taking taylor expansion of 0.5 in k 0.646 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.646 * [taylor]: Taking taylor expansion of 1.0 in k 0.646 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.646 * [taylor]: Taking taylor expansion of k in k 0.647 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.647 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.647 * [taylor]: Taking taylor expansion of 2.0 in k 0.647 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.647 * [taylor]: Taking taylor expansion of PI in k 0.647 * [taylor]: Taking taylor expansion of n in k 0.648 * [taylor]: Taking taylor expansion of 0 in n 0.649 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.649 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.649 * [taylor]: Taking taylor expansion of +nan.0 in n 0.649 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.649 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.649 * [taylor]: Taking taylor expansion of 0.5 in n 0.649 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.649 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.649 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.649 * [taylor]: Taking taylor expansion of 2.0 in n 0.649 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.649 * [taylor]: Taking taylor expansion of PI in n 0.649 * [taylor]: Taking taylor expansion of n in n 0.651 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.651 * [taylor]: Taking taylor expansion of 1.0 in n 0.651 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.651 * [taylor]: Taking taylor expansion of k in n 0.659 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.659 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.659 * [taylor]: Taking taylor expansion of +nan.0 in n 0.659 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.659 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.659 * [taylor]: Taking taylor expansion of 0.5 in n 0.659 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.659 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.659 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.659 * [taylor]: Taking taylor expansion of 2.0 in n 0.659 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.659 * [taylor]: Taking taylor expansion of PI in n 0.659 * [taylor]: Taking taylor expansion of n in n 0.661 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.661 * [taylor]: Taking taylor expansion of 1.0 in n 0.661 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.661 * [taylor]: Taking taylor expansion of k in n 0.684 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.684 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.684 * [taylor]: Taking taylor expansion of +nan.0 in n 0.684 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.684 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.684 * [taylor]: Taking taylor expansion of 0.5 in n 0.684 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.684 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.685 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.685 * [taylor]: Taking taylor expansion of 2.0 in n 0.685 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.685 * [taylor]: Taking taylor expansion of PI in n 0.685 * [taylor]: Taking taylor expansion of n in n 0.686 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.686 * [taylor]: Taking taylor expansion of 1.0 in n 0.686 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.686 * [taylor]: Taking taylor expansion of k in n 0.695 * [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 0.695 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.695 * [taylor]: Taking taylor expansion of 1.0 in n 0.695 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.695 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.695 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.695 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.695 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.695 * [taylor]: Taking taylor expansion of 0.5 in n 0.695 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.695 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.695 * [taylor]: Taking taylor expansion of k in n 0.695 * [taylor]: Taking taylor expansion of 1.0 in n 0.695 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.695 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.695 * [taylor]: Taking taylor expansion of -2.0 in n 0.695 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.695 * [taylor]: Taking taylor expansion of PI in n 0.695 * [taylor]: Taking taylor expansion of n in n 0.699 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.699 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.699 * [taylor]: Taking taylor expansion of -1 in n 0.699 * [taylor]: Taking taylor expansion of k in n 0.700 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.700 * [taylor]: Taking taylor expansion of 1.0 in k 0.700 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.700 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.700 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.700 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.700 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.700 * [taylor]: Taking taylor expansion of 0.5 in k 0.700 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.700 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.700 * [taylor]: Taking taylor expansion of k in k 0.701 * [taylor]: Taking taylor expansion of 1.0 in k 0.701 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.701 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.701 * [taylor]: Taking taylor expansion of -2.0 in k 0.701 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.701 * [taylor]: Taking taylor expansion of PI in k 0.701 * [taylor]: Taking taylor expansion of n in k 0.702 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.702 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.702 * [taylor]: Taking taylor expansion of -1 in k 0.702 * [taylor]: Taking taylor expansion of k in k 0.703 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.703 * [taylor]: Taking taylor expansion of 1.0 in k 0.703 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.703 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.703 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.703 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.703 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.703 * [taylor]: Taking taylor expansion of 0.5 in k 0.703 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.703 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.703 * [taylor]: Taking taylor expansion of k in k 0.704 * [taylor]: Taking taylor expansion of 1.0 in k 0.704 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.704 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.704 * [taylor]: Taking taylor expansion of -2.0 in k 0.704 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.704 * [taylor]: Taking taylor expansion of PI in k 0.704 * [taylor]: Taking taylor expansion of n in k 0.705 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.705 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.705 * [taylor]: Taking taylor expansion of -1 in k 0.705 * [taylor]: Taking taylor expansion of k in k 0.706 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.706 * [taylor]: Taking taylor expansion of +nan.0 in n 0.706 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.706 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.706 * [taylor]: Taking taylor expansion of 0.5 in n 0.706 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.706 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.706 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.706 * [taylor]: Taking taylor expansion of k in n 0.707 * [taylor]: Taking taylor expansion of 1.0 in n 0.707 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.707 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.707 * [taylor]: Taking taylor expansion of -2.0 in n 0.707 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.707 * [taylor]: Taking taylor expansion of PI in n 0.707 * [taylor]: Taking taylor expansion of n in n 0.716 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.716 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.716 * [taylor]: Taking taylor expansion of +nan.0 in n 0.716 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.716 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.716 * [taylor]: Taking taylor expansion of 0.5 in n 0.716 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.716 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.716 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.716 * [taylor]: Taking taylor expansion of k in n 0.716 * [taylor]: Taking taylor expansion of 1.0 in n 0.716 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.716 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.716 * [taylor]: Taking taylor expansion of -2.0 in n 0.716 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.716 * [taylor]: Taking taylor expansion of PI in n 0.716 * [taylor]: Taking taylor expansion of n in n 0.734 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.734 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.734 * [taylor]: Taking taylor expansion of +nan.0 in n 0.735 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.735 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.735 * [taylor]: Taking taylor expansion of 0.5 in n 0.735 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.735 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.735 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.735 * [taylor]: Taking taylor expansion of k in n 0.735 * [taylor]: Taking taylor expansion of 1.0 in n 0.735 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.735 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.735 * [taylor]: Taking taylor expansion of -2.0 in n 0.735 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.735 * [taylor]: Taking taylor expansion of PI in n 0.735 * [taylor]: Taking taylor expansion of n in n 0.744 * * * [progress]: simplifying candidates 0.747 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 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) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (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))) 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1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt 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))) (fma (- 0.5) (fma (* k (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n))) (* (* k (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log n))) (fma (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (pow (log (* 2.0 PI)) 2) (fma (* (* 0.125 (pow k 2)) (pow (log n) 2)) (pow (* (* 2.0 PI) n) 0.5) (fma (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (pow (* (* 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)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (fma (- k) +nan.0 (fma +nan.0 (pow k 2) (- +nan.0))) (fma +nan.0 (- (/ 1 k) (/ 1 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (fma +nan.0 (/ 1 k) (- +nan.0)) (/ (- +nan.0) (pow k 2))) (fma (- (* +nan.0 (* (pow k 2) (pow (log (* 2.0 PI)) 2)))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (fma +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)) (fma (- (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (log n))))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (fma +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (fma (- (* +nan.0 (* k (log (* 2.0 PI))))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (fma +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)) (fma (- (* +nan.0 (* k (log n)))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (fma (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0 (fma (- (* +nan.0 (pow k 2))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))) (fma (- +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) (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))) (fma (- +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)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) 0.854 * * * [progress]: adding candidates to table 1.316 * * [progress]: iteration 2 / 4 1.316 * * * [progress]: picking best candidate 1.341 * * * * [pick]: Picked # 1.341 * * * [progress]: localizing error 1.356 * * * [progress]: generating rewritten candidates 1.356 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.365 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 1.383 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 1.395 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 1.432 * * * [progress]: generating series expansions 1.432 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.433 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.434 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.434 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.434 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.434 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.434 * [taylor]: Taking taylor expansion of 0.5 in k 1.434 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.434 * [taylor]: Taking taylor expansion of 1.0 in k 1.434 * [taylor]: Taking taylor expansion of k in k 1.434 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.434 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.434 * [taylor]: Taking taylor expansion of 2.0 in k 1.434 * [taylor]: Taking taylor expansion of (* n PI) in k 1.434 * [taylor]: Taking taylor expansion of n in k 1.434 * [taylor]: Taking taylor expansion of PI in k 1.435 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.435 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.435 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.435 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.435 * [taylor]: Taking taylor expansion of 0.5 in n 1.435 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.435 * [taylor]: Taking taylor expansion of 1.0 in n 1.435 * [taylor]: Taking taylor expansion of k in n 1.435 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.435 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.435 * [taylor]: Taking taylor expansion of 2.0 in n 1.435 * [taylor]: Taking taylor expansion of (* n PI) in n 1.435 * [taylor]: Taking taylor expansion of n in n 1.435 * [taylor]: Taking taylor expansion of PI in n 1.441 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.441 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.441 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.441 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.441 * [taylor]: Taking taylor expansion of 0.5 in n 1.441 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.441 * [taylor]: Taking taylor expansion of 1.0 in n 1.441 * [taylor]: Taking taylor expansion of k in n 1.441 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.441 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.441 * [taylor]: Taking taylor expansion of 2.0 in n 1.441 * [taylor]: Taking taylor expansion of (* n PI) in n 1.441 * [taylor]: Taking taylor expansion of n in n 1.441 * [taylor]: Taking taylor expansion of PI in n 1.447 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.447 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.447 * [taylor]: Taking taylor expansion of 0.5 in k 1.447 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.447 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.447 * [taylor]: Taking taylor expansion of 1.0 in k 1.447 * [taylor]: Taking taylor expansion of k in k 1.447 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.447 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.447 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.447 * [taylor]: Taking taylor expansion of 2.0 in k 1.447 * [taylor]: Taking taylor expansion of PI in k 1.448 * [taylor]: Taking taylor expansion of (log n) in k 1.448 * [taylor]: Taking taylor expansion of n in k 1.458 * [taylor]: Taking taylor expansion of 0 in k 1.687 * [taylor]: Taking taylor expansion of 0 in k 1.706 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.706 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.706 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.706 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.706 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.706 * [taylor]: Taking taylor expansion of 0.5 in k 1.706 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.706 * [taylor]: Taking taylor expansion of 1.0 in k 1.706 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.706 * [taylor]: Taking taylor expansion of k in k 1.706 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.706 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.706 * [taylor]: Taking taylor expansion of 2.0 in k 1.706 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.706 * [taylor]: Taking taylor expansion of PI in k 1.706 * [taylor]: Taking taylor expansion of n in k 1.707 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.707 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.707 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.707 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.708 * [taylor]: Taking taylor expansion of 0.5 in n 1.708 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.708 * [taylor]: Taking taylor expansion of 1.0 in n 1.708 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.708 * [taylor]: Taking taylor expansion of k in n 1.708 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.708 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.708 * [taylor]: Taking taylor expansion of 2.0 in n 1.708 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.708 * [taylor]: Taking taylor expansion of PI in n 1.708 * [taylor]: Taking taylor expansion of n in n 1.711 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.711 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.711 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.711 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.712 * [taylor]: Taking taylor expansion of 0.5 in n 1.712 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.712 * [taylor]: Taking taylor expansion of 1.0 in n 1.712 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.712 * [taylor]: Taking taylor expansion of k in n 1.712 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.712 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.712 * [taylor]: Taking taylor expansion of 2.0 in n 1.712 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.712 * [taylor]: Taking taylor expansion of PI in n 1.712 * [taylor]: Taking taylor expansion of n in n 1.715 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.715 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.716 * [taylor]: Taking taylor expansion of 0.5 in k 1.716 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.716 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.716 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.716 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.716 * [taylor]: Taking taylor expansion of 2.0 in k 1.716 * [taylor]: Taking taylor expansion of PI in k 1.717 * [taylor]: Taking taylor expansion of (log n) in k 1.717 * [taylor]: Taking taylor expansion of n in k 1.717 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.717 * [taylor]: Taking taylor expansion of 1.0 in k 1.717 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.717 * [taylor]: Taking taylor expansion of k in k 1.727 * [taylor]: Taking taylor expansion of 0 in k 1.734 * [taylor]: Taking taylor expansion of 0 in k 1.743 * [taylor]: Taking taylor expansion of 0 in k 1.744 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.745 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.745 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.745 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.745 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.745 * [taylor]: Taking taylor expansion of 0.5 in k 1.745 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.745 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.745 * [taylor]: Taking taylor expansion of k in k 1.745 * [taylor]: Taking taylor expansion of 1.0 in k 1.745 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.745 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.745 * [taylor]: Taking taylor expansion of -2.0 in k 1.745 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.745 * [taylor]: Taking taylor expansion of PI in k 1.745 * [taylor]: Taking taylor expansion of n in k 1.746 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.746 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.746 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.746 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.746 * [taylor]: Taking taylor expansion of 0.5 in n 1.746 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.746 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.746 * [taylor]: Taking taylor expansion of k in n 1.746 * [taylor]: Taking taylor expansion of 1.0 in n 1.746 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.746 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.746 * [taylor]: Taking taylor expansion of -2.0 in n 1.746 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.746 * [taylor]: Taking taylor expansion of PI in n 1.746 * [taylor]: Taking taylor expansion of n in n 1.750 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.750 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.750 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.750 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.750 * [taylor]: Taking taylor expansion of 0.5 in n 1.750 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.750 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.750 * [taylor]: Taking taylor expansion of k in n 1.750 * [taylor]: Taking taylor expansion of 1.0 in n 1.750 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.750 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.750 * [taylor]: Taking taylor expansion of -2.0 in n 1.750 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.750 * [taylor]: Taking taylor expansion of PI in n 1.750 * [taylor]: Taking taylor expansion of n in n 1.754 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.754 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.754 * [taylor]: Taking taylor expansion of 0.5 in k 1.754 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.754 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.754 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.754 * [taylor]: Taking taylor expansion of k in k 1.754 * [taylor]: Taking taylor expansion of 1.0 in k 1.754 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.755 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.755 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.755 * [taylor]: Taking taylor expansion of -2.0 in k 1.755 * [taylor]: Taking taylor expansion of PI in k 1.756 * [taylor]: Taking taylor expansion of (log n) in k 1.756 * [taylor]: Taking taylor expansion of n in k 1.769 * [taylor]: Taking taylor expansion of 0 in k 1.776 * [taylor]: Taking taylor expansion of 0 in k 1.785 * [taylor]: Taking taylor expansion of 0 in k 1.786 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 1.786 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.786 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.786 * [taylor]: Taking taylor expansion of 1.0 in k 1.786 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.786 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.786 * [taylor]: Taking taylor expansion of k in k 1.788 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.788 * [taylor]: Taking taylor expansion of 1.0 in k 1.788 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.788 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.788 * [taylor]: Taking taylor expansion of k in k 1.799 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.799 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.800 * [taylor]: Taking taylor expansion of 1.0 in k 1.800 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.800 * [taylor]: Taking taylor expansion of k in k 1.801 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.801 * [taylor]: Taking taylor expansion of 1.0 in k 1.801 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.801 * [taylor]: Taking taylor expansion of k in k 1.811 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.812 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.812 * [taylor]: Taking taylor expansion of 1.0 in k 1.812 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.812 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.812 * [taylor]: Taking taylor expansion of -1 in k 1.812 * [taylor]: Taking taylor expansion of k in k 1.813 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.813 * [taylor]: Taking taylor expansion of 1.0 in k 1.813 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.813 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.813 * [taylor]: Taking taylor expansion of -1 in k 1.813 * [taylor]: Taking taylor expansion of k in k 1.826 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 1.826 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.826 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.826 * [taylor]: Taking taylor expansion of 2.0 in n 1.826 * [taylor]: Taking taylor expansion of (* n PI) in n 1.826 * [taylor]: Taking taylor expansion of n in n 1.826 * [taylor]: Taking taylor expansion of PI in n 1.826 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.826 * [taylor]: Taking taylor expansion of 2.0 in n 1.826 * [taylor]: Taking taylor expansion of (* n PI) in n 1.826 * [taylor]: Taking taylor expansion of n in n 1.826 * [taylor]: Taking taylor expansion of PI in n 1.839 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.839 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.839 * [taylor]: Taking taylor expansion of 2.0 in n 1.839 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.839 * [taylor]: Taking taylor expansion of PI in n 1.839 * [taylor]: Taking taylor expansion of n in n 1.839 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.839 * [taylor]: Taking taylor expansion of 2.0 in n 1.839 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.839 * [taylor]: Taking taylor expansion of PI in n 1.839 * [taylor]: Taking taylor expansion of n in n 1.852 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.852 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.852 * [taylor]: Taking taylor expansion of -2.0 in n 1.852 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.852 * [taylor]: Taking taylor expansion of PI in n 1.852 * [taylor]: Taking taylor expansion of n in n 1.852 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.852 * [taylor]: Taking taylor expansion of -2.0 in n 1.852 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.852 * [taylor]: Taking taylor expansion of PI in n 1.853 * [taylor]: Taking taylor expansion of n in n 1.861 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 1.861 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 1.862 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 1.862 * [taylor]: Taking taylor expansion of 1.0 in k 1.862 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1.862 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1.862 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1.862 * [taylor]: Taking taylor expansion of 1/4 in k 1.862 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 1.862 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.862 * [taylor]: Taking taylor expansion of k in k 1.863 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 1.863 * [taylor]: Taking taylor expansion of 1.0 in k 1.863 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1.863 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1.863 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1.863 * [taylor]: Taking taylor expansion of 1/4 in k 1.863 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 1.863 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.863 * [taylor]: Taking taylor expansion of k in k 1.925 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 1.925 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 1.925 * [taylor]: Taking taylor expansion of 1.0 in k 1.925 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 1.925 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1.925 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 1.925 * [taylor]: Taking taylor expansion of 1/4 in k 1.925 * [taylor]: Taking taylor expansion of (log k) in k 1.925 * [taylor]: Taking taylor expansion of k in k 1.926 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 1.926 * [taylor]: Taking taylor expansion of 1.0 in k 1.926 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 1.926 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1.926 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 1.926 * [taylor]: Taking taylor expansion of 1/4 in k 1.926 * [taylor]: Taking taylor expansion of (log k) in k 1.926 * [taylor]: Taking taylor expansion of k in k 1.981 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 1.981 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 1.981 * [taylor]: Taking taylor expansion of 1.0 in k 1.981 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 1.981 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1.981 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.981 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.981 * [taylor]: Taking taylor expansion of -1 in k 1.981 * [taylor]: Taking taylor expansion of k in k 1.988 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 1.988 * [taylor]: Taking taylor expansion of 1.0 in k 1.988 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 1.988 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1.988 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.988 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.988 * [taylor]: Taking taylor expansion of -1 in k 1.988 * [taylor]: Taking taylor expansion of k in k 2.029 * * * [progress]: simplifying candidates 2.038 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (log1p (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (- (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) 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[simplify]: iteration 0 : 1355 enodes (cost 5833 ) 2.080 * * [simplify]: iteration 1 : 5001 enodes (cost 5050 ) 2.099 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 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) (/ 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(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) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 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) (expm1 (/ 1.0 (sqrt (sqrt k)))) (log1p (/ 1.0 (sqrt (sqrt k)))) (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)))))) (- (fma (* 0.25 (pow k 2)) (* (* (log n) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (* (* 0.5 k) (+ (* (pow (exp 0.5) (log (* (* 2.0 PI) n))) (log (* 2.0 PI))) (* (log n) (pow (exp 0.5) (log (* (* 2.0 PI) 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)) (fma +nan.0 (pow k 2) (- +nan.0))) (+ (- (* +nan.0 (/ 1 (pow k 2)))) (fma +nan.0 (/ 1 k) (- (* +nan.0 (/ 1 (pow k 3)))))) (+ (- (* +nan.0 (/ 1 (pow k 2)))) (fma +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)))))) 2.108 * * * [progress]: adding candidates to table 2.890 * * [progress]: iteration 3 / 4 2.890 * * * [progress]: picking best candidate 2.913 * * * * [pick]: Picked # 2.913 * * * [progress]: localizing error 2.928 * * * [progress]: generating rewritten candidates 2.928 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 2.938 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 2.944 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 2.947 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 2.955 * * * [progress]: generating series expansions 2.955 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 2.956 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.956 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.956 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.956 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.956 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.956 * [taylor]: Taking taylor expansion of 0.5 in k 2.956 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.956 * [taylor]: Taking taylor expansion of 1.0 in k 2.956 * [taylor]: Taking taylor expansion of k in k 2.956 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.956 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.956 * [taylor]: Taking taylor expansion of 2.0 in k 2.956 * [taylor]: Taking taylor expansion of (* n PI) in k 2.956 * [taylor]: Taking taylor expansion of n in k 2.956 * [taylor]: Taking taylor expansion of PI in k 2.957 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.957 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.957 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.957 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.957 * [taylor]: Taking taylor expansion of 0.5 in n 2.957 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.957 * [taylor]: Taking taylor expansion of 1.0 in n 2.957 * [taylor]: Taking taylor expansion of k in n 2.957 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.957 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.958 * [taylor]: Taking taylor expansion of 2.0 in n 2.958 * [taylor]: Taking taylor expansion of (* n PI) in n 2.958 * [taylor]: Taking taylor expansion of n in n 2.958 * [taylor]: Taking taylor expansion of PI in n 2.963 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.963 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.963 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.963 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.963 * [taylor]: Taking taylor expansion of 0.5 in n 2.963 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.963 * [taylor]: Taking taylor expansion of 1.0 in n 2.963 * [taylor]: Taking taylor expansion of k in n 2.963 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.963 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.963 * [taylor]: Taking taylor expansion of 2.0 in n 2.963 * [taylor]: Taking taylor expansion of (* n PI) in n 2.963 * [taylor]: Taking taylor expansion of n in n 2.963 * [taylor]: Taking taylor expansion of PI in n 2.969 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.969 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.969 * [taylor]: Taking taylor expansion of 0.5 in k 2.969 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.969 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.969 * [taylor]: Taking taylor expansion of 1.0 in k 2.969 * [taylor]: Taking taylor expansion of k in k 2.969 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.969 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.969 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.969 * [taylor]: Taking taylor expansion of 2.0 in k 2.969 * [taylor]: Taking taylor expansion of PI in k 2.970 * [taylor]: Taking taylor expansion of (log n) in k 2.970 * [taylor]: Taking taylor expansion of n in k 2.980 * [taylor]: Taking taylor expansion of 0 in k 3.001 * [taylor]: Taking taylor expansion of 0 in k 3.020 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.020 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.020 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.020 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.020 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.020 * [taylor]: Taking taylor expansion of 0.5 in k 3.020 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.020 * [taylor]: Taking taylor expansion of 1.0 in k 3.020 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.020 * [taylor]: Taking taylor expansion of k in k 3.021 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.021 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.021 * [taylor]: Taking taylor expansion of 2.0 in k 3.021 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.021 * [taylor]: Taking taylor expansion of PI in k 3.021 * [taylor]: Taking taylor expansion of n in k 3.022 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.022 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.022 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.022 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.022 * [taylor]: Taking taylor expansion of 0.5 in n 3.022 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.022 * [taylor]: Taking taylor expansion of 1.0 in n 3.022 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.022 * [taylor]: Taking taylor expansion of k in n 3.022 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.022 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.022 * [taylor]: Taking taylor expansion of 2.0 in n 3.022 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.022 * [taylor]: Taking taylor expansion of PI in n 3.022 * [taylor]: Taking taylor expansion of n in n 3.026 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.026 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.026 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.026 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.026 * [taylor]: Taking taylor expansion of 0.5 in n 3.026 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.026 * [taylor]: Taking taylor expansion of 1.0 in n 3.026 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.026 * [taylor]: Taking taylor expansion of k in n 3.026 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.026 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.026 * [taylor]: Taking taylor expansion of 2.0 in n 3.026 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.026 * [taylor]: Taking taylor expansion of PI in n 3.026 * [taylor]: Taking taylor expansion of n in n 3.030 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.030 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.030 * [taylor]: Taking taylor expansion of 0.5 in k 3.030 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.030 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.030 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.030 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.030 * [taylor]: Taking taylor expansion of 2.0 in k 3.030 * [taylor]: Taking taylor expansion of PI in k 3.031 * [taylor]: Taking taylor expansion of (log n) in k 3.031 * [taylor]: Taking taylor expansion of n in k 3.031 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.031 * [taylor]: Taking taylor expansion of 1.0 in k 3.031 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.031 * [taylor]: Taking taylor expansion of k in k 3.041 * [taylor]: Taking taylor expansion of 0 in k 3.048 * [taylor]: Taking taylor expansion of 0 in k 3.058 * [taylor]: Taking taylor expansion of 0 in k 3.059 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.059 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.059 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.059 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.059 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.059 * [taylor]: Taking taylor expansion of 0.5 in k 3.059 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.059 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.059 * [taylor]: Taking taylor expansion of k in k 3.059 * [taylor]: Taking taylor expansion of 1.0 in k 3.059 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.059 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.059 * [taylor]: Taking taylor expansion of -2.0 in k 3.059 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.059 * [taylor]: Taking taylor expansion of PI in k 3.059 * [taylor]: Taking taylor expansion of n in k 3.060 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.060 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.060 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.060 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.060 * [taylor]: Taking taylor expansion of 0.5 in n 3.060 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.060 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.060 * [taylor]: Taking taylor expansion of k in n 3.060 * [taylor]: Taking taylor expansion of 1.0 in n 3.060 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.060 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.061 * [taylor]: Taking taylor expansion of -2.0 in n 3.061 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.061 * [taylor]: Taking taylor expansion of PI in n 3.061 * [taylor]: Taking taylor expansion of n in n 3.064 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.064 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.064 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.064 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.064 * [taylor]: Taking taylor expansion of 0.5 in n 3.064 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.064 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.064 * [taylor]: Taking taylor expansion of k in n 3.064 * [taylor]: Taking taylor expansion of 1.0 in n 3.064 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.064 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.065 * [taylor]: Taking taylor expansion of -2.0 in n 3.065 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.065 * [taylor]: Taking taylor expansion of PI in n 3.065 * [taylor]: Taking taylor expansion of n in n 3.068 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 3.069 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 3.069 * [taylor]: Taking taylor expansion of 0.5 in k 3.069 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 3.069 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.069 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.069 * [taylor]: Taking taylor expansion of k in k 3.069 * [taylor]: Taking taylor expansion of 1.0 in k 3.069 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.069 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.069 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.069 * [taylor]: Taking taylor expansion of -2.0 in k 3.069 * [taylor]: Taking taylor expansion of PI in k 3.070 * [taylor]: Taking taylor expansion of (log n) in k 3.070 * [taylor]: Taking taylor expansion of n in k 3.085 * [taylor]: Taking taylor expansion of 0 in k 3.092 * [taylor]: Taking taylor expansion of 0 in k 3.101 * [taylor]: Taking taylor expansion of 0 in k 3.102 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 3.102 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.102 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.102 * [taylor]: Taking taylor expansion of 2.0 in n 3.102 * [taylor]: Taking taylor expansion of (* n PI) in n 3.102 * [taylor]: Taking taylor expansion of n in n 3.102 * [taylor]: Taking taylor expansion of PI in n 3.102 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.102 * [taylor]: Taking taylor expansion of 2.0 in n 3.102 * [taylor]: Taking taylor expansion of (* n PI) in n 3.102 * [taylor]: Taking taylor expansion of n in n 3.102 * [taylor]: Taking taylor expansion of PI in n 3.115 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.115 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.115 * [taylor]: Taking taylor expansion of 2.0 in n 3.115 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.115 * [taylor]: Taking taylor expansion of PI in n 3.115 * [taylor]: Taking taylor expansion of n in n 3.115 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.115 * [taylor]: Taking taylor expansion of 2.0 in n 3.115 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.115 * [taylor]: Taking taylor expansion of PI in n 3.115 * [taylor]: Taking taylor expansion of n in n 3.124 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.124 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.124 * [taylor]: Taking taylor expansion of -2.0 in n 3.124 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.125 * [taylor]: Taking taylor expansion of PI in n 3.125 * [taylor]: Taking taylor expansion of n in n 3.125 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.125 * [taylor]: Taking taylor expansion of -2.0 in n 3.125 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.125 * [taylor]: Taking taylor expansion of PI in n 3.125 * [taylor]: Taking taylor expansion of n in n 3.134 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 3.134 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.134 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.134 * [taylor]: Taking taylor expansion of 1.0 in k 3.134 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.134 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.134 * [taylor]: Taking taylor expansion of k in k 3.135 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.135 * [taylor]: Taking taylor expansion of 1.0 in k 3.135 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.135 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.135 * [taylor]: Taking taylor expansion of k in k 3.147 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.147 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.147 * [taylor]: Taking taylor expansion of 1.0 in k 3.147 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.147 * [taylor]: Taking taylor expansion of k in k 3.148 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.148 * [taylor]: Taking taylor expansion of 1.0 in k 3.148 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.148 * [taylor]: Taking taylor expansion of k in k 3.158 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.158 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.159 * [taylor]: Taking taylor expansion of 1.0 in k 3.159 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.159 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.159 * [taylor]: Taking taylor expansion of -1 in k 3.159 * [taylor]: Taking taylor expansion of k in k 3.160 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.160 * [taylor]: Taking taylor expansion of 1.0 in k 3.160 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.160 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.160 * [taylor]: Taking taylor expansion of -1 in k 3.160 * [taylor]: Taking taylor expansion of k in k 3.178 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 3.178 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.178 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.178 * [taylor]: Taking taylor expansion of 1.0 in k 3.178 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.178 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.178 * [taylor]: Taking taylor expansion of k in k 3.180 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.180 * [taylor]: Taking taylor expansion of 1.0 in k 3.180 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.180 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.180 * [taylor]: Taking taylor expansion of k in k 3.191 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.191 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.191 * [taylor]: Taking taylor expansion of 1.0 in k 3.191 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.191 * [taylor]: Taking taylor expansion of k in k 3.192 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.192 * [taylor]: Taking taylor expansion of 1.0 in k 3.192 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.192 * [taylor]: Taking taylor expansion of k in k 3.203 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.203 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.203 * [taylor]: Taking taylor expansion of 1.0 in k 3.203 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.203 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.203 * [taylor]: Taking taylor expansion of -1 in k 3.203 * [taylor]: Taking taylor expansion of k in k 3.204 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.204 * [taylor]: Taking taylor expansion of 1.0 in k 3.204 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.205 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.205 * [taylor]: Taking taylor expansion of -1 in k 3.205 * [taylor]: Taking taylor expansion of k in k 3.217 * * * [progress]: simplifying candidates 3.219 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 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) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 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))))) 3.226 * * [simplify]: iteration 0 : 579 enodes (cost 912 ) 3.236 * * [simplify]: iteration 1 : 2248 enodes (cost 843 ) 3.276 * * [simplify]: iteration 2 : 5001 enodes (cost 807 ) 3.280 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 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)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 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) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (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) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (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) (fma (- 0.5) (fma (* k (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n))) (* (* k (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log n))) (fma (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (pow (log (* 2.0 PI)) 2) (fma (* (* 0.125 (pow k 2)) (pow (log n) 2)) (pow (* (* 2.0 PI) n) 0.5) (fma (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (pow (* (* 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) (fma (- k) +nan.0 (fma +nan.0 (pow k 2) (- +nan.0))) (fma +nan.0 (- (/ 1 k) (/ 1 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (/ +nan.0 k) (- (fma +nan.0 1 (/ +nan.0 (pow k 2))))) (fma (- k) +nan.0 (fma +nan.0 (pow k 2) (- +nan.0))) (fma +nan.0 (- (/ 1 k) (/ 1 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (/ +nan.0 k) (- (fma +nan.0 1 (/ +nan.0 (pow k 2))))) 3.281 * * * [progress]: adding candidates to table 3.730 * * [progress]: iteration 4 / 4 3.730 * * * [progress]: picking best candidate 3.747 * * * * [pick]: Picked # 3.747 * * * [progress]: localizing error 3.774 * * * [progress]: generating rewritten candidates 3.774 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.784 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2 1 1) 3.785 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1 2 1 1 2) 3.785 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1 2 1 1 1) 3.788 * * * [progress]: generating series expansions 3.788 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.789 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.789 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.789 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.789 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.789 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.789 * [taylor]: Taking taylor expansion of 0.5 in k 3.789 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.789 * [taylor]: Taking taylor expansion of 1.0 in k 3.789 * [taylor]: Taking taylor expansion of k in k 3.789 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.789 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.789 * [taylor]: Taking taylor expansion of 2.0 in k 3.789 * [taylor]: Taking taylor expansion of (* n PI) in k 3.789 * [taylor]: Taking taylor expansion of n in k 3.789 * [taylor]: Taking taylor expansion of PI in k 3.790 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.790 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.790 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.790 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.790 * [taylor]: Taking taylor expansion of 0.5 in n 3.790 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.790 * [taylor]: Taking taylor expansion of 1.0 in n 3.790 * [taylor]: Taking taylor expansion of k in n 3.790 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.790 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.790 * [taylor]: Taking taylor expansion of 2.0 in n 3.791 * [taylor]: Taking taylor expansion of (* n PI) in n 3.791 * [taylor]: Taking taylor expansion of n in n 3.791 * [taylor]: Taking taylor expansion of PI in n 3.796 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.796 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.796 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.796 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.796 * [taylor]: Taking taylor expansion of 0.5 in n 3.796 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.796 * [taylor]: Taking taylor expansion of 1.0 in n 3.796 * [taylor]: Taking taylor expansion of k in n 3.796 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.796 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.796 * [taylor]: Taking taylor expansion of 2.0 in n 3.796 * [taylor]: Taking taylor expansion of (* n PI) in n 3.796 * [taylor]: Taking taylor expansion of n in n 3.796 * [taylor]: Taking taylor expansion of PI in n 3.802 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.802 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.802 * [taylor]: Taking taylor expansion of 0.5 in k 3.802 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.802 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.802 * [taylor]: Taking taylor expansion of 1.0 in k 3.802 * [taylor]: Taking taylor expansion of k in k 3.802 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.802 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.802 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.802 * [taylor]: Taking taylor expansion of 2.0 in k 3.802 * [taylor]: Taking taylor expansion of PI in k 3.803 * [taylor]: Taking taylor expansion of (log n) in k 3.803 * [taylor]: Taking taylor expansion of n in k 3.813 * [taylor]: Taking taylor expansion of 0 in k 3.829 * [taylor]: Taking taylor expansion of 0 in k 3.854 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.854 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.854 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.854 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.854 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.854 * [taylor]: Taking taylor expansion of 0.5 in k 3.855 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.855 * [taylor]: Taking taylor expansion of 1.0 in k 3.855 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.855 * [taylor]: Taking taylor expansion of k in k 3.855 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.855 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.855 * [taylor]: Taking taylor expansion of 2.0 in k 3.855 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.855 * [taylor]: Taking taylor expansion of PI in k 3.855 * [taylor]: Taking taylor expansion of n in k 3.856 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.856 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.856 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.856 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.856 * [taylor]: Taking taylor expansion of 0.5 in n 3.856 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.856 * [taylor]: Taking taylor expansion of 1.0 in n 3.856 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.856 * [taylor]: Taking taylor expansion of k in n 3.856 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.856 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.856 * [taylor]: Taking taylor expansion of 2.0 in n 3.856 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.856 * [taylor]: Taking taylor expansion of PI in n 3.856 * [taylor]: Taking taylor expansion of n in n 3.860 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.860 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.860 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.860 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.860 * [taylor]: Taking taylor expansion of 0.5 in n 3.860 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.860 * [taylor]: Taking taylor expansion of 1.0 in n 3.860 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.860 * [taylor]: Taking taylor expansion of k in n 3.860 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.860 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.860 * [taylor]: Taking taylor expansion of 2.0 in n 3.860 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.860 * [taylor]: Taking taylor expansion of PI in n 3.860 * [taylor]: Taking taylor expansion of n in n 3.864 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.864 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.865 * [taylor]: Taking taylor expansion of 0.5 in k 3.865 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.865 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.865 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.865 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.865 * [taylor]: Taking taylor expansion of 2.0 in k 3.865 * [taylor]: Taking taylor expansion of PI in k 3.866 * [taylor]: Taking taylor expansion of (log n) in k 3.866 * [taylor]: Taking taylor expansion of n in k 3.866 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.866 * [taylor]: Taking taylor expansion of 1.0 in k 3.866 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.866 * [taylor]: Taking taylor expansion of k in k 3.875 * [taylor]: Taking taylor expansion of 0 in k 3.883 * [taylor]: Taking taylor expansion of 0 in k 3.892 * [taylor]: Taking taylor expansion of 0 in k 3.893 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.893 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.894 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.894 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.894 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.894 * [taylor]: Taking taylor expansion of 0.5 in k 3.894 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.894 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.894 * [taylor]: Taking taylor expansion of k in k 3.894 * [taylor]: Taking taylor expansion of 1.0 in k 3.894 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.894 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.894 * [taylor]: Taking taylor expansion of -2.0 in k 3.894 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.894 * [taylor]: Taking taylor expansion of PI in k 3.894 * [taylor]: Taking taylor expansion of n in k 3.895 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.895 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.895 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.895 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.895 * [taylor]: Taking taylor expansion of 0.5 in n 3.895 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.895 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.895 * [taylor]: Taking taylor expansion of k in n 3.895 * [taylor]: Taking taylor expansion of 1.0 in n 3.895 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.895 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.895 * [taylor]: Taking taylor expansion of -2.0 in n 3.895 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.895 * [taylor]: Taking taylor expansion of PI in n 3.895 * [taylor]: Taking taylor expansion of n in n 3.899 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.899 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.899 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.899 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.899 * [taylor]: Taking taylor expansion of 0.5 in n 3.899 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.899 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.899 * [taylor]: Taking taylor expansion of k in n 3.899 * [taylor]: Taking taylor expansion of 1.0 in n 3.899 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.899 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.899 * [taylor]: Taking taylor expansion of -2.0 in n 3.899 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.899 * [taylor]: Taking taylor expansion of PI in n 3.899 * [taylor]: Taking taylor expansion of n in n 3.903 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 3.903 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 3.903 * [taylor]: Taking taylor expansion of 0.5 in k 3.903 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 3.903 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.903 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.903 * [taylor]: Taking taylor expansion of k in k 3.903 * [taylor]: Taking taylor expansion of 1.0 in k 3.903 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.903 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.903 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.903 * [taylor]: Taking taylor expansion of -2.0 in k 3.903 * [taylor]: Taking taylor expansion of PI in k 3.904 * [taylor]: Taking taylor expansion of (log n) in k 3.904 * [taylor]: Taking taylor expansion of n in k 3.914 * [taylor]: Taking taylor expansion of 0 in k 3.921 * [taylor]: Taking taylor expansion of 0 in k 3.935 * [taylor]: Taking taylor expansion of 0 in k 3.936 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2 1 1) 3.936 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 3.937 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 3.937 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 3.937 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 3.937 * [taylor]: Taking taylor expansion of 1/3 in k 3.937 * [taylor]: Taking taylor expansion of (log k) in k 3.937 * [taylor]: Taking taylor expansion of k in k 3.937 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 3.937 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 3.937 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 3.937 * [taylor]: Taking taylor expansion of 1/3 in k 3.937 * [taylor]: Taking taylor expansion of (log k) in k 3.937 * [taylor]: Taking taylor expansion of k in k 3.986 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 3.986 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.986 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.986 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.986 * [taylor]: Taking taylor expansion of 1/3 in k 3.986 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.986 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.986 * [taylor]: Taking taylor expansion of k in k 3.987 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 3.987 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 3.987 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 3.987 * [taylor]: Taking taylor expansion of 1/3 in k 3.987 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.987 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.987 * [taylor]: Taking taylor expansion of k in k 4.044 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in (k) around 0 4.044 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 4.044 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.044 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.044 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.044 * [taylor]: Taking taylor expansion of 1/3 in k 4.044 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.044 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.044 * [taylor]: Taking taylor expansion of k in k 4.045 * [taylor]: Taking taylor expansion of (cbrt -1) in k 4.045 * [taylor]: Taking taylor expansion of -1 in k 4.046 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 4.046 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.046 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.046 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.046 * [taylor]: Taking taylor expansion of 1/3 in k 4.046 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.046 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.046 * [taylor]: Taking taylor expansion of k in k 4.047 * [taylor]: Taking taylor expansion of (cbrt -1) in k 4.047 * [taylor]: Taking taylor expansion of -1 in k 4.115 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1 2 1 1 2) 4.115 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 4.115 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 4.115 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 4.115 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 4.115 * [taylor]: Taking taylor expansion of 1/3 in k 4.116 * [taylor]: Taking taylor expansion of (log k) in k 4.116 * [taylor]: Taking taylor expansion of k in k 4.116 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 4.116 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 4.116 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 4.116 * [taylor]: Taking taylor expansion of 1/3 in k 4.116 * [taylor]: Taking taylor expansion of (log k) in k 4.116 * [taylor]: Taking taylor expansion of k in k 4.171 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 4.171 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.171 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.171 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.171 * [taylor]: Taking taylor expansion of 1/3 in k 4.171 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.171 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.171 * [taylor]: Taking taylor expansion of k in k 4.172 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.172 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.172 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.172 * [taylor]: Taking taylor expansion of 1/3 in k 4.172 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.172 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.172 * [taylor]: Taking taylor expansion of k in k 4.223 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in (k) around 0 4.224 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 4.224 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.224 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.224 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.224 * [taylor]: Taking taylor expansion of 1/3 in k 4.224 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.224 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.224 * [taylor]: Taking taylor expansion of k in k 4.225 * [taylor]: Taking taylor expansion of (cbrt -1) in k 4.225 * [taylor]: Taking taylor expansion of -1 in k 4.226 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 4.226 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.226 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.226 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.226 * [taylor]: Taking taylor expansion of 1/3 in k 4.226 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.226 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.226 * [taylor]: Taking taylor expansion of k in k 4.227 * [taylor]: Taking taylor expansion of (cbrt -1) in k 4.227 * [taylor]: Taking taylor expansion of -1 in k 4.295 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1 2 1 1 1) 4.296 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 4.296 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 4.296 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 4.296 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 4.296 * [taylor]: Taking taylor expansion of 1/3 in k 4.296 * [taylor]: Taking taylor expansion of (log k) in k 4.296 * [taylor]: Taking taylor expansion of k in k 4.296 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 4.296 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 4.296 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 4.296 * [taylor]: Taking taylor expansion of 1/3 in k 4.296 * [taylor]: Taking taylor expansion of (log k) in k 4.296 * [taylor]: Taking taylor expansion of k in k 4.352 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 4.352 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.352 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.352 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.352 * [taylor]: Taking taylor expansion of 1/3 in k 4.352 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.352 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.352 * [taylor]: Taking taylor expansion of k in k 4.353 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.353 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.353 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.353 * [taylor]: Taking taylor expansion of 1/3 in k 4.353 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.353 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.353 * [taylor]: Taking taylor expansion of k in k 4.410 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in (k) around 0 4.410 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 4.410 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.410 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.410 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.410 * [taylor]: Taking taylor expansion of 1/3 in k 4.410 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.410 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.410 * [taylor]: Taking taylor expansion of k in k 4.411 * [taylor]: Taking taylor expansion of (cbrt -1) in k 4.411 * [taylor]: Taking taylor expansion of -1 in k 4.412 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 4.412 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 4.412 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 4.412 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 4.412 * [taylor]: Taking taylor expansion of 1/3 in k 4.412 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 4.412 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.412 * [taylor]: Taking taylor expansion of k in k 4.413 * [taylor]: Taking taylor expansion of (cbrt -1) in k 4.413 * [taylor]: Taking taylor expansion of -1 in k 4.480 * * * [progress]: simplifying candidates 4.481 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (cbrt k)) (log1p (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)) (expm1 (cbrt k)) (log1p (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)) (expm1 (cbrt k)) (log1p (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)) 4.486 * * [simplify]: iteration 0 : 364 enodes (cost 467 ) 4.492 * * [simplify]: iteration 1 : 1244 enodes (cost 442 ) 4.515 * * [simplify]: iteration 2 : 5001 enodes (cost 412 ) 4.518 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 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)) (expm1 (cbrt k)) (log1p (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)) (expm1 (cbrt k)) (log1p (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)) (expm1 (cbrt k)) (log1p (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)) (+ (fma (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (pow (* (* 2.0 PI) n) 0.5)) (- (* (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (+ (pow (log (* 2.0 PI)) 2) (pow (log n) 2))) (* (* (* 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)) 4.518 * * * [progress]: adding candidates to table 4.922 * [progress]: [Phase 3 of 3] Extracting. 4.922 * * [regime]: Finding splitpoints for: (# # # # # # #) 4.924 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 4.924 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 4.954 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 4.986 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 5.019 * * * [regime]: Found split indices: #