17.744 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.148 * * * [progress]: [2/2] Setting up program. 0.151 * [progress]: [Phase 2 of 3] Improving. 0.151 * [simplify]: Simplifying using # : (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.153 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.155 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.156 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.159 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.165 * * [simplify]: iteration 4 : 1044 enodes (cost 8 ) 0.187 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.187 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.188 * * [progress]: iteration 1 / 4 0.188 * * * [progress]: picking best candidate 0.190 * * * * [pick]: Picked # 0.190 * * * [progress]: localizing error 0.203 * * * [progress]: generating rewritten candidates 0.203 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.212 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.219 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.224 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.247 * * * [progress]: generating series expansions 0.247 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.248 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.248 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.248 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.248 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.248 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.249 * [taylor]: Taking taylor expansion of 0.5 in k 0.249 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.249 * [taylor]: Taking taylor expansion of 1.0 in k 0.249 * [taylor]: Taking taylor expansion of k in k 0.249 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.249 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.249 * [taylor]: Taking taylor expansion of 2.0 in k 0.249 * [taylor]: Taking taylor expansion of (* n PI) in k 0.249 * [taylor]: Taking taylor expansion of n in k 0.249 * [taylor]: Taking taylor expansion of PI in k 0.250 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.250 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.250 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.250 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.250 * [taylor]: Taking taylor expansion of 0.5 in n 0.250 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.250 * [taylor]: Taking taylor expansion of 1.0 in n 0.250 * [taylor]: Taking taylor expansion of k in n 0.250 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.250 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.250 * [taylor]: Taking taylor expansion of 2.0 in n 0.250 * [taylor]: Taking taylor expansion of (* n PI) in n 0.250 * [taylor]: Taking taylor expansion of n in n 0.250 * [taylor]: Taking taylor expansion of PI in n 0.255 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.255 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.255 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.255 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.255 * [taylor]: Taking taylor expansion of 0.5 in n 0.255 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.255 * [taylor]: Taking taylor expansion of 1.0 in n 0.255 * [taylor]: Taking taylor expansion of k in n 0.255 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.255 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.255 * [taylor]: Taking taylor expansion of 2.0 in n 0.255 * [taylor]: Taking taylor expansion of (* n PI) in n 0.255 * [taylor]: Taking taylor expansion of n in n 0.255 * [taylor]: Taking taylor expansion of PI in n 0.261 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.261 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.261 * [taylor]: Taking taylor expansion of 0.5 in k 0.261 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.261 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.261 * [taylor]: Taking taylor expansion of 1.0 in k 0.261 * [taylor]: Taking taylor expansion of k in k 0.261 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.261 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.261 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.261 * [taylor]: Taking taylor expansion of 2.0 in k 0.261 * [taylor]: Taking taylor expansion of PI in k 0.262 * [taylor]: Taking taylor expansion of (log n) in k 0.262 * [taylor]: Taking taylor expansion of n in k 0.271 * [taylor]: Taking taylor expansion of 0 in k 0.287 * [taylor]: Taking taylor expansion of 0 in k 0.309 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.309 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.309 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.309 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.309 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.309 * [taylor]: Taking taylor expansion of 0.5 in k 0.309 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.309 * [taylor]: Taking taylor expansion of 1.0 in k 0.309 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.309 * [taylor]: Taking taylor expansion of k in k 0.310 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.310 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.310 * [taylor]: Taking taylor expansion of 2.0 in k 0.310 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.310 * [taylor]: Taking taylor expansion of PI in k 0.310 * [taylor]: Taking taylor expansion of n in k 0.311 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.311 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.311 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.311 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.311 * [taylor]: Taking taylor expansion of 0.5 in n 0.311 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.311 * [taylor]: Taking taylor expansion of 1.0 in n 0.311 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.311 * [taylor]: Taking taylor expansion of k in n 0.311 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.311 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.311 * [taylor]: Taking taylor expansion of 2.0 in n 0.311 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.311 * [taylor]: Taking taylor expansion of PI in n 0.311 * [taylor]: Taking taylor expansion of n in n 0.315 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.315 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.315 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.315 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.315 * [taylor]: Taking taylor expansion of 0.5 in n 0.315 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.315 * [taylor]: Taking taylor expansion of 1.0 in n 0.315 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.315 * [taylor]: Taking taylor expansion of k in n 0.315 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.315 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.315 * [taylor]: Taking taylor expansion of 2.0 in n 0.315 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.315 * [taylor]: Taking taylor expansion of PI in n 0.315 * [taylor]: Taking taylor expansion of n in n 0.319 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.319 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.319 * [taylor]: Taking taylor expansion of 0.5 in k 0.319 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.319 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.319 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.319 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.319 * [taylor]: Taking taylor expansion of 2.0 in k 0.319 * [taylor]: Taking taylor expansion of PI in k 0.320 * [taylor]: Taking taylor expansion of (log n) in k 0.320 * [taylor]: Taking taylor expansion of n in k 0.320 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.320 * [taylor]: Taking taylor expansion of 1.0 in k 0.320 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.320 * [taylor]: Taking taylor expansion of k in k 0.329 * [taylor]: Taking taylor expansion of 0 in k 0.336 * [taylor]: Taking taylor expansion of 0 in k 0.345 * [taylor]: Taking taylor expansion of 0 in k 0.346 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.346 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.346 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.346 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.346 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.346 * [taylor]: Taking taylor expansion of 0.5 in k 0.346 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.346 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.346 * [taylor]: Taking taylor expansion of k in k 0.347 * [taylor]: Taking taylor expansion of 1.0 in k 0.347 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.347 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.347 * [taylor]: Taking taylor expansion of -2.0 in k 0.347 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.347 * [taylor]: Taking taylor expansion of PI in k 0.347 * [taylor]: Taking taylor expansion of n in k 0.347 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.347 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.348 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.348 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.348 * [taylor]: Taking taylor expansion of 0.5 in n 0.348 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.348 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.348 * [taylor]: Taking taylor expansion of k in n 0.348 * [taylor]: Taking taylor expansion of 1.0 in n 0.348 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.348 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.348 * [taylor]: Taking taylor expansion of -2.0 in n 0.348 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.348 * [taylor]: Taking taylor expansion of PI in n 0.348 * [taylor]: Taking taylor expansion of n in n 0.351 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.351 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.351 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.351 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.351 * [taylor]: Taking taylor expansion of 0.5 in n 0.351 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.351 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.351 * [taylor]: Taking taylor expansion of k in n 0.351 * [taylor]: Taking taylor expansion of 1.0 in n 0.351 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.351 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.351 * [taylor]: Taking taylor expansion of -2.0 in n 0.352 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.352 * [taylor]: Taking taylor expansion of PI in n 0.352 * [taylor]: Taking taylor expansion of n in n 0.355 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.355 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.355 * [taylor]: Taking taylor expansion of 0.5 in k 0.355 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.355 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.355 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.355 * [taylor]: Taking taylor expansion of k in k 0.355 * [taylor]: Taking taylor expansion of 1.0 in k 0.356 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.356 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.356 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.356 * [taylor]: Taking taylor expansion of -2.0 in k 0.356 * [taylor]: Taking taylor expansion of PI in k 0.356 * [taylor]: Taking taylor expansion of (log n) in k 0.357 * [taylor]: Taking taylor expansion of n in k 0.365 * [taylor]: Taking taylor expansion of 0 in k 0.372 * [taylor]: Taking taylor expansion of 0 in k 0.381 * [taylor]: Taking taylor expansion of 0 in k 0.382 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.382 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.382 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.382 * [taylor]: Taking taylor expansion of 2.0 in n 0.382 * [taylor]: Taking taylor expansion of (* n PI) in n 0.382 * [taylor]: Taking taylor expansion of n in n 0.382 * [taylor]: Taking taylor expansion of PI in n 0.382 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.382 * [taylor]: Taking taylor expansion of 2.0 in n 0.382 * [taylor]: Taking taylor expansion of (* n PI) in n 0.382 * [taylor]: Taking taylor expansion of n in n 0.382 * [taylor]: Taking taylor expansion of PI in n 0.397 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.397 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.397 * [taylor]: Taking taylor expansion of 2.0 in n 0.397 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.397 * [taylor]: Taking taylor expansion of PI in n 0.397 * [taylor]: Taking taylor expansion of n in n 0.398 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.398 * [taylor]: Taking taylor expansion of 2.0 in n 0.398 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.398 * [taylor]: Taking taylor expansion of PI in n 0.398 * [taylor]: Taking taylor expansion of n in n 0.406 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.406 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.406 * [taylor]: Taking taylor expansion of -2.0 in n 0.406 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.406 * [taylor]: Taking taylor expansion of PI in n 0.406 * [taylor]: Taking taylor expansion of n in n 0.407 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.407 * [taylor]: Taking taylor expansion of -2.0 in n 0.407 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.407 * [taylor]: Taking taylor expansion of PI in n 0.407 * [taylor]: Taking taylor expansion of n in n 0.415 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.415 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.415 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.415 * [taylor]: Taking taylor expansion of 1.0 in k 0.415 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.415 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.415 * [taylor]: Taking taylor expansion of k in k 0.416 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.417 * [taylor]: Taking taylor expansion of 1.0 in k 0.417 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.417 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.417 * [taylor]: Taking taylor expansion of k in k 0.427 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.428 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.428 * [taylor]: Taking taylor expansion of 1.0 in k 0.428 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.428 * [taylor]: Taking taylor expansion of k in k 0.429 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.429 * [taylor]: Taking taylor expansion of 1.0 in k 0.429 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.429 * [taylor]: Taking taylor expansion of k in k 0.439 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.439 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.439 * [taylor]: Taking taylor expansion of 1.0 in k 0.439 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.439 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.439 * [taylor]: Taking taylor expansion of -1 in k 0.439 * [taylor]: Taking taylor expansion of k in k 0.441 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.441 * [taylor]: Taking taylor expansion of 1.0 in k 0.441 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.441 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.441 * [taylor]: Taking taylor expansion of -1 in k 0.441 * [taylor]: Taking taylor expansion of k in k 0.452 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.452 * [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 0.452 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.452 * [taylor]: Taking taylor expansion of 1.0 in n 0.453 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.453 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.453 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.453 * [taylor]: Taking taylor expansion of k in n 0.453 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.453 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.453 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.453 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.453 * [taylor]: Taking taylor expansion of 0.5 in n 0.453 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.453 * [taylor]: Taking taylor expansion of 1.0 in n 0.453 * [taylor]: Taking taylor expansion of k in n 0.453 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.453 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.453 * [taylor]: Taking taylor expansion of 2.0 in n 0.453 * [taylor]: Taking taylor expansion of (* n PI) in n 0.453 * [taylor]: Taking taylor expansion of n in n 0.453 * [taylor]: Taking taylor expansion of PI in n 0.458 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.458 * [taylor]: Taking taylor expansion of 1.0 in k 0.458 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.458 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.458 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.458 * [taylor]: Taking taylor expansion of k in k 0.459 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.459 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.460 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.460 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.460 * [taylor]: Taking taylor expansion of 0.5 in k 0.460 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.460 * [taylor]: Taking taylor expansion of 1.0 in k 0.460 * [taylor]: Taking taylor expansion of k in k 0.460 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.460 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.460 * [taylor]: Taking taylor expansion of 2.0 in k 0.460 * [taylor]: Taking taylor expansion of (* n PI) in k 0.460 * [taylor]: Taking taylor expansion of n in k 0.460 * [taylor]: Taking taylor expansion of PI in k 0.461 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.461 * [taylor]: Taking taylor expansion of 1.0 in k 0.461 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.461 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.461 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.461 * [taylor]: Taking taylor expansion of k in k 0.462 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.462 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.462 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.462 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.462 * [taylor]: Taking taylor expansion of 0.5 in k 0.462 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.462 * [taylor]: Taking taylor expansion of 1.0 in k 0.462 * [taylor]: Taking taylor expansion of k in k 0.462 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.462 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.462 * [taylor]: Taking taylor expansion of 2.0 in k 0.462 * [taylor]: Taking taylor expansion of (* n PI) in k 0.462 * [taylor]: Taking taylor expansion of n in k 0.462 * [taylor]: Taking taylor expansion of PI in k 0.467 * [taylor]: Taking taylor expansion of 0 in n 0.472 * [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 0.472 * [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 0.472 * [taylor]: Taking taylor expansion of +nan.0 in n 0.472 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.472 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.472 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.472 * [taylor]: Taking taylor expansion of 0.5 in n 0.472 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.472 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.472 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.472 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.472 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.472 * [taylor]: Taking taylor expansion of 1.0 in n 0.472 * [taylor]: Taking taylor expansion of (log PI) in n 0.472 * [taylor]: Taking taylor expansion of PI in n 0.474 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.474 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.474 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.474 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.474 * [taylor]: Taking taylor expansion of 1.0 in n 0.474 * [taylor]: Taking taylor expansion of (log n) in n 0.474 * [taylor]: Taking taylor expansion of n in n 0.475 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.475 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.475 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.475 * [taylor]: Taking taylor expansion of 1.0 in n 0.475 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.475 * [taylor]: Taking taylor expansion of 2.0 in n 0.493 * [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 0.494 * [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 0.494 * [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 0.494 * [taylor]: Taking taylor expansion of +nan.0 in n 0.494 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.494 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.494 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.494 * [taylor]: Taking taylor expansion of 0.5 in n 0.494 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.494 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.494 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.494 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.494 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.494 * [taylor]: Taking taylor expansion of 1.0 in n 0.494 * [taylor]: Taking taylor expansion of (log PI) in n 0.494 * [taylor]: Taking taylor expansion of PI in n 0.496 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.496 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.496 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.496 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.496 * [taylor]: Taking taylor expansion of 1.0 in n 0.496 * [taylor]: Taking taylor expansion of (log n) in n 0.496 * [taylor]: Taking taylor expansion of n in n 0.496 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.496 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.496 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.496 * [taylor]: Taking taylor expansion of 1.0 in n 0.496 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.496 * [taylor]: Taking taylor expansion of 2.0 in n 0.501 * [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 0.501 * [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 0.501 * [taylor]: Taking taylor expansion of +nan.0 in n 0.501 * [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 0.502 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.502 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.502 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.502 * [taylor]: Taking taylor expansion of 0.5 in n 0.502 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.502 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.502 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.502 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.502 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.502 * [taylor]: Taking taylor expansion of 1.0 in n 0.502 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.502 * [taylor]: Taking taylor expansion of 2.0 in n 0.503 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.503 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.503 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.503 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.503 * [taylor]: Taking taylor expansion of 1.0 in n 0.503 * [taylor]: Taking taylor expansion of (log PI) in n 0.504 * [taylor]: Taking taylor expansion of PI in n 0.505 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.505 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.505 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.505 * [taylor]: Taking taylor expansion of 1.0 in n 0.505 * [taylor]: Taking taylor expansion of (log n) in n 0.505 * [taylor]: Taking taylor expansion of n in n 0.509 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.509 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.509 * [taylor]: Taking taylor expansion of 2.0 in n 0.509 * [taylor]: Taking taylor expansion of (* n PI) in n 0.510 * [taylor]: Taking taylor expansion of n in n 0.510 * [taylor]: Taking taylor expansion of PI in n 0.561 * [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 0.561 * [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 0.561 * [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 0.561 * [taylor]: Taking taylor expansion of +nan.0 in n 0.561 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.561 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.561 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.561 * [taylor]: Taking taylor expansion of 0.5 in n 0.561 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.561 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.561 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.561 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.561 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.561 * [taylor]: Taking taylor expansion of 1.0 in n 0.561 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.561 * [taylor]: Taking taylor expansion of 2.0 in n 0.563 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.563 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.563 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.563 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.563 * [taylor]: Taking taylor expansion of 1.0 in n 0.563 * [taylor]: Taking taylor expansion of (log n) in n 0.563 * [taylor]: Taking taylor expansion of n in n 0.564 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.564 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.564 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.564 * [taylor]: Taking taylor expansion of 1.0 in n 0.564 * [taylor]: Taking taylor expansion of (log PI) in n 0.564 * [taylor]: Taking taylor expansion of PI in n 0.569 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (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 0.569 * [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 0.569 * [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 0.569 * [taylor]: Taking taylor expansion of +nan.0 in n 0.569 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 0.569 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.569 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.569 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.569 * [taylor]: Taking taylor expansion of 0.5 in n 0.569 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.569 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.569 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.569 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.569 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.569 * [taylor]: Taking taylor expansion of 1.0 in n 0.569 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.569 * [taylor]: Taking taylor expansion of 2.0 in n 0.571 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.571 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.571 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.571 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.571 * [taylor]: Taking taylor expansion of 1.0 in n 0.571 * [taylor]: Taking taylor expansion of (log PI) in n 0.571 * [taylor]: Taking taylor expansion of PI in n 0.573 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.573 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.573 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.573 * [taylor]: Taking taylor expansion of 1.0 in n 0.573 * [taylor]: Taking taylor expansion of (log n) in n 0.573 * [taylor]: Taking taylor expansion of n in n 0.577 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.577 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.577 * [taylor]: Taking taylor expansion of 2.0 in n 0.577 * [taylor]: Taking taylor expansion of (* n PI) in n 0.577 * [taylor]: Taking taylor expansion of n in n 0.577 * [taylor]: Taking taylor expansion of PI in n 0.580 * [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 0.580 * [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 0.580 * [taylor]: Taking taylor expansion of +nan.0 in n 0.580 * [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 0.580 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.580 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.580 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.580 * [taylor]: Taking taylor expansion of 0.5 in n 0.580 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.580 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.580 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.580 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.580 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.580 * [taylor]: Taking taylor expansion of 1.0 in n 0.580 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.580 * [taylor]: Taking taylor expansion of 2.0 in n 0.582 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.582 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.582 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.582 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.582 * [taylor]: Taking taylor expansion of 1.0 in n 0.582 * [taylor]: Taking taylor expansion of (log PI) in n 0.582 * [taylor]: Taking taylor expansion of PI in n 0.584 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.584 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.584 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.584 * [taylor]: Taking taylor expansion of 1.0 in n 0.584 * [taylor]: Taking taylor expansion of (log n) in n 0.584 * [taylor]: Taking taylor expansion of n in n 0.588 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.588 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.588 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.588 * [taylor]: Taking taylor expansion of 2.0 in n 0.588 * [taylor]: Taking taylor expansion of (* n PI) in n 0.588 * [taylor]: Taking taylor expansion of n in n 0.588 * [taylor]: Taking taylor expansion of PI in n 0.662 * [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 0.662 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.662 * [taylor]: Taking taylor expansion of 1.0 in n 0.662 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.662 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.662 * [taylor]: Taking taylor expansion of k in n 0.662 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.662 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.662 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.662 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.662 * [taylor]: Taking taylor expansion of 0.5 in n 0.662 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.662 * [taylor]: Taking taylor expansion of 1.0 in n 0.662 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.662 * [taylor]: Taking taylor expansion of k in n 0.662 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.662 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.662 * [taylor]: Taking taylor expansion of 2.0 in n 0.662 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.662 * [taylor]: Taking taylor expansion of PI in n 0.662 * [taylor]: Taking taylor expansion of n in n 0.666 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.666 * [taylor]: Taking taylor expansion of 1.0 in k 0.666 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.666 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.666 * [taylor]: Taking taylor expansion of k in k 0.667 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.667 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.667 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.667 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.667 * [taylor]: Taking taylor expansion of 0.5 in k 0.667 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.667 * [taylor]: Taking taylor expansion of 1.0 in k 0.667 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.667 * [taylor]: Taking taylor expansion of k in k 0.668 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.668 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.668 * [taylor]: Taking taylor expansion of 2.0 in k 0.668 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.668 * [taylor]: Taking taylor expansion of PI in k 0.668 * [taylor]: Taking taylor expansion of n in k 0.669 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.669 * [taylor]: Taking taylor expansion of 1.0 in k 0.669 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.669 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.669 * [taylor]: Taking taylor expansion of k in k 0.670 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.670 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.670 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.670 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.670 * [taylor]: Taking taylor expansion of 0.5 in k 0.670 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.670 * [taylor]: Taking taylor expansion of 1.0 in k 0.670 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.670 * [taylor]: Taking taylor expansion of k in k 0.670 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.670 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.670 * [taylor]: Taking taylor expansion of 2.0 in k 0.670 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.670 * [taylor]: Taking taylor expansion of PI in k 0.670 * [taylor]: Taking taylor expansion of n in k 0.672 * [taylor]: Taking taylor expansion of 0 in n 0.672 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.672 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.673 * [taylor]: Taking taylor expansion of +nan.0 in n 0.673 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.673 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.673 * [taylor]: Taking taylor expansion of 0.5 in n 0.673 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.673 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.673 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.673 * [taylor]: Taking taylor expansion of 2.0 in n 0.673 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.673 * [taylor]: Taking taylor expansion of PI in n 0.673 * [taylor]: Taking taylor expansion of n in n 0.674 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.674 * [taylor]: Taking taylor expansion of 1.0 in n 0.674 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.674 * [taylor]: Taking taylor expansion of k in n 0.682 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.682 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.682 * [taylor]: Taking taylor expansion of +nan.0 in n 0.682 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.682 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.682 * [taylor]: Taking taylor expansion of 0.5 in n 0.682 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.682 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.682 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.682 * [taylor]: Taking taylor expansion of 2.0 in n 0.682 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.682 * [taylor]: Taking taylor expansion of PI in n 0.682 * [taylor]: Taking taylor expansion of n in n 0.684 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.684 * [taylor]: Taking taylor expansion of 1.0 in n 0.684 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.684 * [taylor]: Taking taylor expansion of k in n 0.700 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.700 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.700 * [taylor]: Taking taylor expansion of +nan.0 in n 0.700 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.700 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.700 * [taylor]: Taking taylor expansion of 0.5 in n 0.700 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.700 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.700 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.700 * [taylor]: Taking taylor expansion of 2.0 in n 0.700 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.700 * [taylor]: Taking taylor expansion of PI in n 0.700 * [taylor]: Taking taylor expansion of n in n 0.701 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.701 * [taylor]: Taking taylor expansion of 1.0 in n 0.701 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.701 * [taylor]: Taking taylor expansion of k in n 0.710 * [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 0.710 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.710 * [taylor]: Taking taylor expansion of 1.0 in n 0.710 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.710 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.710 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.710 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.710 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.710 * [taylor]: Taking taylor expansion of 0.5 in n 0.710 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.710 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.710 * [taylor]: Taking taylor expansion of k in n 0.710 * [taylor]: Taking taylor expansion of 1.0 in n 0.710 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.710 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.710 * [taylor]: Taking taylor expansion of -2.0 in n 0.710 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.710 * [taylor]: Taking taylor expansion of PI in n 0.710 * [taylor]: Taking taylor expansion of n in n 0.714 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.714 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.714 * [taylor]: Taking taylor expansion of -1 in n 0.714 * [taylor]: Taking taylor expansion of k in n 0.715 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.715 * [taylor]: Taking taylor expansion of 1.0 in k 0.715 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.715 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.715 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.715 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.715 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.715 * [taylor]: Taking taylor expansion of 0.5 in k 0.715 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.715 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.715 * [taylor]: Taking taylor expansion of k in k 0.715 * [taylor]: Taking taylor expansion of 1.0 in k 0.715 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.715 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.715 * [taylor]: Taking taylor expansion of -2.0 in k 0.715 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.715 * [taylor]: Taking taylor expansion of PI in k 0.715 * [taylor]: Taking taylor expansion of n in k 0.716 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.716 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.716 * [taylor]: Taking taylor expansion of -1 in k 0.716 * [taylor]: Taking taylor expansion of k in k 0.717 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.717 * [taylor]: Taking taylor expansion of 1.0 in k 0.717 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.717 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.717 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.718 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.718 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.718 * [taylor]: Taking taylor expansion of 0.5 in k 0.718 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.718 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.718 * [taylor]: Taking taylor expansion of k in k 0.718 * [taylor]: Taking taylor expansion of 1.0 in k 0.718 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.718 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.718 * [taylor]: Taking taylor expansion of -2.0 in k 0.718 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.718 * [taylor]: Taking taylor expansion of PI in k 0.718 * [taylor]: Taking taylor expansion of n in k 0.722 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.722 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.722 * [taylor]: Taking taylor expansion of -1 in k 0.722 * [taylor]: Taking taylor expansion of k in k 0.724 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.724 * [taylor]: Taking taylor expansion of +nan.0 in n 0.724 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.724 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.724 * [taylor]: Taking taylor expansion of 0.5 in n 0.724 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.724 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.724 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.724 * [taylor]: Taking taylor expansion of k in n 0.724 * [taylor]: Taking taylor expansion of 1.0 in n 0.724 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.724 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.724 * [taylor]: Taking taylor expansion of -2.0 in n 0.724 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.724 * [taylor]: Taking taylor expansion of PI in n 0.724 * [taylor]: Taking taylor expansion of n in n 0.733 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.733 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.733 * [taylor]: Taking taylor expansion of +nan.0 in n 0.733 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.733 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.733 * [taylor]: Taking taylor expansion of 0.5 in n 0.733 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.733 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.733 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.733 * [taylor]: Taking taylor expansion of k in n 0.733 * [taylor]: Taking taylor expansion of 1.0 in n 0.733 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.733 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.733 * [taylor]: Taking taylor expansion of -2.0 in n 0.733 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.733 * [taylor]: Taking taylor expansion of PI in n 0.733 * [taylor]: Taking taylor expansion of n in n 0.750 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.751 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.751 * [taylor]: Taking taylor expansion of +nan.0 in n 0.751 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.751 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.751 * [taylor]: Taking taylor expansion of 0.5 in n 0.751 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.751 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.751 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.751 * [taylor]: Taking taylor expansion of k in n 0.751 * [taylor]: Taking taylor expansion of 1.0 in n 0.751 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.751 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.751 * [taylor]: Taking taylor expansion of -2.0 in n 0.751 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.751 * [taylor]: Taking taylor expansion of PI in n 0.751 * [taylor]: Taking taylor expansion of n in n 0.760 * * * [progress]: simplifying candidates 0.762 * [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))))))))) 0.861 * * * [progress]: adding candidates to table 1.286 * * [progress]: iteration 2 / 4 1.286 * * * [progress]: picking best candidate 1.309 * * * * [pick]: Picked # 1.309 * * * [progress]: localizing error 1.324 * * * [progress]: generating rewritten candidates 1.324 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.337 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 1.350 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 1.357 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1) 1.375 * * * [progress]: generating series expansions 1.375 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.375 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 1.375 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 1.376 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.376 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.376 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 1.376 * [taylor]: Taking taylor expansion of 0.25 in k 1.376 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.376 * [taylor]: Taking taylor expansion of 1.0 in k 1.376 * [taylor]: Taking taylor expansion of k in k 1.376 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.376 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.376 * [taylor]: Taking taylor expansion of 2.0 in k 1.376 * [taylor]: Taking taylor expansion of (* n PI) in k 1.376 * [taylor]: Taking taylor expansion of n in k 1.376 * [taylor]: Taking taylor expansion of PI in k 1.377 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.377 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.377 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.377 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.377 * [taylor]: Taking taylor expansion of 0.25 in n 1.377 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.377 * [taylor]: Taking taylor expansion of 1.0 in n 1.377 * [taylor]: Taking taylor expansion of k in n 1.377 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.377 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.377 * [taylor]: Taking taylor expansion of 2.0 in n 1.377 * [taylor]: Taking taylor expansion of (* n PI) in n 1.377 * [taylor]: Taking taylor expansion of n in n 1.377 * [taylor]: Taking taylor expansion of PI in n 1.386 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.386 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.386 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.386 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.386 * [taylor]: Taking taylor expansion of 0.25 in n 1.387 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.387 * [taylor]: Taking taylor expansion of 1.0 in n 1.387 * [taylor]: Taking taylor expansion of k in n 1.387 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.387 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.387 * [taylor]: Taking taylor expansion of 2.0 in n 1.387 * [taylor]: Taking taylor expansion of (* n PI) in n 1.387 * [taylor]: Taking taylor expansion of n in n 1.387 * [taylor]: Taking taylor expansion of PI in n 1.392 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.392 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.392 * [taylor]: Taking taylor expansion of 0.25 in k 1.392 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.392 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.392 * [taylor]: Taking taylor expansion of 1.0 in k 1.392 * [taylor]: Taking taylor expansion of k in k 1.392 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.392 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.392 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.392 * [taylor]: Taking taylor expansion of 2.0 in k 1.392 * [taylor]: Taking taylor expansion of PI in k 1.393 * [taylor]: Taking taylor expansion of (log n) in k 1.393 * [taylor]: Taking taylor expansion of n in k 1.402 * [taylor]: Taking taylor expansion of 0 in k 1.417 * [taylor]: Taking taylor expansion of 0 in k 1.436 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 1.436 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 1.436 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.436 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.436 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 1.436 * [taylor]: Taking taylor expansion of 0.25 in k 1.436 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.436 * [taylor]: Taking taylor expansion of 1.0 in k 1.436 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.436 * [taylor]: Taking taylor expansion of k in k 1.437 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.437 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.437 * [taylor]: Taking taylor expansion of 2.0 in k 1.437 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.437 * [taylor]: Taking taylor expansion of PI in k 1.437 * [taylor]: Taking taylor expansion of n in k 1.438 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.438 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.438 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.438 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.438 * [taylor]: Taking taylor expansion of 0.25 in n 1.438 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.438 * [taylor]: Taking taylor expansion of 1.0 in n 1.438 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.438 * [taylor]: Taking taylor expansion of k in n 1.438 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.438 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.438 * [taylor]: Taking taylor expansion of 2.0 in n 1.438 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.438 * [taylor]: Taking taylor expansion of PI in n 1.438 * [taylor]: Taking taylor expansion of n in n 1.442 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.442 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.442 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.442 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.442 * [taylor]: Taking taylor expansion of 0.25 in n 1.442 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.442 * [taylor]: Taking taylor expansion of 1.0 in n 1.442 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.442 * [taylor]: Taking taylor expansion of k in n 1.442 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.442 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.442 * [taylor]: Taking taylor expansion of 2.0 in n 1.442 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.442 * [taylor]: Taking taylor expansion of PI in n 1.442 * [taylor]: Taking taylor expansion of n in n 1.446 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.446 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.446 * [taylor]: Taking taylor expansion of 0.25 in k 1.446 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.446 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.446 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.446 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.446 * [taylor]: Taking taylor expansion of 2.0 in k 1.446 * [taylor]: Taking taylor expansion of PI in k 1.447 * [taylor]: Taking taylor expansion of (log n) in k 1.447 * [taylor]: Taking taylor expansion of n in k 1.447 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.447 * [taylor]: Taking taylor expansion of 1.0 in k 1.447 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.447 * [taylor]: Taking taylor expansion of k in k 1.457 * [taylor]: Taking taylor expansion of 0 in k 1.464 * [taylor]: Taking taylor expansion of 0 in k 1.477 * [taylor]: Taking taylor expansion of 0 in k 1.479 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 1.479 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 1.479 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.479 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.479 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 1.479 * [taylor]: Taking taylor expansion of 0.25 in k 1.479 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.479 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.479 * [taylor]: Taking taylor expansion of k in k 1.479 * [taylor]: Taking taylor expansion of 1.0 in k 1.479 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.479 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.479 * [taylor]: Taking taylor expansion of -2.0 in k 1.479 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.479 * [taylor]: Taking taylor expansion of PI in k 1.479 * [taylor]: Taking taylor expansion of n in k 1.480 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.480 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.480 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.480 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.480 * [taylor]: Taking taylor expansion of 0.25 in n 1.480 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.480 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.480 * [taylor]: Taking taylor expansion of k in n 1.480 * [taylor]: Taking taylor expansion of 1.0 in n 1.480 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.480 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.480 * [taylor]: Taking taylor expansion of -2.0 in n 1.480 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.480 * [taylor]: Taking taylor expansion of PI in n 1.480 * [taylor]: Taking taylor expansion of n in n 1.484 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.484 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.484 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.484 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.484 * [taylor]: Taking taylor expansion of 0.25 in n 1.484 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.484 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.484 * [taylor]: Taking taylor expansion of k in n 1.484 * [taylor]: Taking taylor expansion of 1.0 in n 1.484 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.484 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.484 * [taylor]: Taking taylor expansion of -2.0 in n 1.484 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.484 * [taylor]: Taking taylor expansion of PI in n 1.484 * [taylor]: Taking taylor expansion of n in n 1.488 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.488 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.488 * [taylor]: Taking taylor expansion of 0.25 in k 1.488 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.488 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.488 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.488 * [taylor]: Taking taylor expansion of k in k 1.488 * [taylor]: Taking taylor expansion of 1.0 in k 1.489 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.489 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.489 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.489 * [taylor]: Taking taylor expansion of -2.0 in k 1.489 * [taylor]: Taking taylor expansion of PI in k 1.490 * [taylor]: Taking taylor expansion of (log n) in k 1.490 * [taylor]: Taking taylor expansion of n in k 1.499 * [taylor]: Taking taylor expansion of 0 in k 1.506 * [taylor]: Taking taylor expansion of 0 in k 1.515 * [taylor]: Taking taylor expansion of 0 in k 1.516 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 1.517 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 1.517 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 1.517 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.517 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.517 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 1.517 * [taylor]: Taking taylor expansion of 0.25 in k 1.517 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.517 * [taylor]: Taking taylor expansion of 1.0 in k 1.517 * [taylor]: Taking taylor expansion of k in k 1.517 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.517 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.517 * [taylor]: Taking taylor expansion of 2.0 in k 1.517 * [taylor]: Taking taylor expansion of (* n PI) in k 1.517 * [taylor]: Taking taylor expansion of n in k 1.517 * [taylor]: Taking taylor expansion of PI in k 1.518 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.518 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.518 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.518 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.518 * [taylor]: Taking taylor expansion of 0.25 in n 1.518 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.518 * [taylor]: Taking taylor expansion of 1.0 in n 1.518 * [taylor]: Taking taylor expansion of k in n 1.518 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.518 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.518 * [taylor]: Taking taylor expansion of 2.0 in n 1.518 * [taylor]: Taking taylor expansion of (* n PI) in n 1.518 * [taylor]: Taking taylor expansion of n in n 1.518 * [taylor]: Taking taylor expansion of PI in n 1.523 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.523 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.523 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.523 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.524 * [taylor]: Taking taylor expansion of 0.25 in n 1.524 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.524 * [taylor]: Taking taylor expansion of 1.0 in n 1.524 * [taylor]: Taking taylor expansion of k in n 1.524 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.524 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.524 * [taylor]: Taking taylor expansion of 2.0 in n 1.524 * [taylor]: Taking taylor expansion of (* n PI) in n 1.524 * [taylor]: Taking taylor expansion of n in n 1.524 * [taylor]: Taking taylor expansion of PI in n 1.529 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.529 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.529 * [taylor]: Taking taylor expansion of 0.25 in k 1.529 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.529 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.529 * [taylor]: Taking taylor expansion of 1.0 in k 1.529 * [taylor]: Taking taylor expansion of k in k 1.529 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.529 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.529 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.529 * [taylor]: Taking taylor expansion of 2.0 in k 1.529 * [taylor]: Taking taylor expansion of PI in k 1.530 * [taylor]: Taking taylor expansion of (log n) in k 1.530 * [taylor]: Taking taylor expansion of n in k 1.539 * [taylor]: Taking taylor expansion of 0 in k 1.559 * [taylor]: Taking taylor expansion of 0 in k 1.577 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 1.577 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 1.577 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.577 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.577 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 1.577 * [taylor]: Taking taylor expansion of 0.25 in k 1.577 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.577 * [taylor]: Taking taylor expansion of 1.0 in k 1.577 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.577 * [taylor]: Taking taylor expansion of k in k 1.577 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.577 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.577 * [taylor]: Taking taylor expansion of 2.0 in k 1.578 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.578 * [taylor]: Taking taylor expansion of PI in k 1.578 * [taylor]: Taking taylor expansion of n in k 1.579 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.579 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.579 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.579 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.579 * [taylor]: Taking taylor expansion of 0.25 in n 1.579 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.579 * [taylor]: Taking taylor expansion of 1.0 in n 1.579 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.579 * [taylor]: Taking taylor expansion of k in n 1.579 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.579 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.579 * [taylor]: Taking taylor expansion of 2.0 in n 1.579 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.579 * [taylor]: Taking taylor expansion of PI in n 1.579 * [taylor]: Taking taylor expansion of n in n 1.582 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.582 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.582 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.582 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.582 * [taylor]: Taking taylor expansion of 0.25 in n 1.582 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.582 * [taylor]: Taking taylor expansion of 1.0 in n 1.582 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.582 * [taylor]: Taking taylor expansion of k in n 1.583 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.583 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.583 * [taylor]: Taking taylor expansion of 2.0 in n 1.583 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.583 * [taylor]: Taking taylor expansion of PI in n 1.583 * [taylor]: Taking taylor expansion of n in n 1.586 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.586 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.586 * [taylor]: Taking taylor expansion of 0.25 in k 1.586 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.586 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.586 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.586 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.586 * [taylor]: Taking taylor expansion of 2.0 in k 1.586 * [taylor]: Taking taylor expansion of PI in k 1.587 * [taylor]: Taking taylor expansion of (log n) in k 1.587 * [taylor]: Taking taylor expansion of n in k 1.587 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.587 * [taylor]: Taking taylor expansion of 1.0 in k 1.587 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.587 * [taylor]: Taking taylor expansion of k in k 1.597 * [taylor]: Taking taylor expansion of 0 in k 1.603 * [taylor]: Taking taylor expansion of 0 in k 1.612 * [taylor]: Taking taylor expansion of 0 in k 1.614 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 1.614 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 1.614 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.614 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.614 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 1.614 * [taylor]: Taking taylor expansion of 0.25 in k 1.614 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.614 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.614 * [taylor]: Taking taylor expansion of k in k 1.614 * [taylor]: Taking taylor expansion of 1.0 in k 1.614 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.614 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.614 * [taylor]: Taking taylor expansion of -2.0 in k 1.614 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.614 * [taylor]: Taking taylor expansion of PI in k 1.614 * [taylor]: Taking taylor expansion of n in k 1.615 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.615 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.615 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.615 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.615 * [taylor]: Taking taylor expansion of 0.25 in n 1.615 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.615 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.615 * [taylor]: Taking taylor expansion of k in n 1.615 * [taylor]: Taking taylor expansion of 1.0 in n 1.615 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.615 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.615 * [taylor]: Taking taylor expansion of -2.0 in n 1.615 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.615 * [taylor]: Taking taylor expansion of PI in n 1.615 * [taylor]: Taking taylor expansion of n in n 1.619 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.619 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.619 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.619 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.619 * [taylor]: Taking taylor expansion of 0.25 in n 1.619 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.619 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.619 * [taylor]: Taking taylor expansion of k in n 1.619 * [taylor]: Taking taylor expansion of 1.0 in n 1.619 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.619 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.619 * [taylor]: Taking taylor expansion of -2.0 in n 1.619 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.619 * [taylor]: Taking taylor expansion of PI in n 1.619 * [taylor]: Taking taylor expansion of n in n 1.623 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.623 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.623 * [taylor]: Taking taylor expansion of 0.25 in k 1.623 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.623 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.623 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.623 * [taylor]: Taking taylor expansion of k in k 1.623 * [taylor]: Taking taylor expansion of 1.0 in k 1.623 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.623 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.623 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.623 * [taylor]: Taking taylor expansion of -2.0 in k 1.623 * [taylor]: Taking taylor expansion of PI in k 1.624 * [taylor]: Taking taylor expansion of (log n) in k 1.624 * [taylor]: Taking taylor expansion of n in k 1.633 * [taylor]: Taking taylor expansion of 0 in k 1.643 * [taylor]: Taking taylor expansion of 0 in k 1.651 * [taylor]: Taking taylor expansion of 0 in k 1.652 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 1.653 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.653 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.653 * [taylor]: Taking taylor expansion of 2.0 in n 1.653 * [taylor]: Taking taylor expansion of (* n PI) in n 1.653 * [taylor]: Taking taylor expansion of n in n 1.653 * [taylor]: Taking taylor expansion of PI in n 1.653 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.653 * [taylor]: Taking taylor expansion of 2.0 in n 1.653 * [taylor]: Taking taylor expansion of (* n PI) in n 1.653 * [taylor]: Taking taylor expansion of n in n 1.653 * [taylor]: Taking taylor expansion of PI in n 1.665 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.665 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.665 * [taylor]: Taking taylor expansion of 2.0 in n 1.665 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.665 * [taylor]: Taking taylor expansion of PI in n 1.665 * [taylor]: Taking taylor expansion of n in n 1.665 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.665 * [taylor]: Taking taylor expansion of 2.0 in n 1.665 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.665 * [taylor]: Taking taylor expansion of PI in n 1.665 * [taylor]: Taking taylor expansion of n in n 1.674 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.674 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.674 * [taylor]: Taking taylor expansion of -2.0 in n 1.674 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.674 * [taylor]: Taking taylor expansion of PI in n 1.674 * [taylor]: Taking taylor expansion of n in n 1.674 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.674 * [taylor]: Taking taylor expansion of -2.0 in n 1.674 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.675 * [taylor]: Taking taylor expansion of PI in n 1.675 * [taylor]: Taking taylor expansion of n in n 1.683 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1) 1.683 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.683 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.683 * [taylor]: Taking taylor expansion of 2.0 in n 1.683 * [taylor]: Taking taylor expansion of (* n PI) in n 1.683 * [taylor]: Taking taylor expansion of n in n 1.683 * [taylor]: Taking taylor expansion of PI in n 1.683 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.683 * [taylor]: Taking taylor expansion of 2.0 in n 1.683 * [taylor]: Taking taylor expansion of (* n PI) in n 1.683 * [taylor]: Taking taylor expansion of n in n 1.684 * [taylor]: Taking taylor expansion of PI in n 1.695 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.695 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.695 * [taylor]: Taking taylor expansion of 2.0 in n 1.695 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.695 * [taylor]: Taking taylor expansion of PI in n 1.695 * [taylor]: Taking taylor expansion of n in n 1.696 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.696 * [taylor]: Taking taylor expansion of 2.0 in n 1.696 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.696 * [taylor]: Taking taylor expansion of PI in n 1.696 * [taylor]: Taking taylor expansion of n in n 1.704 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.704 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.704 * [taylor]: Taking taylor expansion of -2.0 in n 1.704 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.704 * [taylor]: Taking taylor expansion of PI in n 1.704 * [taylor]: Taking taylor expansion of n in n 1.705 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.705 * [taylor]: Taking taylor expansion of -2.0 in n 1.705 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.705 * [taylor]: Taking taylor expansion of PI in n 1.705 * [taylor]: Taking taylor expansion of n in n 1.716 * * * [progress]: simplifying candidates 1.719 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* 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(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (- 1.0 k)) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (expm1 (* (* 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 (* (* 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) (fma (- 0.25) (fma (* k (log (* 2.0 PI))) (pow (exp 0.25) (log (* (* 2.0 PI) n))) (* (* k (pow (exp 0.25) (log (* (* 2.0 PI) n)))) (log n))) (fma (* (* 0.03125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.25)) (pow (log (* 2.0 PI)) 2) (fma (* 0.0625 (pow k 2)) (* (* (log (* 2.0 PI)) (log n)) (pow (* (* 2.0 PI) n) 0.25)) (+ (* (* (* (pow k 2) (pow (exp 0.25) (log (* (* 2.0 PI) n)))) (pow (log n) 2)) 0.03125) (pow (* (* 2.0 PI) n) 0.25))))) (pow (* (* 2.0 PI) n) (* 0.25 (- 1.0 k))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- 0.25) (fma (* k (log (* 2.0 PI))) (pow (exp 0.25) (log (* (* 2.0 PI) n))) (* (* k (pow (exp 0.25) (log (* (* 2.0 PI) n)))) (log n))) (fma (* (* 0.03125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.25)) (pow (log (* 2.0 PI)) 2) (fma (* 0.0625 (pow k 2)) (* (* (log (* 2.0 PI)) (log n)) (pow (* (* 2.0 PI) n) 0.25)) (+ (* (* (* (pow k 2) (pow (exp 0.25) (log (* (* 2.0 PI) n)))) (pow (log n) 2)) 0.03125) (pow (* (* 2.0 PI) n) 0.25))))) (pow (* (* 2.0 PI) n) (* 0.25 (- 1.0 k))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) 1.790 * * * [progress]: adding candidates to table 2.457 * * [progress]: iteration 3 / 4 2.457 * * * [progress]: picking best candidate 2.481 * * * * [pick]: Picked # 2.481 * * * [progress]: localizing error 2.497 * * * [progress]: generating rewritten candidates 2.497 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.551 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 2) 2.552 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 2 2) 2.552 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 2 1) 2.555 * * * [progress]: generating series expansions 2.555 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.556 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.556 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.556 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.556 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.556 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.556 * [taylor]: Taking taylor expansion of 0.5 in k 2.556 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.556 * [taylor]: Taking taylor expansion of 1.0 in k 2.556 * [taylor]: Taking taylor expansion of k in k 2.556 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.556 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.556 * [taylor]: Taking taylor expansion of 2.0 in k 2.556 * [taylor]: Taking taylor expansion of (* n PI) in k 2.556 * [taylor]: Taking taylor expansion of n in k 2.556 * [taylor]: Taking taylor expansion of PI in k 2.557 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.557 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.558 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.558 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.558 * [taylor]: Taking taylor expansion of 0.5 in n 2.558 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.558 * [taylor]: Taking taylor expansion of 1.0 in n 2.558 * [taylor]: Taking taylor expansion of k in n 2.558 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.558 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.558 * [taylor]: Taking taylor expansion of 2.0 in n 2.558 * [taylor]: Taking taylor expansion of (* n PI) in n 2.558 * [taylor]: Taking taylor expansion of n in n 2.558 * [taylor]: Taking taylor expansion of PI in n 2.563 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.563 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.563 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.563 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.563 * [taylor]: Taking taylor expansion of 0.5 in n 2.563 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.563 * [taylor]: Taking taylor expansion of 1.0 in n 2.563 * [taylor]: Taking taylor expansion of k in n 2.563 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.563 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.563 * [taylor]: Taking taylor expansion of 2.0 in n 2.563 * [taylor]: Taking taylor expansion of (* n PI) in n 2.563 * [taylor]: Taking taylor expansion of n in n 2.563 * [taylor]: Taking taylor expansion of PI in n 2.569 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.569 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.569 * [taylor]: Taking taylor expansion of 0.5 in k 2.569 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.569 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.569 * [taylor]: Taking taylor expansion of 1.0 in k 2.569 * [taylor]: Taking taylor expansion of k in k 2.569 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.569 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.569 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.569 * [taylor]: Taking taylor expansion of 2.0 in k 2.569 * [taylor]: Taking taylor expansion of PI in k 2.570 * [taylor]: Taking taylor expansion of (log n) in k 2.570 * [taylor]: Taking taylor expansion of n in k 2.579 * [taylor]: Taking taylor expansion of 0 in k 2.595 * [taylor]: Taking taylor expansion of 0 in k 2.613 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.613 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.613 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.613 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.613 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.613 * [taylor]: Taking taylor expansion of 0.5 in k 2.613 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.613 * [taylor]: Taking taylor expansion of 1.0 in k 2.613 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.613 * [taylor]: Taking taylor expansion of k in k 2.613 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.613 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.614 * [taylor]: Taking taylor expansion of 2.0 in k 2.614 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.614 * [taylor]: Taking taylor expansion of PI in k 2.614 * [taylor]: Taking taylor expansion of n in k 2.615 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.615 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.615 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.615 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.615 * [taylor]: Taking taylor expansion of 0.5 in n 2.615 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.615 * [taylor]: Taking taylor expansion of 1.0 in n 2.615 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.615 * [taylor]: Taking taylor expansion of k in n 2.615 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.615 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.615 * [taylor]: Taking taylor expansion of 2.0 in n 2.615 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.615 * [taylor]: Taking taylor expansion of PI in n 2.615 * [taylor]: Taking taylor expansion of n in n 2.619 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.619 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.619 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.619 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.619 * [taylor]: Taking taylor expansion of 0.5 in n 2.619 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.619 * [taylor]: Taking taylor expansion of 1.0 in n 2.619 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.619 * [taylor]: Taking taylor expansion of k in n 2.619 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.619 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.619 * [taylor]: Taking taylor expansion of 2.0 in n 2.619 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.619 * [taylor]: Taking taylor expansion of PI in n 2.619 * [taylor]: Taking taylor expansion of n in n 2.623 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.623 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.623 * [taylor]: Taking taylor expansion of 0.5 in k 2.623 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.623 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.623 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.623 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.623 * [taylor]: Taking taylor expansion of 2.0 in k 2.623 * [taylor]: Taking taylor expansion of PI in k 2.624 * [taylor]: Taking taylor expansion of (log n) in k 2.624 * [taylor]: Taking taylor expansion of n in k 2.624 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.624 * [taylor]: Taking taylor expansion of 1.0 in k 2.624 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.624 * [taylor]: Taking taylor expansion of k in k 2.639 * [taylor]: Taking taylor expansion of 0 in k 2.646 * [taylor]: Taking taylor expansion of 0 in k 2.654 * [taylor]: Taking taylor expansion of 0 in k 2.656 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.656 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.656 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in k 2.656 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in k 2.656 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.656 * [taylor]: Taking taylor expansion of 0.5 in k 2.656 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.656 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.656 * [taylor]: Taking taylor expansion of k in k 2.656 * [taylor]: Taking taylor expansion of 1.0 in k 2.656 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in k 2.656 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in k 2.657 * [taylor]: Taking taylor expansion of 2.0 in k 2.657 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in k 2.657 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in k 2.657 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in k 2.657 * [taylor]: Taking taylor expansion of (cbrt -1) in k 2.657 * [taylor]: Taking taylor expansion of -1 in k 2.658 * [taylor]: Taking taylor expansion of PI in k 2.658 * [taylor]: Taking taylor expansion of n in k 2.663 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.663 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 2.663 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 2.663 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.663 * [taylor]: Taking taylor expansion of 0.5 in n 2.663 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.663 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.663 * [taylor]: Taking taylor expansion of k in n 2.663 * [taylor]: Taking taylor expansion of 1.0 in n 2.663 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 2.663 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 2.663 * [taylor]: Taking taylor expansion of 2.0 in n 2.663 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 2.663 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 2.663 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 2.663 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.663 * [taylor]: Taking taylor expansion of -1 in n 2.664 * [taylor]: Taking taylor expansion of PI in n 2.664 * [taylor]: Taking taylor expansion of n in n 2.671 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.671 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 2.671 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 2.671 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.671 * [taylor]: Taking taylor expansion of 0.5 in n 2.671 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.671 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.671 * [taylor]: Taking taylor expansion of k in n 2.671 * [taylor]: Taking taylor expansion of 1.0 in n 2.671 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 2.672 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 2.672 * [taylor]: Taking taylor expansion of 2.0 in n 2.672 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 2.672 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 2.672 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 2.672 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.672 * [taylor]: Taking taylor expansion of -1 in n 2.672 * [taylor]: Taking taylor expansion of PI in n 2.672 * [taylor]: Taking taylor expansion of n in n 2.680 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.680 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.680 * [taylor]: Taking taylor expansion of 0.5 in k 2.680 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.680 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.680 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.680 * [taylor]: Taking taylor expansion of k in k 2.680 * [taylor]: Taking taylor expansion of 1.0 in k 2.680 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.680 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.680 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.680 * [taylor]: Taking taylor expansion of -2.0 in k 2.680 * [taylor]: Taking taylor expansion of PI in k 2.681 * [taylor]: Taking taylor expansion of (log n) in k 2.681 * [taylor]: Taking taylor expansion of n in k 2.691 * [taylor]: Taking taylor expansion of 0 in k 2.701 * [taylor]: Taking taylor expansion of 0 in k 2.719 * [taylor]: Taking taylor expansion of 0 in k 2.719 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 2) 2.719 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 2.720 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.720 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.720 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.720 * [taylor]: Taking taylor expansion of 1/3 in n 2.720 * [taylor]: Taking taylor expansion of (log n) in n 2.720 * [taylor]: Taking taylor expansion of n in n 2.720 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.720 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.720 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.720 * [taylor]: Taking taylor expansion of 1/3 in n 2.720 * [taylor]: Taking taylor expansion of (log n) in n 2.720 * [taylor]: Taking taylor expansion of n in n 2.767 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 2.767 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.767 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.767 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.767 * [taylor]: Taking taylor expansion of 1/3 in n 2.767 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.767 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.767 * [taylor]: Taking taylor expansion of n in n 2.768 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.768 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.768 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.768 * [taylor]: Taking taylor expansion of 1/3 in n 2.768 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.768 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.768 * [taylor]: Taking taylor expansion of n in n 2.824 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 2.824 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.824 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.824 * [taylor]: Taking taylor expansion of -1 in n 2.825 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.825 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.825 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.825 * [taylor]: Taking taylor expansion of 1/3 in n 2.825 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.825 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.825 * [taylor]: Taking taylor expansion of n in n 2.826 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.826 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.826 * [taylor]: Taking taylor expansion of -1 in n 2.827 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.827 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.827 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.827 * [taylor]: Taking taylor expansion of 1/3 in n 2.827 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.827 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.827 * [taylor]: Taking taylor expansion of n in n 2.892 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 2 2) 2.892 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 2.892 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.892 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.892 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.892 * [taylor]: Taking taylor expansion of 1/3 in n 2.892 * [taylor]: Taking taylor expansion of (log n) in n 2.892 * [taylor]: Taking taylor expansion of n in n 2.893 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.893 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.893 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.893 * [taylor]: Taking taylor expansion of 1/3 in n 2.893 * [taylor]: Taking taylor expansion of (log n) in n 2.893 * [taylor]: Taking taylor expansion of n in n 2.945 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 2.945 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.945 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.945 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.945 * [taylor]: Taking taylor expansion of 1/3 in n 2.945 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.945 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.945 * [taylor]: Taking taylor expansion of n in n 2.946 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.946 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.946 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.946 * [taylor]: Taking taylor expansion of 1/3 in n 2.946 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.946 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.946 * [taylor]: Taking taylor expansion of n in n 2.996 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 2.996 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.996 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.996 * [taylor]: Taking taylor expansion of -1 in n 2.997 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.997 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.997 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.997 * [taylor]: Taking taylor expansion of 1/3 in n 2.997 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.997 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.997 * [taylor]: Taking taylor expansion of n in n 2.998 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.998 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.998 * [taylor]: Taking taylor expansion of -1 in n 2.999 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.999 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.999 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.999 * [taylor]: Taking taylor expansion of 1/3 in n 2.999 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.999 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.999 * [taylor]: Taking taylor expansion of n in n 3.066 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 2 1) 3.066 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 3.066 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 3.066 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 3.066 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 3.066 * [taylor]: Taking taylor expansion of 1/3 in n 3.066 * [taylor]: Taking taylor expansion of (log n) in n 3.066 * [taylor]: Taking taylor expansion of n in n 3.067 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 3.067 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 3.067 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 3.067 * [taylor]: Taking taylor expansion of 1/3 in n 3.067 * [taylor]: Taking taylor expansion of (log n) in n 3.067 * [taylor]: Taking taylor expansion of n in n 3.120 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 3.120 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 3.120 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 3.120 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 3.120 * [taylor]: Taking taylor expansion of 1/3 in n 3.120 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 3.120 * [taylor]: Taking taylor expansion of (/ 1 n) in n 3.120 * [taylor]: Taking taylor expansion of n in n 3.121 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 3.121 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 3.121 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 3.121 * [taylor]: Taking taylor expansion of 1/3 in n 3.121 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 3.121 * [taylor]: Taking taylor expansion of (/ 1 n) in n 3.121 * [taylor]: Taking taylor expansion of n in n 3.176 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 3.176 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 3.176 * [taylor]: Taking taylor expansion of (cbrt -1) in n 3.176 * [taylor]: Taking taylor expansion of -1 in n 3.177 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 3.177 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 3.177 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 3.177 * [taylor]: Taking taylor expansion of 1/3 in n 3.177 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 3.177 * [taylor]: Taking taylor expansion of (/ 1 n) in n 3.177 * [taylor]: Taking taylor expansion of n in n 3.178 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 3.178 * [taylor]: Taking taylor expansion of (cbrt -1) in n 3.178 * [taylor]: Taking taylor expansion of -1 in n 3.179 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 3.179 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 3.179 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 3.179 * [taylor]: Taking taylor expansion of 1/3 in n 3.179 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 3.179 * [taylor]: Taking taylor expansion of (/ 1 n) in n 3.179 * [taylor]: Taking taylor expansion of n in n 3.245 * * * [progress]: simplifying candidates 3.247 * [simplify]: Simplifying using # : (expm1 (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (+ (+ (+ (log 2.0) (log PI)) (+ (log (cbrt n)) (log (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (+ (log 2.0) (log PI)) (log (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (log (* 2.0 PI)) (+ (log (cbrt n)) (log (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (log (* 2.0 PI)) (log (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (log (* (* 2.0 PI) (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (log (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n))) (/ (- 1.0 k) 2.0)) (* (log (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1.0 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ k 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) 1) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (- 1.0 k)) (pow (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (log (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (exp (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) 3.252 * * [simplify]: iteration 0 : 414 enodes (cost 701 ) 3.258 * * [simplify]: iteration 1 : 1362 enodes (cost 661 ) 3.283 * * [simplify]: iteration 2 : 5001 enodes (cost 599 ) 3.287 * [simplify]: Simplified to: (expm1 (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (* (fma 3 (log (cbrt n)) (log (* 2.0 PI))) 1) (/ (- 1.0 k) 2.0)) (* (* (fma 3 (log (cbrt n)) (log (* 2.0 PI))) 1) (/ (- 1.0 k) 2.0)) (* (* (fma 3 (log (cbrt n)) (log (* 2.0 PI))) 1) (/ (- 1.0 k) 2.0)) (* (* (fma 3 (log (cbrt n)) (log (* 2.0 PI))) 1) (/ (- 1.0 k) 2.0)) (* (* (fma 3 (log (cbrt n)) (log (* 2.0 PI))) 1) (/ (- 1.0 k) 2.0)) (* (* (fma 3 (log (cbrt n)) (log (* 2.0 PI))) 1) (/ (- 1.0 k) 2.0)) (* (* (fma 3 (log (cbrt n)) (log (* 2.0 PI))) 1) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ 1.0 2.0) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ k 2.0) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (sqrt (/ (- 1.0 k) 2.0)) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (sqrt (- 1.0 k)) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ 1 (sqrt 2.0)) 2))) (* (* n PI) 2.0) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (+ (sqrt 1.0) (sqrt k)) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 2))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (/ 1 (sqrt 2.0)) 2))) (* (* n PI) 2.0) (* (* n PI) 2.0) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (* 2 (/ (- 1.0 k) 2))) (pow (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (* (* (fma 3 (log (cbrt n)) (log (* 2.0 PI))) 1) (/ (- 1.0 k) 2.0)) (exp (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (pow (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* PI (* 2.0 (pow (pow n 1/3) 3))) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (pow n 1/3) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (pow n 1/3) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (pow n 1/3) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (+ (fma 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))))) (- (* (* (* 0.125 (pow k 2)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (+ (pow (log (* 2.0 PI)) 2) (pow (log n) 2))) (* (* (* 0.5 k) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (+ (log (* 2.0 PI)) (log n))))) (pow (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) 3.287 * * * [progress]: adding candidates to table 3.637 * * [progress]: iteration 4 / 4 3.637 * * * [progress]: picking best candidate 3.655 * * * * [pick]: Picked # 3.655 * * * [progress]: localizing error 3.671 * * * [progress]: generating rewritten candidates 3.671 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.694 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 3.702 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 2) 3.708 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 2) 3.716 * * * [progress]: generating series expansions 3.716 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.717 * [approximate]: Taking taylor expansion of (pow (* (pow (cbrt 2.0) 3) (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.717 * [taylor]: Taking taylor expansion of (pow (* (pow (cbrt 2.0) 3) (* n PI)) (* 0.5 (- 1.0 k))) in k 3.717 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* (pow (cbrt 2.0) 3) (* n PI))))) in k 3.717 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* (pow (cbrt 2.0) 3) (* n PI)))) in k 3.717 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.717 * [taylor]: Taking taylor expansion of 0.5 in k 3.717 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.717 * [taylor]: Taking taylor expansion of 1.0 in k 3.717 * [taylor]: Taking taylor expansion of k in k 3.717 * [taylor]: Taking taylor expansion of (log (* (pow (cbrt 2.0) 3) (* n PI))) in k 3.717 * [taylor]: Taking taylor expansion of (* (pow (cbrt 2.0) 3) (* n PI)) in k 3.717 * [taylor]: Taking taylor expansion of (pow (cbrt 2.0) 3) in k 3.717 * [taylor]: Taking taylor expansion of (cbrt 2.0) in k 3.717 * [taylor]: Taking taylor expansion of 2.0 in k 3.718 * [taylor]: Taking taylor expansion of (* n PI) in k 3.718 * [taylor]: Taking taylor expansion of n in k 3.718 * [taylor]: Taking taylor expansion of PI in k 3.722 * [taylor]: Taking taylor expansion of (pow (* (pow (cbrt 2.0) 3) (* n PI)) (* 0.5 (- 1.0 k))) in n 3.722 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* (pow (cbrt 2.0) 3) (* n PI))))) in n 3.722 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* (pow (cbrt 2.0) 3) (* n PI)))) in n 3.722 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.722 * [taylor]: Taking taylor expansion of 0.5 in n 3.722 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.722 * [taylor]: Taking taylor expansion of 1.0 in n 3.722 * [taylor]: Taking taylor expansion of k in n 3.722 * [taylor]: Taking taylor expansion of (log (* (pow (cbrt 2.0) 3) (* n PI))) in n 3.722 * [taylor]: Taking taylor expansion of (* (pow (cbrt 2.0) 3) (* n PI)) in n 3.722 * [taylor]: Taking taylor expansion of (pow (cbrt 2.0) 3) in n 3.722 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 3.722 * [taylor]: Taking taylor expansion of 2.0 in n 3.723 * [taylor]: Taking taylor expansion of (* n PI) in n 3.723 * [taylor]: Taking taylor expansion of n in n 3.723 * [taylor]: Taking taylor expansion of PI in n 3.732 * [taylor]: Taking taylor expansion of (pow (* (pow (cbrt 2.0) 3) (* n PI)) (* 0.5 (- 1.0 k))) in n 3.732 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* (pow (cbrt 2.0) 3) (* n PI))))) in n 3.732 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* (pow (cbrt 2.0) 3) (* n PI)))) in n 3.732 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.732 * [taylor]: Taking taylor expansion of 0.5 in n 3.732 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.732 * [taylor]: Taking taylor expansion of 1.0 in n 3.732 * [taylor]: Taking taylor expansion of k in n 3.732 * [taylor]: Taking taylor expansion of (log (* (pow (cbrt 2.0) 3) (* n PI))) in n 3.732 * [taylor]: Taking taylor expansion of (* (pow (cbrt 2.0) 3) (* n PI)) in n 3.732 * [taylor]: Taking taylor expansion of (pow (cbrt 2.0) 3) in n 3.732 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 3.732 * [taylor]: Taking taylor expansion of 2.0 in n 3.733 * [taylor]: Taking taylor expansion of (* n PI) in n 3.733 * [taylor]: Taking taylor expansion of n in n 3.733 * [taylor]: Taking taylor expansion of PI in n 3.742 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.742 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.742 * [taylor]: Taking taylor expansion of 0.5 in k 3.742 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.742 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.742 * [taylor]: Taking taylor expansion of 1.0 in k 3.742 * [taylor]: Taking taylor expansion of k in k 3.742 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.742 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.742 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.742 * [taylor]: Taking taylor expansion of 2.0 in k 3.742 * [taylor]: Taking taylor expansion of PI in k 3.743 * [taylor]: Taking taylor expansion of (log n) in k 3.743 * [taylor]: Taking taylor expansion of n in k 3.754 * [taylor]: Taking taylor expansion of 0 in k 3.771 * [taylor]: Taking taylor expansion of 0 in k 3.796 * [approximate]: Taking taylor expansion of (pow (/ (* (pow (cbrt 2.0) 3) PI) n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.796 * [taylor]: Taking taylor expansion of (pow (/ (* (pow (cbrt 2.0) 3) PI) n) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.796 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ (* (pow (cbrt 2.0) 3) PI) n)))) in k 3.796 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ (* (pow (cbrt 2.0) 3) PI) n))) in k 3.796 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.796 * [taylor]: Taking taylor expansion of 0.5 in k 3.796 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.796 * [taylor]: Taking taylor expansion of 1.0 in k 3.796 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.796 * [taylor]: Taking taylor expansion of k in k 3.796 * [taylor]: Taking taylor expansion of (log (/ (* (pow (cbrt 2.0) 3) PI) n)) in k 3.796 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt 2.0) 3) PI) n) in k 3.796 * [taylor]: Taking taylor expansion of (* (pow (cbrt 2.0) 3) PI) in k 3.796 * [taylor]: Taking taylor expansion of (pow (cbrt 2.0) 3) in k 3.796 * [taylor]: Taking taylor expansion of (cbrt 2.0) in k 3.796 * [taylor]: Taking taylor expansion of 2.0 in k 3.797 * [taylor]: Taking taylor expansion of PI in k 3.797 * [taylor]: Taking taylor expansion of n in k 3.802 * [taylor]: Taking taylor expansion of (pow (/ (* (pow (cbrt 2.0) 3) PI) n) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.802 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ (* (pow (cbrt 2.0) 3) PI) n)))) in n 3.802 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ (* (pow (cbrt 2.0) 3) PI) n))) in n 3.802 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.802 * [taylor]: Taking taylor expansion of 0.5 in n 3.802 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.802 * [taylor]: Taking taylor expansion of 1.0 in n 3.802 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.802 * [taylor]: Taking taylor expansion of k in n 3.802 * [taylor]: Taking taylor expansion of (log (/ (* (pow (cbrt 2.0) 3) PI) n)) in n 3.802 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt 2.0) 3) PI) n) in n 3.802 * [taylor]: Taking taylor expansion of (* (pow (cbrt 2.0) 3) PI) in n 3.802 * [taylor]: Taking taylor expansion of (pow (cbrt 2.0) 3) in n 3.802 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 3.802 * [taylor]: Taking taylor expansion of 2.0 in n 3.803 * [taylor]: Taking taylor expansion of PI in n 3.803 * [taylor]: Taking taylor expansion of n in n 3.810 * [taylor]: Taking taylor expansion of (pow (/ (* (pow (cbrt 2.0) 3) PI) n) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.810 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ (* (pow (cbrt 2.0) 3) PI) n)))) in n 3.810 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ (* (pow (cbrt 2.0) 3) PI) n))) in n 3.810 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.810 * [taylor]: Taking taylor expansion of 0.5 in n 3.810 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.810 * [taylor]: Taking taylor expansion of 1.0 in n 3.810 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.810 * [taylor]: Taking taylor expansion of k in n 3.810 * [taylor]: Taking taylor expansion of (log (/ (* (pow (cbrt 2.0) 3) PI) n)) in n 3.810 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt 2.0) 3) PI) n) in n 3.810 * [taylor]: Taking taylor expansion of (* (pow (cbrt 2.0) 3) PI) in n 3.810 * [taylor]: Taking taylor expansion of (pow (cbrt 2.0) 3) in n 3.810 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 3.810 * [taylor]: Taking taylor expansion of 2.0 in n 3.811 * [taylor]: Taking taylor expansion of PI in n 3.811 * [taylor]: Taking taylor expansion of n in n 3.818 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.818 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.818 * [taylor]: Taking taylor expansion of 0.5 in k 3.818 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.818 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.818 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.818 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.818 * [taylor]: Taking taylor expansion of 2.0 in k 3.818 * [taylor]: Taking taylor expansion of PI in k 3.819 * [taylor]: Taking taylor expansion of (log n) in k 3.819 * [taylor]: Taking taylor expansion of n in k 3.819 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.819 * [taylor]: Taking taylor expansion of 1.0 in k 3.819 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.819 * [taylor]: Taking taylor expansion of k in k 3.829 * [taylor]: Taking taylor expansion of 0 in k 3.838 * [taylor]: Taking taylor expansion of 0 in k 3.850 * [taylor]: Taking taylor expansion of 0 in k 3.852 * [approximate]: Taking taylor expansion of (pow (/ (* PI (pow (cbrt -2.0) 3)) n) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.852 * [taylor]: Taking taylor expansion of (pow (/ (* PI (pow (cbrt -2.0) 3)) n) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.852 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ (* PI (pow (cbrt -2.0) 3)) n)))) in k 3.852 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ (* PI (pow (cbrt -2.0) 3)) n))) in k 3.852 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.852 * [taylor]: Taking taylor expansion of 0.5 in k 3.852 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.852 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.852 * [taylor]: Taking taylor expansion of k in k 3.852 * [taylor]: Taking taylor expansion of 1.0 in k 3.852 * [taylor]: Taking taylor expansion of (log (/ (* PI (pow (cbrt -2.0) 3)) n)) in k 3.852 * [taylor]: Taking taylor expansion of (/ (* PI (pow (cbrt -2.0) 3)) n) in k 3.852 * [taylor]: Taking taylor expansion of (* PI (pow (cbrt -2.0) 3)) in k 3.852 * [taylor]: Taking taylor expansion of PI in k 3.852 * [taylor]: Taking taylor expansion of (pow (cbrt -2.0) 3) in k 3.852 * [taylor]: Taking taylor expansion of (cbrt -2.0) in k 3.852 * [taylor]: Taking taylor expansion of -2.0 in k 3.853 * [taylor]: Taking taylor expansion of n in k 3.864 * [taylor]: Taking taylor expansion of (pow (/ (* PI (pow (cbrt -2.0) 3)) n) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.864 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ (* PI (pow (cbrt -2.0) 3)) n)))) in n 3.864 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ (* PI (pow (cbrt -2.0) 3)) n))) in n 3.864 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.864 * [taylor]: Taking taylor expansion of 0.5 in n 3.864 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.864 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.865 * [taylor]: Taking taylor expansion of k in n 3.865 * [taylor]: Taking taylor expansion of 1.0 in n 3.865 * [taylor]: Taking taylor expansion of (log (/ (* PI (pow (cbrt -2.0) 3)) n)) in n 3.865 * [taylor]: Taking taylor expansion of (/ (* PI (pow (cbrt -2.0) 3)) n) in n 3.865 * [taylor]: Taking taylor expansion of (* PI (pow (cbrt -2.0) 3)) in n 3.865 * [taylor]: Taking taylor expansion of PI in n 3.865 * [taylor]: Taking taylor expansion of (pow (cbrt -2.0) 3) in n 3.865 * [taylor]: Taking taylor expansion of (cbrt -2.0) in n 3.865 * [taylor]: Taking taylor expansion of -2.0 in n 3.865 * [taylor]: Taking taylor expansion of n in n 3.872 * [taylor]: Taking taylor expansion of (pow (/ (* PI (pow (cbrt -2.0) 3)) n) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.872 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ (* PI (pow (cbrt -2.0) 3)) n)))) in n 3.872 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ (* PI (pow (cbrt -2.0) 3)) n))) in n 3.872 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.872 * [taylor]: Taking taylor expansion of 0.5 in n 3.872 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.872 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.872 * [taylor]: Taking taylor expansion of k in n 3.872 * [taylor]: Taking taylor expansion of 1.0 in n 3.872 * [taylor]: Taking taylor expansion of (log (/ (* PI (pow (cbrt -2.0) 3)) n)) in n 3.872 * [taylor]: Taking taylor expansion of (/ (* PI (pow (cbrt -2.0) 3)) n) in n 3.872 * [taylor]: Taking taylor expansion of (* PI (pow (cbrt -2.0) 3)) in n 3.872 * [taylor]: Taking taylor expansion of PI in n 3.872 * [taylor]: Taking taylor expansion of (pow (cbrt -2.0) 3) in n 3.872 * [taylor]: Taking taylor expansion of (cbrt -2.0) in n 3.872 * [taylor]: Taking taylor expansion of -2.0 in n 3.873 * [taylor]: Taking taylor expansion of n in n 3.880 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 3.880 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 3.880 * [taylor]: Taking taylor expansion of 0.5 in k 3.880 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 3.880 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.880 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.880 * [taylor]: Taking taylor expansion of k in k 3.880 * [taylor]: Taking taylor expansion of 1.0 in k 3.880 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.880 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.880 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.880 * [taylor]: Taking taylor expansion of -2.0 in k 3.880 * [taylor]: Taking taylor expansion of PI in k 3.881 * [taylor]: Taking taylor expansion of (log n) in k 3.881 * [taylor]: Taking taylor expansion of n in k 3.891 * [taylor]: Taking taylor expansion of 0 in k 3.900 * [taylor]: Taking taylor expansion of 0 in k 3.912 * [taylor]: Taking taylor expansion of 0 in k 3.913 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 3.914 * [approximate]: Taking taylor expansion of (* (pow (cbrt 2.0) 2) (pow (* (pow n 2) (pow PI 2)) 1/3)) in (n) around 0 3.914 * [taylor]: Taking taylor expansion of (* (pow (cbrt 2.0) 2) (pow (* (pow n 2) (pow PI 2)) 1/3)) in n 3.914 * [taylor]: Taking taylor expansion of (pow (cbrt 2.0) 2) in n 3.914 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 3.914 * [taylor]: Taking taylor expansion of 2.0 in n 3.915 * [taylor]: Taking taylor expansion of (pow (* (pow n 2) (pow PI 2)) 1/3) in n 3.915 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* (pow n 2) (pow PI 2))))) in n 3.915 * [taylor]: Taking taylor expansion of (* 1/3 (log (* (pow n 2) (pow PI 2)))) in n 3.915 * [taylor]: Taking taylor expansion of 1/3 in n 3.915 * [taylor]: Taking taylor expansion of (log (* (pow n 2) (pow PI 2))) in n 3.915 * [taylor]: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 3.915 * [taylor]: Taking taylor expansion of (pow n 2) in n 3.915 * [taylor]: Taking taylor expansion of n in n 3.915 * [taylor]: Taking taylor expansion of (pow PI 2) in n 3.915 * [taylor]: Taking taylor expansion of PI in n 3.919 * [taylor]: Taking taylor expansion of (* (pow (cbrt 2.0) 2) (pow (* (pow n 2) (pow PI 2)) 1/3)) in n 3.919 * [taylor]: Taking taylor expansion of (pow (cbrt 2.0) 2) in n 3.919 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 3.919 * [taylor]: Taking taylor expansion of 2.0 in n 3.920 * [taylor]: Taking taylor expansion of (pow (* (pow n 2) (pow PI 2)) 1/3) in n 3.920 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* (pow n 2) (pow PI 2))))) in n 3.920 * [taylor]: Taking taylor expansion of (* 1/3 (log (* (pow n 2) (pow PI 2)))) in n 3.920 * [taylor]: Taking taylor expansion of 1/3 in n 3.920 * [taylor]: Taking taylor expansion of (log (* (pow n 2) (pow PI 2))) in n 3.920 * [taylor]: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 3.920 * [taylor]: Taking taylor expansion of (pow n 2) in n 3.920 * [taylor]: Taking taylor expansion of n in n 3.920 * [taylor]: Taking taylor expansion of (pow PI 2) in n 3.920 * [taylor]: Taking taylor expansion of PI in n 4.033 * [approximate]: Taking taylor expansion of (* (pow (cbrt 2.0) 2) (pow (/ (pow PI 2) (pow n 2)) 1/3)) in (n) around 0 4.033 * [taylor]: Taking taylor expansion of (* (pow (cbrt 2.0) 2) (pow (/ (pow PI 2) (pow n 2)) 1/3)) in n 4.033 * [taylor]: Taking taylor expansion of (pow (cbrt 2.0) 2) in n 4.033 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 4.033 * [taylor]: Taking taylor expansion of 2.0 in n 4.034 * [taylor]: Taking taylor expansion of (pow (/ (pow PI 2) (pow n 2)) 1/3) in n 4.034 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (pow PI 2) (pow n 2))))) in n 4.034 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (pow PI 2) (pow n 2)))) in n 4.034 * [taylor]: Taking taylor expansion of 1/3 in n 4.034 * [taylor]: Taking taylor expansion of (log (/ (pow PI 2) (pow n 2))) in n 4.034 * [taylor]: Taking taylor expansion of (/ (pow PI 2) (pow n 2)) in n 4.034 * [taylor]: Taking taylor expansion of (pow PI 2) in n 4.034 * [taylor]: Taking taylor expansion of PI in n 4.034 * [taylor]: Taking taylor expansion of (pow n 2) in n 4.034 * [taylor]: Taking taylor expansion of n in n 4.038 * [taylor]: Taking taylor expansion of (* (pow (cbrt 2.0) 2) (pow (/ (pow PI 2) (pow n 2)) 1/3)) in n 4.038 * [taylor]: Taking taylor expansion of (pow (cbrt 2.0) 2) in n 4.038 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 4.038 * [taylor]: Taking taylor expansion of 2.0 in n 4.039 * [taylor]: Taking taylor expansion of (pow (/ (pow PI 2) (pow n 2)) 1/3) in n 4.039 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (pow PI 2) (pow n 2))))) in n 4.039 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (pow PI 2) (pow n 2)))) in n 4.039 * [taylor]: Taking taylor expansion of 1/3 in n 4.039 * [taylor]: Taking taylor expansion of (log (/ (pow PI 2) (pow n 2))) in n 4.039 * [taylor]: Taking taylor expansion of (/ (pow PI 2) (pow n 2)) in n 4.039 * [taylor]: Taking taylor expansion of (pow PI 2) in n 4.039 * [taylor]: Taking taylor expansion of PI in n 4.039 * [taylor]: Taking taylor expansion of (pow n 2) in n 4.039 * [taylor]: Taking taylor expansion of n in n 4.145 * [approximate]: Taking taylor expansion of (* (pow (/ (pow PI 2) (pow n 2)) 1/3) (pow (cbrt -2.0) 2)) in (n) around 0 4.145 * [taylor]: Taking taylor expansion of (* (pow (/ (pow PI 2) (pow n 2)) 1/3) (pow (cbrt -2.0) 2)) in n 4.145 * [taylor]: Taking taylor expansion of (pow (/ (pow PI 2) (pow n 2)) 1/3) in n 4.145 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (pow PI 2) (pow n 2))))) in n 4.145 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (pow PI 2) (pow n 2)))) in n 4.145 * [taylor]: Taking taylor expansion of 1/3 in n 4.145 * [taylor]: Taking taylor expansion of (log (/ (pow PI 2) (pow n 2))) in n 4.145 * [taylor]: Taking taylor expansion of (/ (pow PI 2) (pow n 2)) in n 4.145 * [taylor]: Taking taylor expansion of (pow PI 2) in n 4.145 * [taylor]: Taking taylor expansion of PI in n 4.145 * [taylor]: Taking taylor expansion of (pow n 2) in n 4.145 * [taylor]: Taking taylor expansion of n in n 4.149 * [taylor]: Taking taylor expansion of (pow (cbrt -2.0) 2) in n 4.149 * [taylor]: Taking taylor expansion of (cbrt -2.0) in n 4.150 * [taylor]: Taking taylor expansion of -2.0 in n 4.150 * [taylor]: Taking taylor expansion of (* (pow (/ (pow PI 2) (pow n 2)) 1/3) (pow (cbrt -2.0) 2)) in n 4.150 * [taylor]: Taking taylor expansion of (pow (/ (pow PI 2) (pow n 2)) 1/3) in n 4.150 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (pow PI 2) (pow n 2))))) in n 4.150 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (pow PI 2) (pow n 2)))) in n 4.150 * [taylor]: Taking taylor expansion of 1/3 in n 4.150 * [taylor]: Taking taylor expansion of (log (/ (pow PI 2) (pow n 2))) in n 4.150 * [taylor]: Taking taylor expansion of (/ (pow PI 2) (pow n 2)) in n 4.150 * [taylor]: Taking taylor expansion of (pow PI 2) in n 4.150 * [taylor]: Taking taylor expansion of PI in n 4.150 * [taylor]: Taking taylor expansion of (pow n 2) in n 4.150 * [taylor]: Taking taylor expansion of n in n 4.154 * [taylor]: Taking taylor expansion of (pow (cbrt -2.0) 2) in n 4.155 * [taylor]: Taking taylor expansion of (cbrt -2.0) in n 4.155 * [taylor]: Taking taylor expansion of -2.0 in n 4.254 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 2) 4.255 * [approximate]: Taking taylor expansion of (* (cbrt 2.0) (pow (* n PI) 1/3)) in (n) around 0 4.255 * [taylor]: Taking taylor expansion of (* (cbrt 2.0) (pow (* n PI) 1/3)) in n 4.255 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 4.255 * [taylor]: Taking taylor expansion of 2.0 in n 4.255 * [taylor]: Taking taylor expansion of (pow (* n PI) 1/3) in n 4.255 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* n PI)))) in n 4.255 * [taylor]: Taking taylor expansion of (* 1/3 (log (* n PI))) in n 4.255 * [taylor]: Taking taylor expansion of 1/3 in n 4.255 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 4.255 * [taylor]: Taking taylor expansion of (* n PI) in n 4.255 * [taylor]: Taking taylor expansion of n in n 4.256 * [taylor]: Taking taylor expansion of PI in n 4.258 * [taylor]: Taking taylor expansion of (* (cbrt 2.0) (pow (* n PI) 1/3)) in n 4.258 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 4.258 * [taylor]: Taking taylor expansion of 2.0 in n 4.259 * [taylor]: Taking taylor expansion of (pow (* n PI) 1/3) in n 4.259 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* n PI)))) in n 4.259 * [taylor]: Taking taylor expansion of (* 1/3 (log (* n PI))) in n 4.259 * [taylor]: Taking taylor expansion of 1/3 in n 4.259 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 4.259 * [taylor]: Taking taylor expansion of (* n PI) in n 4.259 * [taylor]: Taking taylor expansion of n in n 4.259 * [taylor]: Taking taylor expansion of PI in n 4.337 * [approximate]: Taking taylor expansion of (* (cbrt 2.0) (pow (/ PI n) 1/3)) in (n) around 0 4.338 * [taylor]: Taking taylor expansion of (* (cbrt 2.0) (pow (/ PI n) 1/3)) in n 4.338 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 4.338 * [taylor]: Taking taylor expansion of 2.0 in n 4.344 * [taylor]: Taking taylor expansion of (pow (/ PI n) 1/3) in n 4.344 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ PI n)))) in n 4.344 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ PI n))) in n 4.344 * [taylor]: Taking taylor expansion of 1/3 in n 4.344 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 4.344 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.344 * [taylor]: Taking taylor expansion of PI in n 4.344 * [taylor]: Taking taylor expansion of n in n 4.346 * [taylor]: Taking taylor expansion of (* (cbrt 2.0) (pow (/ PI n) 1/3)) in n 4.346 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 4.346 * [taylor]: Taking taylor expansion of 2.0 in n 4.347 * [taylor]: Taking taylor expansion of (pow (/ PI n) 1/3) in n 4.347 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ PI n)))) in n 4.347 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ PI n))) in n 4.347 * [taylor]: Taking taylor expansion of 1/3 in n 4.347 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 4.347 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.347 * [taylor]: Taking taylor expansion of PI in n 4.347 * [taylor]: Taking taylor expansion of n in n 4.423 * [approximate]: Taking taylor expansion of (* (pow (/ PI n) 1/3) (cbrt -2.0)) in (n) around 0 4.423 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) 1/3) (cbrt -2.0)) in n 4.423 * [taylor]: Taking taylor expansion of (pow (/ PI n) 1/3) in n 4.423 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ PI n)))) in n 4.423 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ PI n))) in n 4.423 * [taylor]: Taking taylor expansion of 1/3 in n 4.423 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 4.423 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.423 * [taylor]: Taking taylor expansion of PI in n 4.423 * [taylor]: Taking taylor expansion of n in n 4.425 * [taylor]: Taking taylor expansion of (cbrt -2.0) in n 4.425 * [taylor]: Taking taylor expansion of -2.0 in n 4.426 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) 1/3) (cbrt -2.0)) in n 4.426 * [taylor]: Taking taylor expansion of (pow (/ PI n) 1/3) in n 4.426 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ PI n)))) in n 4.426 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ PI n))) in n 4.426 * [taylor]: Taking taylor expansion of 1/3 in n 4.426 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 4.426 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.426 * [taylor]: Taking taylor expansion of PI in n 4.426 * [taylor]: Taking taylor expansion of n in n 4.428 * [taylor]: Taking taylor expansion of (cbrt -2.0) in n 4.428 * [taylor]: Taking taylor expansion of -2.0 in n 4.500 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 2) 4.501 * [approximate]: Taking taylor expansion of (* (cbrt 2.0) (pow (* n PI) 1/3)) in (n) around 0 4.501 * [taylor]: Taking taylor expansion of (* (cbrt 2.0) (pow (* n PI) 1/3)) in n 4.501 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 4.501 * [taylor]: Taking taylor expansion of 2.0 in n 4.501 * [taylor]: Taking taylor expansion of (pow (* n PI) 1/3) in n 4.501 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* n PI)))) in n 4.501 * [taylor]: Taking taylor expansion of (* 1/3 (log (* n PI))) in n 4.501 * [taylor]: Taking taylor expansion of 1/3 in n 4.501 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 4.501 * [taylor]: Taking taylor expansion of (* n PI) in n 4.501 * [taylor]: Taking taylor expansion of n in n 4.501 * [taylor]: Taking taylor expansion of PI in n 4.504 * [taylor]: Taking taylor expansion of (* (cbrt 2.0) (pow (* n PI) 1/3)) in n 4.504 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 4.504 * [taylor]: Taking taylor expansion of 2.0 in n 4.505 * [taylor]: Taking taylor expansion of (pow (* n PI) 1/3) in n 4.505 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* n PI)))) in n 4.505 * [taylor]: Taking taylor expansion of (* 1/3 (log (* n PI))) in n 4.505 * [taylor]: Taking taylor expansion of 1/3 in n 4.505 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 4.505 * [taylor]: Taking taylor expansion of (* n PI) in n 4.505 * [taylor]: Taking taylor expansion of n in n 4.505 * [taylor]: Taking taylor expansion of PI in n 4.582 * [approximate]: Taking taylor expansion of (* (cbrt 2.0) (pow (/ PI n) 1/3)) in (n) around 0 4.582 * [taylor]: Taking taylor expansion of (* (cbrt 2.0) (pow (/ PI n) 1/3)) in n 4.582 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 4.582 * [taylor]: Taking taylor expansion of 2.0 in n 4.583 * [taylor]: Taking taylor expansion of (pow (/ PI n) 1/3) in n 4.583 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ PI n)))) in n 4.583 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ PI n))) in n 4.583 * [taylor]: Taking taylor expansion of 1/3 in n 4.583 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 4.583 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.583 * [taylor]: Taking taylor expansion of PI in n 4.583 * [taylor]: Taking taylor expansion of n in n 4.585 * [taylor]: Taking taylor expansion of (* (cbrt 2.0) (pow (/ PI n) 1/3)) in n 4.585 * [taylor]: Taking taylor expansion of (cbrt 2.0) in n 4.585 * [taylor]: Taking taylor expansion of 2.0 in n 4.585 * [taylor]: Taking taylor expansion of (pow (/ PI n) 1/3) in n 4.585 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ PI n)))) in n 4.585 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ PI n))) in n 4.585 * [taylor]: Taking taylor expansion of 1/3 in n 4.585 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 4.585 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.585 * [taylor]: Taking taylor expansion of PI in n 4.586 * [taylor]: Taking taylor expansion of n in n 4.661 * [approximate]: Taking taylor expansion of (* (pow (/ PI n) 1/3) (cbrt -2.0)) in (n) around 0 4.661 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) 1/3) (cbrt -2.0)) in n 4.661 * [taylor]: Taking taylor expansion of (pow (/ PI n) 1/3) in n 4.661 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ PI n)))) in n 4.661 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ PI n))) in n 4.661 * [taylor]: Taking taylor expansion of 1/3 in n 4.661 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 4.661 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.661 * [taylor]: Taking taylor expansion of PI in n 4.661 * [taylor]: Taking taylor expansion of n in n 4.663 * [taylor]: Taking taylor expansion of (cbrt -2.0) in n 4.663 * [taylor]: Taking taylor expansion of -2.0 in n 4.664 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) 1/3) (cbrt -2.0)) in n 4.664 * [taylor]: Taking taylor expansion of (pow (/ PI n) 1/3) in n 4.664 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ PI n)))) in n 4.664 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ PI n))) in n 4.664 * [taylor]: Taking taylor expansion of 1/3 in n 4.664 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 4.664 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.664 * [taylor]: Taking taylor expansion of PI in n 4.664 * [taylor]: Taking taylor expansion of n in n 4.666 * [taylor]: Taking taylor expansion of (cbrt -2.0) in n 4.666 * [taylor]: Taking taylor expansion of -2.0 in n 4.739 * * * [progress]: simplifying candidates 4.741 * [simplify]: Simplifying using # : (expm1 (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (* (+ (+ (log (cbrt (* (* 2.0 PI) n))) (log (cbrt (* (* 2.0 PI) n)))) (log (cbrt (* (* 2.0 PI) n)))) (/ (- 1.0 k) 2.0)) (* (+ (log (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (log (cbrt (* (* 2.0 PI) n)))) (/ (- 1.0 k) 2.0)) (* (log (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)))) (/ (- 1.0 k) 2.0)) (* (log (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)))) (/ (- 1.0 k) 2.0)) (* (+ (+ 1/3 1/3) 1/3) (/ (- 1.0 k) 2.0)) (* (+ (+ 1 1) 1) (/ (- 1.0 k) 2.0)) (* (+ 2 1) (/ (- 1.0 k) 2.0)) (* (+ (+ 1 1) 1) (/ (- 1.0 k) 2.0)) (* (+ (* 2 1/3) 1/3) (/ (- 1.0 k) 2.0)) (* (+ (* 2 1) 1) (/ (- 1.0 k) 2.0)) (* 1/3 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 3 (/ (- 1.0 k) 2.0)) (* (+ (+ 1 1) 1) (/ (- 1.0 k) 2.0)) (* (+ 2 1) (/ (- 1.0 k) 2.0)) (* (+ (+ 1 1) 1) (/ (- 1.0 k) 2.0)) (* (+ (* 2 1) 1) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ 1.0 2.0)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ k 2.0)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ 1 (sqrt 2.0))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ 1 1)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ 1 (sqrt 2.0))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ 1 1)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) 1) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (- 1.0 k)) (pow (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0)) (pow (cbrt (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (log (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (exp (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (log1p (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (+ 1/3 1/3) (+ 1 1) (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (+ 1 1) (+ (log (cbrt (* (* 2.0 PI) n))) (log (cbrt (* (* 2.0 PI) n)))) (log (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (exp (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (cbrt (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (cbrt (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))))) (cbrt (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (* (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (sqrt (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (sqrt (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (* (cbrt (* 2.0 PI)) (cbrt (* 2.0 PI))) (* (cbrt n) (cbrt n)) (* (* (cbrt (cbrt (* (* 2.0 PI) n))) (cbrt (cbrt (* (* 2.0 PI) n)))) (* (cbrt (cbrt (* (* 2.0 PI) n))) (cbrt (cbrt (* (* 2.0 PI) n))))) (* (cbrt (cbrt (* (* 2.0 PI) n))) (cbrt (cbrt (* (* 2.0 PI) n)))) (* (sqrt (cbrt (* (* 2.0 PI) n))) (sqrt (cbrt (* (* 2.0 PI) n)))) (* (sqrt (cbrt (* (* 2.0 PI) n))) (sqrt (cbrt (* (* 2.0 PI) n)))) (* 1 1) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (* (sqrt (cbrt (* (* 2.0 PI) n))) (sqrt (cbrt (* (* 2.0 PI) n)))) (* (sqrt (cbrt (* (* 2.0 PI) n))) (sqrt (cbrt (* (* 2.0 PI) n)))) (* 2 1/3) (* 2 1) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* 2.0 PI))) (* (cbrt (* (* 2.0 PI) n)) (* (cbrt (cbrt (* (* 2.0 PI) n))) (cbrt (cbrt (* (* 2.0 PI) n))))) (* (cbrt (* (* 2.0 PI) n)) (sqrt (cbrt (* (* 2.0 PI) n)))) (* (cbrt (* (* 2.0 PI) n)) 1) (* (cbrt n) (cbrt (* (* 2.0 PI) n))) (* (cbrt (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (* (sqrt (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (expm1 (cbrt (* (* 2.0 PI) n))) (log1p (cbrt (* (* 2.0 PI) n))) (log (cbrt (* (* 2.0 PI) n))) (exp (cbrt (* (* 2.0 PI) n))) (cbrt (* 2.0 PI)) (cbrt n) (* (cbrt (cbrt (* (* 2.0 PI) n))) (cbrt (cbrt (* (* 2.0 PI) n)))) (cbrt (cbrt (* (* 2.0 PI) n))) (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (sqrt (cbrt (* (* 2.0 PI) n))) (sqrt (cbrt (* (* 2.0 PI) n))) (expm1 (cbrt (* (* 2.0 PI) n))) (log1p (cbrt (* (* 2.0 PI) n))) (log (cbrt (* (* 2.0 PI) n))) (exp (cbrt (* (* 2.0 PI) n))) (cbrt (* 2.0 PI)) (cbrt n) (* (cbrt (cbrt (* (* 2.0 PI) n))) (cbrt (cbrt (* (* 2.0 PI) n)))) (cbrt (cbrt (* (* 2.0 PI) n))) (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (sqrt (cbrt (* (* 2.0 PI) n))) (sqrt (cbrt (* (* 2.0 PI) n))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (pow (cbrt 2.0) 2) (exp (* 1/3 (+ (log (pow PI 2)) (* 2 (log n)))))) (* (pow (cbrt 2.0) 2) (exp (* 1/3 (- (log (pow PI 2)) (* 2 (log (/ 1 n))))))) (* (exp (* 1/3 (- (log (pow PI 2)) (* 2 (log (/ -1 n)))))) (pow (cbrt -2.0) 2)) (* (cbrt 2.0) (exp (* 1/3 (+ (log n) (log PI))))) (* (cbrt 2.0) (exp (* 1/3 (- (log PI) (log (/ 1 n)))))) (* (exp (* 1/3 (- (log PI) (log (/ -1 n))))) (cbrt -2.0)) (* (cbrt 2.0) (exp (* 1/3 (+ (log n) (log PI))))) (* (cbrt 2.0) (exp (* 1/3 (- (log PI) (log (/ 1 n)))))) (* (exp (* 1/3 (- (log PI) (log (/ -1 n))))) (cbrt -2.0)) 4.748 * * [simplify]: iteration 0 : 529 enodes (cost 1113 ) 4.758 * * [simplify]: iteration 1 : 2032 enodes (cost 892 ) 4.800 * * [simplify]: iteration 2 : 5003 enodes (cost 861 ) 4.804 * [simplify]: Simplified to: (expm1 (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (/ (* (* 3 (log (cbrt (* (* 2.0 PI) n)))) (- 1.0 k)) 2.0) (/ (* (* 3 (log (cbrt (* (* 2.0 PI) n)))) (- 1.0 k)) 2.0) (/ (* (* 3 (log (cbrt (* (* 2.0 PI) n)))) (- 1.0 k)) 2.0) (/ (* (* 3 (log (cbrt (* (* 2.0 PI) n)))) (- 1.0 k)) 2.0) (/ (- 1.0 k) 2.0) (* 3 (/ (- 1.0 k) 2.0)) (* 3 (/ (- 1.0 k) 2.0)) (* 3 (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (* 3 (/ (- 1.0 k) 2.0)) (* 1/3 (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (* 3 (/ (- 1.0 k) 2.0)) (* 3 (/ (- 1.0 k) 2.0)) (* 3 (/ (- 1.0 k) 2.0)) (* 3 (/ (- 1.0 k) 2.0)) (* 3 (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ 1.0 2.0) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ k 2.0) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (sqrt (/ (- 1.0 k) 2.0)) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (sqrt (- 1.0 k)) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ 1 (sqrt 2.0)) 2))) (* (* 2.0 PI) n) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (+ (sqrt 1.0) (sqrt k)) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 2))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (/ 1 (sqrt 2.0)) 2))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) (* 2 (/ (- 1.0 k) 2))) (pow (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0)) (pow (cbrt (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (* (* 3 (log (cbrt (* (* 2.0 PI) n)))) (- 1.0 k)) 2.0) (exp (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (pow (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 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 (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (log1p (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) 2/3 2 (pow (pow (cbrt (* (* 2.0 PI) n)) 3) 2) (pow (sqrt (cbrt (* (* 2.0 PI) n))) 4) 2 (* 2 (log (cbrt (* (* 2.0 PI) n)))) (* 2 (log (cbrt (* (* 2.0 PI) n)))) (pow (exp 1) (pow (sqrt (cbrt (* (* 2.0 PI) n))) 4)) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) 2) (* (cbrt (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (cbrt (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))))) (cbrt (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))) (pow (pow (cbrt (* (* 2.0 PI) n)) 3) 2) (fabs (cbrt (* (* 2.0 PI) n))) (fabs (cbrt (* (* 2.0 PI) n))) (* (cbrt (* 2.0 PI)) (cbrt (* 2.0 PI))) (* (cbrt n) (cbrt n)) (pow (cbrt (cbrt (* (* 2.0 PI) n))) 4) (* (cbrt (cbrt (* (* 2.0 PI) n))) (cbrt (cbrt (* (* 2.0 PI) n)))) (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)) 1 (pow (sqrt (cbrt (* (* 2.0 PI) n))) 4) (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)) 2/3 2 (* (cbrt (* (* 2.0 PI) n)) (cbrt (* 2.0 PI))) (* (cbrt (* (* 2.0 PI) n)) (* (cbrt (cbrt (* (* 2.0 PI) n))) (cbrt (cbrt (* (* 2.0 PI) n))))) (pow (sqrt (cbrt (* (* 2.0 PI) n))) 3) (cbrt (* (* 2.0 PI) n)) (* (cbrt n) (cbrt (* (* 2.0 PI) n))) (pow (cbrt (cbrt (* (* 2.0 PI) n))) 4) (pow (sqrt (cbrt (* (* 2.0 PI) n))) 3) (pow (sqrt (cbrt (* (* 2.0 PI) n))) 4) (expm1 (cbrt (* (* 2.0 PI) n))) (log1p (cbrt (* (* 2.0 PI) n))) (log (cbrt (* (* 2.0 PI) n))) (exp (cbrt (* (* 2.0 PI) n))) (cbrt (* 2.0 PI)) (cbrt n) (* (cbrt (cbrt (* (* 2.0 PI) n))) (cbrt (cbrt (* (* 2.0 PI) n)))) (cbrt (cbrt (* (* 2.0 PI) n))) (* (* 2.0 PI) n) (sqrt (cbrt (* (* 2.0 PI) n))) (sqrt (cbrt (* (* 2.0 PI) n))) (expm1 (cbrt (* (* 2.0 PI) n))) (log1p (cbrt (* (* 2.0 PI) n))) (log (cbrt (* (* 2.0 PI) n))) (exp (cbrt (* (* 2.0 PI) n))) (cbrt (* 2.0 PI)) (cbrt n) (* (cbrt (cbrt (* (* 2.0 PI) n))) (cbrt (cbrt (* (* 2.0 PI) n)))) (cbrt (cbrt (* (* 2.0 PI) n))) (* (* 2.0 PI) n) (sqrt (cbrt (* (* 2.0 PI) n))) (sqrt (cbrt (* (* 2.0 PI) n))) (fma (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (fma 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))))) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (pow (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (pow (cbrt 2.0) 2) (exp (* 1/3 (+ (log (pow PI 2)) (* 2 (log n)))))) (* (pow (cbrt 2.0) 2) (exp (* 1/3 (+ (log (pow PI 2)) (* 2 (log n)))))) (* (exp (* 1/3 (- (log (pow PI 2)) (* 2 (log (/ -1 n)))))) (pow (cbrt -2.0) 2)) (* (cbrt 2.0) (exp (* 1/3 (+ (log n) (log PI))))) (* (cbrt 2.0) (exp (* 1/3 (+ (log n) (log PI))))) (* (exp (* 1/3 (- (log PI) (log (/ -1 n))))) (cbrt -2.0)) (* (cbrt 2.0) (exp (* 1/3 (+ (log n) (log PI))))) (* (cbrt 2.0) (exp (* 1/3 (+ (log n) (log PI))))) (* (exp (* 1/3 (- (log PI) (log (/ -1 n))))) (cbrt -2.0)) 4.805 * * * [progress]: adding candidates to table 5.143 * [progress]: [Phase 3 of 3] Extracting. 5.144 * * [regime]: Finding splitpoints for: (# # # # # # # # #) 5.147 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2.0 PI) n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) n k) 5.147 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # # #) 5.186 * * * * [regimes]: Trying to branch on (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) from (# # # # # # # # #) 5.225 * * * * [regimes]: Trying to branch on n from (# # # # # # # # #) 5.263 * * * * [regimes]: Trying to branch on k from (# # # # # # # # #) 5.300 * * * [regime]: Found split indices: #