14.460 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.083 * * * [progress]: [2/2] Setting up program. 0.085 * [progress]: [Phase 2 of 3] Improving. 0.086 * [simplify]: Simplifying using # : (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.088 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.090 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.091 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.094 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.100 * * [simplify]: iteration 4 : 1044 enodes (cost 8 ) 0.123 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.123 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.124 * * [progress]: iteration 1 / 4 0.124 * * * [progress]: picking best candidate 0.126 * * * * [pick]: Picked # 0.126 * * * [progress]: localizing error 0.139 * * * [progress]: generating rewritten candidates 0.139 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.164 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.181 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.187 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.230 * * * [progress]: generating series expansions 0.230 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.231 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.231 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.231 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.231 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.231 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.231 * [taylor]: Taking taylor expansion of 0.5 in k 0.231 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.231 * [taylor]: Taking taylor expansion of 1.0 in k 0.231 * [taylor]: Taking taylor expansion of k in k 0.231 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.231 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.231 * [taylor]: Taking taylor expansion of 2.0 in k 0.232 * [taylor]: Taking taylor expansion of (* n PI) in k 0.232 * [taylor]: Taking taylor expansion of n in k 0.232 * [taylor]: Taking taylor expansion of PI in k 0.232 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.232 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.233 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.233 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.233 * [taylor]: Taking taylor expansion of 0.5 in n 0.233 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.233 * [taylor]: Taking taylor expansion of 1.0 in n 0.233 * [taylor]: Taking taylor expansion of k in n 0.233 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.233 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.233 * [taylor]: Taking taylor expansion of 2.0 in n 0.233 * [taylor]: Taking taylor expansion of (* n PI) in n 0.233 * [taylor]: Taking taylor expansion of n in n 0.233 * [taylor]: Taking taylor expansion of PI in n 0.238 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.238 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.238 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.238 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.238 * [taylor]: Taking taylor expansion of 0.5 in n 0.238 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.238 * [taylor]: Taking taylor expansion of 1.0 in n 0.238 * [taylor]: Taking taylor expansion of k in n 0.238 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.238 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.238 * [taylor]: Taking taylor expansion of 2.0 in n 0.238 * [taylor]: Taking taylor expansion of (* n PI) in n 0.238 * [taylor]: Taking taylor expansion of n in n 0.238 * [taylor]: Taking taylor expansion of PI in n 0.243 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.243 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.243 * [taylor]: Taking taylor expansion of 0.5 in k 0.243 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.243 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.243 * [taylor]: Taking taylor expansion of 1.0 in k 0.243 * [taylor]: Taking taylor expansion of k in k 0.243 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.243 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.243 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.243 * [taylor]: Taking taylor expansion of 2.0 in k 0.243 * [taylor]: Taking taylor expansion of PI in k 0.244 * [taylor]: Taking taylor expansion of (log n) in k 0.244 * [taylor]: Taking taylor expansion of n in k 0.253 * [taylor]: Taking taylor expansion of 0 in k 0.268 * [taylor]: Taking taylor expansion of 0 in k 0.291 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.291 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.291 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.291 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.291 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.291 * [taylor]: Taking taylor expansion of 0.5 in k 0.291 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.291 * [taylor]: Taking taylor expansion of 1.0 in k 0.291 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.291 * [taylor]: Taking taylor expansion of k in k 0.292 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.292 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.292 * [taylor]: Taking taylor expansion of 2.0 in k 0.292 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.292 * [taylor]: Taking taylor expansion of PI in k 0.292 * [taylor]: Taking taylor expansion of n in k 0.293 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.293 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.293 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.293 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.293 * [taylor]: Taking taylor expansion of 0.5 in n 0.293 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.293 * [taylor]: Taking taylor expansion of 1.0 in n 0.293 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.293 * [taylor]: Taking taylor expansion of k in n 0.293 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.293 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.293 * [taylor]: Taking taylor expansion of 2.0 in n 0.293 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.293 * [taylor]: Taking taylor expansion of PI in n 0.293 * [taylor]: Taking taylor expansion of n in n 0.296 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.296 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.296 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.296 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.296 * [taylor]: Taking taylor expansion of 0.5 in n 0.296 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.296 * [taylor]: Taking taylor expansion of 1.0 in n 0.296 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.297 * [taylor]: Taking taylor expansion of k in n 0.297 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.297 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.297 * [taylor]: Taking taylor expansion of 2.0 in n 0.297 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.297 * [taylor]: Taking taylor expansion of PI in n 0.297 * [taylor]: Taking taylor expansion of n in n 0.300 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.300 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.300 * [taylor]: Taking taylor expansion of 0.5 in k 0.300 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.300 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.300 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.300 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.300 * [taylor]: Taking taylor expansion of 2.0 in k 0.300 * [taylor]: Taking taylor expansion of PI in k 0.301 * [taylor]: Taking taylor expansion of (log n) in k 0.301 * [taylor]: Taking taylor expansion of n in k 0.301 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.301 * [taylor]: Taking taylor expansion of 1.0 in k 0.301 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.301 * [taylor]: Taking taylor expansion of k in k 0.310 * [taylor]: Taking taylor expansion of 0 in k 0.317 * [taylor]: Taking taylor expansion of 0 in k 0.326 * [taylor]: Taking taylor expansion of 0 in k 0.327 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.327 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.327 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.327 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.327 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.327 * [taylor]: Taking taylor expansion of 0.5 in k 0.328 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.328 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.328 * [taylor]: Taking taylor expansion of k in k 0.328 * [taylor]: Taking taylor expansion of 1.0 in k 0.328 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.328 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.328 * [taylor]: Taking taylor expansion of -2.0 in k 0.328 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.328 * [taylor]: Taking taylor expansion of PI in k 0.328 * [taylor]: Taking taylor expansion of n in k 0.329 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.329 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.329 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.329 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.329 * [taylor]: Taking taylor expansion of 0.5 in n 0.329 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.329 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.329 * [taylor]: Taking taylor expansion of k in n 0.329 * [taylor]: Taking taylor expansion of 1.0 in n 0.329 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.329 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.329 * [taylor]: Taking taylor expansion of -2.0 in n 0.329 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.329 * [taylor]: Taking taylor expansion of PI in n 0.329 * [taylor]: Taking taylor expansion of n in n 0.333 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.333 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.333 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.334 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.334 * [taylor]: Taking taylor expansion of 0.5 in n 0.334 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.334 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.334 * [taylor]: Taking taylor expansion of k in n 0.334 * [taylor]: Taking taylor expansion of 1.0 in n 0.334 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.334 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.334 * [taylor]: Taking taylor expansion of -2.0 in n 0.334 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.334 * [taylor]: Taking taylor expansion of PI in n 0.334 * [taylor]: Taking taylor expansion of n in n 0.337 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.337 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.337 * [taylor]: Taking taylor expansion of 0.5 in k 0.337 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.337 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.337 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.337 * [taylor]: Taking taylor expansion of k in k 0.338 * [taylor]: Taking taylor expansion of 1.0 in k 0.338 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.338 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.338 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.338 * [taylor]: Taking taylor expansion of -2.0 in k 0.338 * [taylor]: Taking taylor expansion of PI in k 0.338 * [taylor]: Taking taylor expansion of (log n) in k 0.339 * [taylor]: Taking taylor expansion of n in k 0.347 * [taylor]: Taking taylor expansion of 0 in k 0.353 * [taylor]: Taking taylor expansion of 0 in k 0.362 * [taylor]: Taking taylor expansion of 0 in k 0.363 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.363 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.363 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.363 * [taylor]: Taking taylor expansion of 2.0 in n 0.363 * [taylor]: Taking taylor expansion of (* n PI) in n 0.363 * [taylor]: Taking taylor expansion of n in n 0.363 * [taylor]: Taking taylor expansion of PI in n 0.363 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.364 * [taylor]: Taking taylor expansion of 2.0 in n 0.364 * [taylor]: Taking taylor expansion of (* n PI) in n 0.364 * [taylor]: Taking taylor expansion of n in n 0.364 * [taylor]: Taking taylor expansion of PI in n 0.382 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.382 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.382 * [taylor]: Taking taylor expansion of 2.0 in n 0.382 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.383 * [taylor]: Taking taylor expansion of PI in n 0.383 * [taylor]: Taking taylor expansion of n in n 0.383 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.383 * [taylor]: Taking taylor expansion of 2.0 in n 0.383 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.383 * [taylor]: Taking taylor expansion of PI in n 0.383 * [taylor]: Taking taylor expansion of n in n 0.392 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.392 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.392 * [taylor]: Taking taylor expansion of -2.0 in n 0.392 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.392 * [taylor]: Taking taylor expansion of PI in n 0.392 * [taylor]: Taking taylor expansion of n in n 0.392 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.392 * [taylor]: Taking taylor expansion of -2.0 in n 0.392 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.392 * [taylor]: Taking taylor expansion of PI in n 0.392 * [taylor]: Taking taylor expansion of n in n 0.401 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.401 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.401 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.401 * [taylor]: Taking taylor expansion of 1.0 in k 0.401 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.401 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.401 * [taylor]: Taking taylor expansion of k in k 0.402 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.402 * [taylor]: Taking taylor expansion of 1.0 in k 0.402 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.402 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.402 * [taylor]: Taking taylor expansion of k in k 0.413 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.413 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.413 * [taylor]: Taking taylor expansion of 1.0 in k 0.413 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.413 * [taylor]: Taking taylor expansion of k in k 0.414 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.414 * [taylor]: Taking taylor expansion of 1.0 in k 0.414 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.414 * [taylor]: Taking taylor expansion of k in k 0.423 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.423 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.423 * [taylor]: Taking taylor expansion of 1.0 in k 0.423 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.423 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.423 * [taylor]: Taking taylor expansion of -1 in k 0.423 * [taylor]: Taking taylor expansion of k in k 0.425 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.425 * [taylor]: Taking taylor expansion of 1.0 in k 0.425 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.425 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.425 * [taylor]: Taking taylor expansion of -1 in k 0.425 * [taylor]: Taking taylor expansion of k in k 0.436 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.437 * [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 0.437 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.437 * [taylor]: Taking taylor expansion of 1.0 in n 0.437 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.437 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.437 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.437 * [taylor]: Taking taylor expansion of k in n 0.437 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.437 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.437 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.437 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.437 * [taylor]: Taking taylor expansion of 0.5 in n 0.437 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.437 * [taylor]: Taking taylor expansion of 1.0 in n 0.437 * [taylor]: Taking taylor expansion of k in n 0.437 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.437 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.437 * [taylor]: Taking taylor expansion of 2.0 in n 0.437 * [taylor]: Taking taylor expansion of (* n PI) in n 0.437 * [taylor]: Taking taylor expansion of n in n 0.437 * [taylor]: Taking taylor expansion of PI in n 0.442 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.442 * [taylor]: Taking taylor expansion of 1.0 in k 0.442 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.442 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.442 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.442 * [taylor]: Taking taylor expansion of k in k 0.443 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.443 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.443 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.443 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.443 * [taylor]: Taking taylor expansion of 0.5 in k 0.443 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.443 * [taylor]: Taking taylor expansion of 1.0 in k 0.443 * [taylor]: Taking taylor expansion of k in k 0.443 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.443 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.444 * [taylor]: Taking taylor expansion of 2.0 in k 0.444 * [taylor]: Taking taylor expansion of (* n PI) in k 0.444 * [taylor]: Taking taylor expansion of n in k 0.444 * [taylor]: Taking taylor expansion of PI in k 0.444 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.444 * [taylor]: Taking taylor expansion of 1.0 in k 0.444 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.444 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.445 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.445 * [taylor]: Taking taylor expansion of k in k 0.446 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.446 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.446 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.446 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.446 * [taylor]: Taking taylor expansion of 0.5 in k 0.446 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.446 * [taylor]: Taking taylor expansion of 1.0 in k 0.446 * [taylor]: Taking taylor expansion of k in k 0.446 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.446 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.446 * [taylor]: Taking taylor expansion of 2.0 in k 0.446 * [taylor]: Taking taylor expansion of (* n PI) in k 0.446 * [taylor]: Taking taylor expansion of n in k 0.446 * [taylor]: Taking taylor expansion of PI in k 0.447 * [taylor]: Taking taylor expansion of 0 in n 0.453 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 0.453 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 0.453 * [taylor]: Taking taylor expansion of +nan.0 in n 0.453 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.453 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.453 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.453 * [taylor]: Taking taylor expansion of 0.5 in n 0.453 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.453 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.453 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.453 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.453 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.453 * [taylor]: Taking taylor expansion of 1.0 in n 0.453 * [taylor]: Taking taylor expansion of (log PI) in n 0.453 * [taylor]: Taking taylor expansion of PI in n 0.455 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.455 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.455 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.455 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.455 * [taylor]: Taking taylor expansion of 1.0 in n 0.455 * [taylor]: Taking taylor expansion of (log n) in n 0.455 * [taylor]: Taking taylor expansion of n in n 0.455 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.455 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.455 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.455 * [taylor]: Taking taylor expansion of 1.0 in n 0.455 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.455 * [taylor]: Taking taylor expansion of 2.0 in n 0.479 * [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 0.479 * [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 0.480 * [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 0.480 * [taylor]: Taking taylor expansion of +nan.0 in n 0.480 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.480 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.480 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.480 * [taylor]: Taking taylor expansion of 0.5 in n 0.480 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.480 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.480 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.480 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.480 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.480 * [taylor]: Taking taylor expansion of 1.0 in n 0.480 * [taylor]: Taking taylor expansion of (log PI) in n 0.480 * [taylor]: Taking taylor expansion of PI in n 0.481 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.481 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.482 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.482 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.482 * [taylor]: Taking taylor expansion of 1.0 in n 0.482 * [taylor]: Taking taylor expansion of (log n) in n 0.482 * [taylor]: Taking taylor expansion of n in n 0.482 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.482 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.482 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.482 * [taylor]: Taking taylor expansion of 1.0 in n 0.482 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.482 * [taylor]: Taking taylor expansion of 2.0 in n 0.487 * [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 0.487 * [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 0.488 * [taylor]: Taking taylor expansion of +nan.0 in n 0.488 * [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 0.488 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.488 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.488 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.488 * [taylor]: Taking taylor expansion of 0.5 in n 0.488 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.488 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.488 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.488 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.488 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.488 * [taylor]: Taking taylor expansion of 1.0 in n 0.488 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.488 * [taylor]: Taking taylor expansion of 2.0 in n 0.489 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.489 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.489 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.489 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.489 * [taylor]: Taking taylor expansion of 1.0 in n 0.489 * [taylor]: Taking taylor expansion of (log PI) in n 0.489 * [taylor]: Taking taylor expansion of PI in n 0.491 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.491 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.491 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.491 * [taylor]: Taking taylor expansion of 1.0 in n 0.491 * [taylor]: Taking taylor expansion of (log n) in n 0.491 * [taylor]: Taking taylor expansion of n in n 0.495 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.495 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.495 * [taylor]: Taking taylor expansion of 2.0 in n 0.495 * [taylor]: Taking taylor expansion of (* n PI) in n 0.495 * [taylor]: Taking taylor expansion of n in n 0.495 * [taylor]: Taking taylor expansion of PI in n 0.543 * [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 0.543 * [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 0.543 * [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 0.543 * [taylor]: Taking taylor expansion of +nan.0 in n 0.543 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.543 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.543 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.543 * [taylor]: Taking taylor expansion of 0.5 in n 0.543 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.543 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.543 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.543 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.544 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.544 * [taylor]: Taking taylor expansion of 1.0 in n 0.544 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.544 * [taylor]: Taking taylor expansion of 2.0 in n 0.545 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.545 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.545 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.545 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.545 * [taylor]: Taking taylor expansion of 1.0 in n 0.545 * [taylor]: Taking taylor expansion of (log n) in n 0.545 * [taylor]: Taking taylor expansion of n in n 0.546 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.546 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.546 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.546 * [taylor]: Taking taylor expansion of 1.0 in n 0.546 * [taylor]: Taking taylor expansion of (log PI) in n 0.546 * [taylor]: Taking taylor expansion of PI in n 0.551 * [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 0.551 * [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 0.551 * [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 0.551 * [taylor]: Taking taylor expansion of +nan.0 in n 0.551 * [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 0.551 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.551 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.551 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.551 * [taylor]: Taking taylor expansion of 0.5 in n 0.551 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.551 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.551 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.551 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.551 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.551 * [taylor]: Taking taylor expansion of 1.0 in n 0.551 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.551 * [taylor]: Taking taylor expansion of 2.0 in n 0.553 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.553 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.553 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.553 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.553 * [taylor]: Taking taylor expansion of 1.0 in n 0.553 * [taylor]: Taking taylor expansion of (log PI) in n 0.553 * [taylor]: Taking taylor expansion of PI in n 0.555 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.555 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.555 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.555 * [taylor]: Taking taylor expansion of 1.0 in n 0.555 * [taylor]: Taking taylor expansion of (log n) in n 0.555 * [taylor]: Taking taylor expansion of n in n 0.559 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.559 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.559 * [taylor]: Taking taylor expansion of 2.0 in n 0.559 * [taylor]: Taking taylor expansion of (* n PI) in n 0.559 * [taylor]: Taking taylor expansion of n in n 0.559 * [taylor]: Taking taylor expansion of PI in n 0.562 * [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 0.562 * [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 0.562 * [taylor]: Taking taylor expansion of +nan.0 in n 0.562 * [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 0.562 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.562 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.562 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.562 * [taylor]: Taking taylor expansion of 0.5 in n 0.562 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.562 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.562 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.562 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.562 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.562 * [taylor]: Taking taylor expansion of 1.0 in n 0.562 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.562 * [taylor]: Taking taylor expansion of 2.0 in n 0.564 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) 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 0.571 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.571 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.571 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.571 * [taylor]: Taking taylor expansion of 1.0 in n 0.571 * [taylor]: Taking taylor expansion of (log n) in n 0.571 * [taylor]: Taking taylor expansion of n in n 0.575 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.575 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.575 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.575 * [taylor]: Taking taylor expansion of 2.0 in n 0.575 * [taylor]: Taking taylor expansion of (* n PI) in n 0.575 * [taylor]: Taking taylor expansion of n in n 0.575 * [taylor]: Taking taylor expansion of PI in n 0.647 * [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 0.647 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.647 * [taylor]: Taking taylor expansion of 1.0 in n 0.647 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.647 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.647 * [taylor]: Taking taylor expansion of k in n 0.647 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.647 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.647 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.647 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.647 * [taylor]: Taking taylor expansion of 0.5 in n 0.647 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.647 * [taylor]: Taking taylor expansion of 1.0 in n 0.647 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.647 * [taylor]: Taking taylor expansion of k in n 0.647 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.647 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.647 * [taylor]: Taking taylor expansion of 2.0 in n 0.647 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.647 * [taylor]: Taking taylor expansion of PI in n 0.647 * [taylor]: Taking taylor expansion of n in n 0.651 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.651 * [taylor]: Taking taylor expansion of 1.0 in k 0.651 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.651 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.651 * [taylor]: Taking taylor expansion of k in k 0.652 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.652 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.652 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.652 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.652 * [taylor]: Taking taylor expansion of 0.5 in k 0.652 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.652 * [taylor]: Taking taylor expansion of 1.0 in k 0.652 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.652 * [taylor]: Taking taylor expansion of k in k 0.652 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.652 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.652 * [taylor]: Taking taylor expansion of 2.0 in k 0.652 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.652 * [taylor]: Taking taylor expansion of PI in k 0.652 * [taylor]: Taking taylor expansion of n in k 0.653 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.653 * [taylor]: Taking taylor expansion of 1.0 in k 0.653 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.653 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.653 * [taylor]: Taking taylor expansion of k in k 0.654 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.654 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.654 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.654 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.654 * [taylor]: Taking taylor expansion of 0.5 in k 0.654 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.654 * [taylor]: Taking taylor expansion of 1.0 in k 0.654 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.654 * [taylor]: Taking taylor expansion of k in k 0.655 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.655 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.655 * [taylor]: Taking taylor expansion of 2.0 in k 0.655 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.655 * [taylor]: Taking taylor expansion of PI in k 0.655 * [taylor]: Taking taylor expansion of n in k 0.661 * [taylor]: Taking taylor expansion of 0 in n 0.662 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.662 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.662 * [taylor]: Taking taylor expansion of +nan.0 in n 0.662 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.662 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.662 * [taylor]: Taking taylor expansion of 0.5 in n 0.662 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 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 0.664 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.664 * [taylor]: Taking taylor expansion of 1.0 in n 0.664 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.664 * [taylor]: Taking taylor expansion of k in n 0.671 * [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 0.672 * [taylor]: Taking taylor expansion of +nan.0 in n 0.672 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.672 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.672 * [taylor]: Taking taylor expansion of 0.5 in n 0.672 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.672 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.672 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.672 * [taylor]: Taking taylor expansion of 2.0 in n 0.672 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.672 * [taylor]: Taking taylor expansion of PI in n 0.672 * [taylor]: Taking taylor expansion of n in n 0.673 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.673 * [taylor]: Taking taylor expansion of 1.0 in n 0.673 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.673 * [taylor]: Taking taylor expansion of k in n 0.689 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.689 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.689 * [taylor]: Taking taylor expansion of +nan.0 in n 0.689 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.689 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.689 * [taylor]: Taking taylor expansion of 0.5 in n 0.689 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.689 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.689 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.689 * [taylor]: Taking taylor expansion of 2.0 in n 0.689 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.689 * [taylor]: Taking taylor expansion of PI in n 0.689 * [taylor]: Taking taylor expansion of n in n 0.690 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.690 * [taylor]: Taking taylor expansion of 1.0 in n 0.690 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.690 * [taylor]: Taking taylor expansion of k in n 0.698 * [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 0.699 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.699 * [taylor]: Taking taylor expansion of 1.0 in n 0.699 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.699 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.699 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.699 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.699 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.699 * [taylor]: Taking taylor expansion of 0.5 in n 0.699 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.699 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.699 * [taylor]: Taking taylor expansion of k in n 0.699 * [taylor]: Taking taylor expansion of 1.0 in n 0.699 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.699 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.699 * [taylor]: Taking taylor expansion of -2.0 in n 0.699 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.699 * [taylor]: Taking taylor expansion of PI in n 0.699 * [taylor]: Taking taylor expansion of n in n 0.702 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.702 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.702 * [taylor]: Taking taylor expansion of -1 in n 0.702 * [taylor]: Taking taylor expansion of k in n 0.703 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.703 * [taylor]: Taking taylor expansion of 1.0 in k 0.703 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.703 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.703 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.703 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.703 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.703 * [taylor]: Taking taylor expansion of 0.5 in k 0.703 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.703 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.703 * [taylor]: Taking taylor expansion of k in k 0.704 * [taylor]: Taking taylor expansion of 1.0 in k 0.704 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.704 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.704 * [taylor]: Taking taylor expansion of -2.0 in k 0.704 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.704 * [taylor]: Taking taylor expansion of PI in k 0.704 * [taylor]: Taking taylor expansion of n in k 0.704 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.704 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.704 * [taylor]: Taking taylor expansion of -1 in k 0.705 * [taylor]: Taking taylor expansion of k in k 0.706 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.706 * [taylor]: Taking taylor expansion of 1.0 in k 0.706 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.706 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.706 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.706 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.706 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.706 * [taylor]: Taking taylor expansion of 0.5 in k 0.706 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.706 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.706 * [taylor]: Taking taylor expansion of k in k 0.706 * [taylor]: Taking taylor expansion of 1.0 in k 0.706 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.706 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.706 * [taylor]: Taking taylor expansion of -2.0 in k 0.706 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.706 * [taylor]: Taking taylor expansion of PI in k 0.706 * [taylor]: Taking taylor expansion of n in k 0.707 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.707 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.707 * [taylor]: Taking taylor expansion of -1 in k 0.707 * [taylor]: Taking taylor expansion of k in k 0.709 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.709 * [taylor]: Taking taylor expansion of +nan.0 in n 0.709 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.709 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.709 * [taylor]: Taking taylor expansion of 0.5 in n 0.709 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.709 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.709 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.709 * [taylor]: Taking taylor expansion of k in n 0.709 * [taylor]: Taking taylor expansion of 1.0 in n 0.709 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.709 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.709 * [taylor]: Taking taylor expansion of -2.0 in n 0.709 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.709 * [taylor]: Taking taylor expansion of PI in n 0.709 * [taylor]: Taking taylor expansion of n in n 0.718 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.718 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.718 * [taylor]: Taking taylor expansion of +nan.0 in n 0.718 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.718 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.718 * [taylor]: Taking taylor expansion of 0.5 in n 0.718 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.718 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.718 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.718 * [taylor]: Taking taylor expansion of k in n 0.718 * [taylor]: Taking taylor expansion of 1.0 in n 0.718 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.718 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.718 * [taylor]: Taking taylor expansion of -2.0 in n 0.718 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.718 * [taylor]: Taking taylor expansion of PI in n 0.718 * [taylor]: Taking taylor expansion of n in n 0.735 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.735 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.735 * [taylor]: Taking taylor expansion of +nan.0 in n 0.735 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.735 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.735 * [taylor]: Taking taylor expansion of 0.5 in n 0.735 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.735 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.735 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.735 * [taylor]: Taking taylor expansion of k in n 0.735 * [taylor]: Taking taylor expansion of 1.0 in n 0.735 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.735 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.735 * [taylor]: Taking taylor expansion of -2.0 in n 0.735 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.735 * [taylor]: Taking taylor expansion of PI in n 0.735 * [taylor]: Taking taylor expansion of n in n 0.744 * * * [progress]: simplifying candidates 0.746 * [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))))))))) 0.850 * * * [progress]: adding candidates to table 1.301 * * [progress]: iteration 2 / 4 1.301 * * * [progress]: picking best candidate 1.324 * * * * [pick]: Picked # 1.324 * * * [progress]: localizing error 1.340 * * * [progress]: generating rewritten candidates 1.340 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 1.361 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 1.381 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 1.387 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 1.397 * * * [progress]: generating series expansions 1.397 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 1.398 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.398 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.398 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.398 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.398 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.398 * [taylor]: Taking taylor expansion of 0.5 in k 1.398 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.398 * [taylor]: Taking taylor expansion of 1.0 in k 1.398 * [taylor]: Taking taylor expansion of k in k 1.398 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.398 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.398 * [taylor]: Taking taylor expansion of 2.0 in k 1.398 * [taylor]: Taking taylor expansion of (* n PI) in k 1.399 * [taylor]: Taking taylor expansion of n in k 1.399 * [taylor]: Taking taylor expansion of PI in k 1.400 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.400 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.400 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.400 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.400 * [taylor]: Taking taylor expansion of 0.5 in n 1.400 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.400 * [taylor]: Taking taylor expansion of 1.0 in n 1.400 * [taylor]: Taking taylor expansion of k in n 1.400 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.400 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.400 * [taylor]: Taking taylor expansion of 2.0 in n 1.400 * [taylor]: Taking taylor expansion of (* n PI) in n 1.400 * [taylor]: Taking taylor expansion of n in n 1.400 * [taylor]: Taking taylor expansion of PI in n 1.405 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.405 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.405 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.405 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.405 * [taylor]: Taking taylor expansion of 0.5 in n 1.405 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.405 * [taylor]: Taking taylor expansion of 1.0 in n 1.405 * [taylor]: Taking taylor expansion of k in n 1.405 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.405 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.405 * [taylor]: Taking taylor expansion of 2.0 in n 1.405 * [taylor]: Taking taylor expansion of (* n PI) in n 1.405 * [taylor]: Taking taylor expansion of n in n 1.405 * [taylor]: Taking taylor expansion of PI in n 1.411 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.411 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.411 * [taylor]: Taking taylor expansion of 0.5 in k 1.411 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.411 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.411 * [taylor]: Taking taylor expansion of 1.0 in k 1.411 * [taylor]: Taking taylor expansion of k in k 1.411 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.411 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.411 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.411 * [taylor]: Taking taylor expansion of 2.0 in k 1.411 * [taylor]: Taking taylor expansion of PI in k 1.412 * [taylor]: Taking taylor expansion of (log n) in k 1.412 * [taylor]: Taking taylor expansion of n in k 1.421 * [taylor]: Taking taylor expansion of 0 in k 1.436 * [taylor]: Taking taylor expansion of 0 in k 1.460 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.461 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.461 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.461 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.461 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.461 * [taylor]: Taking taylor expansion of 0.5 in k 1.461 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.461 * [taylor]: Taking taylor expansion of 1.0 in k 1.461 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.461 * [taylor]: Taking taylor expansion of k in k 1.461 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.461 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.461 * [taylor]: Taking taylor expansion of 2.0 in k 1.461 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.461 * [taylor]: Taking taylor expansion of PI in k 1.461 * [taylor]: Taking taylor expansion of n in k 1.462 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.462 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.462 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.462 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.462 * [taylor]: Taking taylor expansion of 0.5 in n 1.462 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.462 * [taylor]: Taking taylor expansion of 1.0 in n 1.462 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.462 * [taylor]: Taking taylor expansion of k in n 1.462 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.462 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.462 * [taylor]: Taking taylor expansion of 2.0 in n 1.462 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.462 * [taylor]: Taking taylor expansion of PI in n 1.462 * [taylor]: Taking taylor expansion of n in n 1.466 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.466 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.466 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.466 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.466 * [taylor]: Taking taylor expansion of 0.5 in n 1.466 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.466 * [taylor]: Taking taylor expansion of 1.0 in n 1.466 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.466 * [taylor]: Taking taylor expansion of k in n 1.466 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.466 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.466 * [taylor]: Taking taylor expansion of 2.0 in n 1.466 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.466 * [taylor]: Taking taylor expansion of PI in n 1.466 * [taylor]: Taking taylor expansion of n in n 1.469 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.469 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.470 * [taylor]: Taking taylor expansion of 0.5 in k 1.470 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.470 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.470 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.470 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.470 * [taylor]: Taking taylor expansion of 2.0 in k 1.470 * [taylor]: Taking taylor expansion of PI in k 1.471 * [taylor]: Taking taylor expansion of (log n) in k 1.471 * [taylor]: Taking taylor expansion of n in k 1.471 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.471 * [taylor]: Taking taylor expansion of 1.0 in k 1.471 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.471 * [taylor]: Taking taylor expansion of k in k 1.480 * [taylor]: Taking taylor expansion of 0 in k 1.487 * [taylor]: Taking taylor expansion of 0 in k 1.496 * [taylor]: Taking taylor expansion of 0 in k 1.497 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.497 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.497 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.497 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.497 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.497 * [taylor]: Taking taylor expansion of 0.5 in k 1.497 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.497 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.497 * [taylor]: Taking taylor expansion of k in k 1.497 * [taylor]: Taking taylor expansion of 1.0 in k 1.497 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.497 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.497 * [taylor]: Taking taylor expansion of -2.0 in k 1.497 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.497 * [taylor]: Taking taylor expansion of PI in k 1.497 * [taylor]: Taking taylor expansion of n in k 1.498 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.498 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.498 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.498 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.498 * [taylor]: Taking taylor expansion of 0.5 in n 1.498 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.498 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.498 * [taylor]: Taking taylor expansion of k in n 1.498 * [taylor]: Taking taylor expansion of 1.0 in n 1.498 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.498 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.498 * [taylor]: Taking taylor expansion of -2.0 in n 1.498 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.498 * [taylor]: Taking taylor expansion of PI in n 1.498 * [taylor]: Taking taylor expansion of n in n 1.502 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.502 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.502 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.502 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.502 * [taylor]: Taking taylor expansion of 0.5 in n 1.502 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.502 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.502 * [taylor]: Taking taylor expansion of k in n 1.502 * [taylor]: Taking taylor expansion of 1.0 in n 1.502 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.502 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.502 * [taylor]: Taking taylor expansion of -2.0 in n 1.502 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.502 * [taylor]: Taking taylor expansion of PI in n 1.502 * [taylor]: Taking taylor expansion of n in n 1.506 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.506 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.506 * [taylor]: Taking taylor expansion of 0.5 in k 1.506 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.506 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.506 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.506 * [taylor]: Taking taylor expansion of k in k 1.506 * [taylor]: Taking taylor expansion of 1.0 in k 1.506 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.506 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.506 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.506 * [taylor]: Taking taylor expansion of -2.0 in k 1.506 * [taylor]: Taking taylor expansion of PI in k 1.507 * [taylor]: Taking taylor expansion of (log n) in k 1.507 * [taylor]: Taking taylor expansion of n in k 1.516 * [taylor]: Taking taylor expansion of 0 in k 1.523 * [taylor]: Taking taylor expansion of 0 in k 1.531 * [taylor]: Taking taylor expansion of 0 in k 1.532 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 1.532 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.532 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.533 * [taylor]: Taking taylor expansion of 2.0 in n 1.533 * [taylor]: Taking taylor expansion of (* n PI) in n 1.533 * [taylor]: Taking taylor expansion of n in n 1.533 * [taylor]: Taking taylor expansion of PI in n 1.533 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.533 * [taylor]: Taking taylor expansion of 2.0 in n 1.533 * [taylor]: Taking taylor expansion of (* n PI) in n 1.533 * [taylor]: Taking taylor expansion of n in n 1.533 * [taylor]: Taking taylor expansion of PI in n 1.552 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.552 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.552 * [taylor]: Taking taylor expansion of 2.0 in n 1.552 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.552 * [taylor]: Taking taylor expansion of PI in n 1.552 * [taylor]: Taking taylor expansion of n in n 1.552 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.552 * [taylor]: Taking taylor expansion of 2.0 in n 1.552 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.552 * [taylor]: Taking taylor expansion of PI in n 1.552 * [taylor]: Taking taylor expansion of n in n 1.561 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.561 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.562 * [taylor]: Taking taylor expansion of -2.0 in n 1.562 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.562 * [taylor]: Taking taylor expansion of PI in n 1.562 * [taylor]: Taking taylor expansion of n in n 1.562 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.562 * [taylor]: Taking taylor expansion of -2.0 in n 1.562 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.562 * [taylor]: Taking taylor expansion of PI in n 1.562 * [taylor]: Taking taylor expansion of n in n 1.570 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 1.571 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.571 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.571 * [taylor]: Taking taylor expansion of 1.0 in k 1.571 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.571 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.571 * [taylor]: Taking taylor expansion of k in k 1.572 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.572 * [taylor]: Taking taylor expansion of 1.0 in k 1.572 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.572 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.572 * [taylor]: Taking taylor expansion of k in k 1.583 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.583 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.583 * [taylor]: Taking taylor expansion of 1.0 in k 1.583 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.583 * [taylor]: Taking taylor expansion of k in k 1.584 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.584 * [taylor]: Taking taylor expansion of 1.0 in k 1.584 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.584 * [taylor]: Taking taylor expansion of k in k 1.594 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.594 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.594 * [taylor]: Taking taylor expansion of 1.0 in k 1.594 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.594 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.594 * [taylor]: Taking taylor expansion of -1 in k 1.594 * [taylor]: Taking taylor expansion of k in k 1.595 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.595 * [taylor]: Taking taylor expansion of 1.0 in k 1.595 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.595 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.595 * [taylor]: Taking taylor expansion of -1 in k 1.595 * [taylor]: Taking taylor expansion of k in k 1.606 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 1.607 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.607 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.607 * [taylor]: Taking taylor expansion of 1.0 in k 1.607 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.607 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.607 * [taylor]: Taking taylor expansion of k in k 1.608 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.608 * [taylor]: Taking taylor expansion of 1.0 in k 1.608 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.608 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.608 * [taylor]: Taking taylor expansion of k in k 1.619 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.619 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.619 * [taylor]: Taking taylor expansion of 1.0 in k 1.619 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.620 * [taylor]: Taking taylor expansion of k in k 1.620 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.620 * [taylor]: Taking taylor expansion of 1.0 in k 1.621 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.621 * [taylor]: Taking taylor expansion of k in k 1.637 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.637 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.637 * [taylor]: Taking taylor expansion of 1.0 in k 1.637 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.637 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.637 * [taylor]: Taking taylor expansion of -1 in k 1.637 * [taylor]: Taking taylor expansion of k in k 1.639 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.639 * [taylor]: Taking taylor expansion of 1.0 in k 1.639 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.639 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.639 * [taylor]: Taking taylor expansion of -1 in k 1.639 * [taylor]: Taking taylor expansion of k in k 1.650 * * * [progress]: simplifying candidates 1.652 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 1.659 * * [simplify]: iteration 0 : 579 enodes (cost 912 ) 1.668 * * [simplify]: iteration 1 : 2248 enodes (cost 843 ) 1.707 * * [simplify]: iteration 2 : 5001 enodes (cost 807 ) 1.712 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 1/2) (pow (* (* 2.0 PI) n) 1/2) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (pow k 1/2)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (* (fabs (cbrt k)) 1)) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (pow k 1/2)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (* (fabs (cbrt k)) 1)) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (fma (- 0.5) (fma (* k (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n))) (* (* k (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log n))) (fma (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (pow (log (* 2.0 PI)) 2) (fma (* (* 0.125 (pow k 2)) (pow (log n) 2)) (pow (* (* 2.0 PI) n) 0.5) (fma (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (pow (* (* 2.0 PI) n) 0.5))))) (pow (* (* 2.0 PI) n) (* 0.5 (- 1.0 k))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (fma (- k) +nan.0 (fma +nan.0 (pow k 2) (- +nan.0))) (fma +nan.0 (- (/ 1 k) (/ 1 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (/ +nan.0 k) (- (fma +nan.0 1 (/ +nan.0 (pow k 2))))) (fma (- k) +nan.0 (fma +nan.0 (pow k 2) (- +nan.0))) (fma +nan.0 (- (/ 1 k) (/ 1 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (/ +nan.0 k) (- (fma +nan.0 1 (/ +nan.0 (pow k 2))))) 1.712 * * * [progress]: adding candidates to table 2.180 * * [progress]: iteration 3 / 4 2.180 * * * [progress]: picking best candidate 2.205 * * * * [pick]: Picked # 2.205 * * * [progress]: localizing error 2.221 * * * [progress]: generating rewritten candidates 2.221 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.246 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 2.253 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 2.277 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 2.325 * * * [progress]: generating series expansions 2.325 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.326 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.326 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.326 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.326 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.326 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.326 * [taylor]: Taking taylor expansion of 0.5 in k 2.326 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.326 * [taylor]: Taking taylor expansion of 1.0 in k 2.326 * [taylor]: Taking taylor expansion of k in k 2.326 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.326 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.326 * [taylor]: Taking taylor expansion of 2.0 in k 2.326 * [taylor]: Taking taylor expansion of (* n PI) in k 2.326 * [taylor]: Taking taylor expansion of n in k 2.326 * [taylor]: Taking taylor expansion of PI in k 2.327 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.327 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.327 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.327 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.327 * [taylor]: Taking taylor expansion of 0.5 in n 2.327 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.327 * [taylor]: Taking taylor expansion of 1.0 in n 2.327 * [taylor]: Taking taylor expansion of k in n 2.327 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.328 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.328 * [taylor]: Taking taylor expansion of 2.0 in n 2.328 * [taylor]: Taking taylor expansion of (* n PI) in n 2.328 * [taylor]: Taking taylor expansion of n in n 2.328 * [taylor]: Taking taylor expansion of PI in n 2.333 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.333 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.333 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.333 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.333 * [taylor]: Taking taylor expansion of 0.5 in n 2.333 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.333 * [taylor]: Taking taylor expansion of 1.0 in n 2.333 * [taylor]: Taking taylor expansion of k in n 2.333 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.333 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.333 * [taylor]: Taking taylor expansion of 2.0 in n 2.333 * [taylor]: Taking taylor expansion of (* n PI) in n 2.333 * [taylor]: Taking taylor expansion of n in n 2.333 * [taylor]: Taking taylor expansion of PI in n 2.338 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.338 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.338 * [taylor]: Taking taylor expansion of 0.5 in k 2.338 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.338 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.338 * [taylor]: Taking taylor expansion of 1.0 in k 2.338 * [taylor]: Taking taylor expansion of k in k 2.338 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.338 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.338 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.338 * [taylor]: Taking taylor expansion of 2.0 in k 2.338 * [taylor]: Taking taylor expansion of PI in k 2.339 * [taylor]: Taking taylor expansion of (log n) in k 2.339 * [taylor]: Taking taylor expansion of n in k 2.348 * [taylor]: Taking taylor expansion of 0 in k 2.364 * [taylor]: Taking taylor expansion of 0 in k 2.390 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.390 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.390 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.390 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.390 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.390 * [taylor]: Taking taylor expansion of 0.5 in k 2.390 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.390 * [taylor]: Taking taylor expansion of 1.0 in k 2.390 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.390 * [taylor]: Taking taylor expansion of k in k 2.390 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.390 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.390 * [taylor]: Taking taylor expansion of 2.0 in k 2.390 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.390 * [taylor]: Taking taylor expansion of PI in k 2.390 * [taylor]: Taking taylor expansion of n in k 2.391 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.391 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.391 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.391 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.391 * [taylor]: Taking taylor expansion of 0.5 in n 2.391 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.391 * [taylor]: Taking taylor expansion of 1.0 in n 2.391 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.391 * [taylor]: Taking taylor expansion of k in n 2.391 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.391 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.392 * [taylor]: Taking taylor expansion of 2.0 in n 2.392 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.392 * [taylor]: Taking taylor expansion of PI in n 2.392 * [taylor]: Taking taylor expansion of n in n 2.395 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.395 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.395 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.395 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.395 * [taylor]: Taking taylor expansion of 0.5 in n 2.395 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.395 * [taylor]: Taking taylor expansion of 1.0 in n 2.395 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.395 * [taylor]: Taking taylor expansion of k in n 2.395 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.395 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.395 * [taylor]: Taking taylor expansion of 2.0 in n 2.395 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.395 * [taylor]: Taking taylor expansion of PI in n 2.395 * [taylor]: Taking taylor expansion of n in n 2.399 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.399 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.399 * [taylor]: Taking taylor expansion of 0.5 in k 2.399 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.399 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.399 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.399 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.399 * [taylor]: Taking taylor expansion of 2.0 in k 2.399 * [taylor]: Taking taylor expansion of PI in k 2.400 * [taylor]: Taking taylor expansion of (log n) in k 2.400 * [taylor]: Taking taylor expansion of n in k 2.400 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.400 * [taylor]: Taking taylor expansion of 1.0 in k 2.400 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.400 * [taylor]: Taking taylor expansion of k in k 2.409 * [taylor]: Taking taylor expansion of 0 in k 2.416 * [taylor]: Taking taylor expansion of 0 in k 2.426 * [taylor]: Taking taylor expansion of 0 in k 2.427 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.427 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.427 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.427 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.427 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.427 * [taylor]: Taking taylor expansion of 0.5 in k 2.427 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.427 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.427 * [taylor]: Taking taylor expansion of k in k 2.427 * [taylor]: Taking taylor expansion of 1.0 in k 2.427 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.427 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.427 * [taylor]: Taking taylor expansion of -2.0 in k 2.427 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.427 * [taylor]: Taking taylor expansion of PI in k 2.428 * [taylor]: Taking taylor expansion of n in k 2.428 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.428 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.428 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.428 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.428 * [taylor]: Taking taylor expansion of 0.5 in n 2.428 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.428 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.428 * [taylor]: Taking taylor expansion of k in n 2.428 * [taylor]: Taking taylor expansion of 1.0 in n 2.428 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.429 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.429 * [taylor]: Taking taylor expansion of -2.0 in n 2.429 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.429 * [taylor]: Taking taylor expansion of PI in n 2.429 * [taylor]: Taking taylor expansion of n in n 2.432 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.432 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.432 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.432 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.432 * [taylor]: Taking taylor expansion of 0.5 in n 2.432 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.432 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.432 * [taylor]: Taking taylor expansion of k in n 2.432 * [taylor]: Taking taylor expansion of 1.0 in n 2.432 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.432 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.432 * [taylor]: Taking taylor expansion of -2.0 in n 2.432 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.432 * [taylor]: Taking taylor expansion of PI in n 2.432 * [taylor]: Taking taylor expansion of n in n 2.436 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.436 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.436 * [taylor]: Taking taylor expansion of 0.5 in k 2.436 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.436 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.436 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.436 * [taylor]: Taking taylor expansion of k in k 2.436 * [taylor]: Taking taylor expansion of 1.0 in k 2.436 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.436 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.436 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.436 * [taylor]: Taking taylor expansion of -2.0 in k 2.436 * [taylor]: Taking taylor expansion of PI in k 2.437 * [taylor]: Taking taylor expansion of (log n) in k 2.437 * [taylor]: Taking taylor expansion of n in k 2.446 * [taylor]: Taking taylor expansion of 0 in k 2.453 * [taylor]: Taking taylor expansion of 0 in k 2.462 * [taylor]: Taking taylor expansion of 0 in k 2.463 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 2.463 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 2.463 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 2.463 * [taylor]: Taking taylor expansion of 1.0 in k 2.463 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 2.463 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 2.463 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 2.463 * [taylor]: Taking taylor expansion of 1/4 in k 2.463 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.463 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.463 * [taylor]: Taking taylor expansion of k in k 2.464 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 2.464 * [taylor]: Taking taylor expansion of 1.0 in k 2.464 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 2.464 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 2.464 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 2.464 * [taylor]: Taking taylor expansion of 1/4 in k 2.464 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.464 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.464 * [taylor]: Taking taylor expansion of k in k 2.528 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 2.528 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 2.528 * [taylor]: Taking taylor expansion of 1.0 in k 2.528 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 2.528 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 2.528 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 2.528 * [taylor]: Taking taylor expansion of 1/4 in k 2.528 * [taylor]: Taking taylor expansion of (log k) in k 2.528 * [taylor]: Taking taylor expansion of k in k 2.528 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 2.528 * [taylor]: Taking taylor expansion of 1.0 in k 2.528 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 2.528 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 2.528 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 2.529 * [taylor]: Taking taylor expansion of 1/4 in k 2.529 * [taylor]: Taking taylor expansion of (log k) in k 2.529 * [taylor]: Taking taylor expansion of k in k 2.589 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 2.589 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 2.589 * [taylor]: Taking taylor expansion of 1.0 in k 2.589 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 2.589 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 2.589 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.589 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.589 * [taylor]: Taking taylor expansion of -1 in k 2.589 * [taylor]: Taking taylor expansion of k in k 2.596 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 2.596 * [taylor]: Taking taylor expansion of 1.0 in k 2.596 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 2.596 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 2.596 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.596 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.596 * [taylor]: Taking taylor expansion of -1 in k 2.596 * [taylor]: Taking taylor expansion of k in k 2.633 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 2.633 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.633 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.633 * [taylor]: Taking taylor expansion of 1.0 in k 2.633 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.633 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.633 * [taylor]: Taking taylor expansion of k in k 2.634 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.634 * [taylor]: Taking taylor expansion of 1.0 in k 2.634 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.634 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.634 * [taylor]: Taking taylor expansion of k in k 2.652 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.652 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.652 * [taylor]: Taking taylor expansion of 1.0 in k 2.652 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.652 * [taylor]: Taking taylor expansion of k in k 2.653 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.653 * [taylor]: Taking taylor expansion of 1.0 in k 2.653 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.653 * [taylor]: Taking taylor expansion of k in k 2.663 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.663 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.663 * [taylor]: Taking taylor expansion of 1.0 in k 2.663 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.664 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.664 * [taylor]: Taking taylor expansion of -1 in k 2.664 * [taylor]: Taking taylor expansion of k in k 2.665 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.665 * [taylor]: Taking taylor expansion of 1.0 in k 2.665 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.665 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.665 * [taylor]: Taking taylor expansion of -1 in k 2.665 * [taylor]: Taking taylor expansion of k in k 2.676 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 2.677 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.677 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.677 * [taylor]: Taking taylor expansion of 2.0 in n 2.677 * [taylor]: Taking taylor expansion of (* n PI) in n 2.677 * [taylor]: Taking taylor expansion of n in n 2.677 * [taylor]: Taking taylor expansion of PI in n 2.677 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.677 * [taylor]: Taking taylor expansion of 2.0 in n 2.677 * [taylor]: Taking taylor expansion of (* n PI) in n 2.677 * [taylor]: Taking taylor expansion of n in n 2.677 * [taylor]: Taking taylor expansion of PI in n 2.689 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.689 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.689 * [taylor]: Taking taylor expansion of 2.0 in n 2.689 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.689 * [taylor]: Taking taylor expansion of PI in n 2.689 * [taylor]: Taking taylor expansion of n in n 2.690 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.690 * [taylor]: Taking taylor expansion of 2.0 in n 2.690 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.690 * [taylor]: Taking taylor expansion of PI in n 2.690 * [taylor]: Taking taylor expansion of n in n 2.698 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.698 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.698 * [taylor]: Taking taylor expansion of -2.0 in n 2.698 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.698 * [taylor]: Taking taylor expansion of PI in n 2.698 * [taylor]: Taking taylor expansion of n in n 2.699 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.699 * [taylor]: Taking taylor expansion of -2.0 in n 2.699 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.699 * [taylor]: Taking taylor expansion of PI in n 2.699 * [taylor]: Taking taylor expansion of n in n 2.707 * * * [progress]: simplifying candidates 2.716 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ 1.0 (sqrt (sqrt k)))) (log1p (/ 1.0 (sqrt (sqrt k)))) (- (log 1.0) (log (sqrt (sqrt k)))) (log (/ 1.0 (sqrt (sqrt k)))) (exp (/ 1.0 (sqrt (sqrt k)))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (cbrt (/ 1.0 (sqrt (sqrt k)))) (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (- 1.0) (- (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt 1))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (cbrt (sqrt (sqrt k)))) (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1.0 (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1.0 (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt 1))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1 1) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) 1.0) (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt 1))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1.0 1) (/ (sqrt (sqrt k)) (cbrt 1.0)) (/ (sqrt (sqrt k)) (sqrt 1.0)) (/ (sqrt (sqrt k)) 1.0) (expm1 (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (log1p (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (- (log 1.0) (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (- (log (/ 1.0 (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (log (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (exp (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (/ 1.0 (sqrt (sqrt k)))) (- (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt 1)) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) 1) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt 1)) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) 1) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt 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PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 2.743 * * [simplify]: iteration 0 : 1355 enodes (cost 5833 ) 2.763 * * [simplify]: iteration 1 : 5001 enodes (cost 5050 ) 2.784 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 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(sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ 1 (* (sqrt (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1 (* 1 (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1 (* 1 (fabs (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1.0 (fabs (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1.0 (/ 1 (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1.0 (/ 1 (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1.0 (/ 1 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ (sqrt k) 1.0) (/ (/ 1.0 (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (* (fabs (cbrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (cbrt (/ 1.0 (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (sqrt (/ 1.0 (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt k) 1.0) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt k) 1.0) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt k) 1.0) (/ (sqrt k) 1.0) (sqrt k) (sqrt k) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 1/2) (pow (* (* 2.0 PI) n) 1/2) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (+ (* (* 0.125 (pow k 2)) (+ (* (pow (exp 0.5) (log (* (* 2.0 PI) n))) (pow (log (* 2.0 PI)) 2)) (* (pow (log n) 2) (pow (exp 0.5) (log (* (* 2.0 PI) n)))))) (- (fma (* 0.25 (pow k 2)) (* (* (log n) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (* (* 0.5 k) (+ (* (pow (exp 0.5) (log (* (* 2.0 PI) n))) (log (* 2.0 PI))) (* (log n) (pow (exp 0.5) (log (* (* 2.0 PI) n)))))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (+ (- (* 1.0 (sqrt +nan.0)) (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))) (* +nan.0 (- (/ 1 (* (sqrt +nan.0) k)) (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))))) (+ (- (* +nan.0 k)) (fma +nan.0 (pow k 2) (- +nan.0))) (+ (- (* +nan.0 (/ 1 (pow k 2)))) (fma +nan.0 (/ 1 k) (- (* +nan.0 (/ 1 (pow k 3)))))) (+ (- (* +nan.0 (/ 1 (pow k 2)))) (fma +nan.0 (/ 1 k) (- +nan.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) 2.788 * * * [progress]: adding candidates to table 3.584 * * [progress]: iteration 4 / 4 3.584 * * * [progress]: picking best candidate 3.609 * * * * [pick]: Picked # 3.609 * * * [progress]: localizing error 3.625 * * * [progress]: generating rewritten candidates 3.625 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2) 3.646 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2) 3.670 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 2 1) 3.686 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 2 1) 3.706 * * * [progress]: generating series expansions 3.706 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2) 3.707 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.707 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.707 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.707 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.707 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.707 * [taylor]: Taking taylor expansion of 0.5 in k 3.707 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.707 * [taylor]: Taking taylor expansion of 1.0 in k 3.707 * [taylor]: Taking taylor expansion of k in k 3.707 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.707 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.707 * [taylor]: Taking taylor expansion of 2.0 in k 3.707 * [taylor]: Taking taylor expansion of (* n PI) in k 3.707 * [taylor]: Taking taylor expansion of n in k 3.707 * [taylor]: Taking taylor expansion of PI in k 3.708 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.708 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.709 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.709 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.709 * [taylor]: Taking taylor expansion of 0.5 in n 3.709 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.709 * [taylor]: Taking taylor expansion of 1.0 in n 3.709 * [taylor]: Taking taylor expansion of k in n 3.709 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.709 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.709 * [taylor]: Taking taylor expansion of 2.0 in n 3.709 * [taylor]: Taking taylor expansion of (* n PI) in n 3.709 * [taylor]: Taking taylor expansion of n in n 3.709 * [taylor]: Taking taylor expansion of PI in n 3.714 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.714 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.714 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.714 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.714 * [taylor]: Taking taylor expansion of 0.5 in n 3.714 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.714 * [taylor]: Taking taylor expansion of 1.0 in n 3.714 * [taylor]: Taking taylor expansion of k in n 3.714 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.714 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.714 * [taylor]: Taking taylor expansion of 2.0 in n 3.714 * [taylor]: Taking taylor expansion of (* n PI) in n 3.714 * [taylor]: Taking taylor expansion of n in n 3.714 * [taylor]: Taking taylor expansion of PI in n 3.719 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.720 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.720 * [taylor]: Taking taylor expansion of 0.5 in k 3.720 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.720 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.720 * [taylor]: Taking taylor expansion of 1.0 in k 3.720 * [taylor]: Taking taylor expansion of k in k 3.720 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.720 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.720 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.720 * [taylor]: Taking taylor expansion of 2.0 in k 3.720 * [taylor]: Taking taylor expansion of PI in k 3.721 * [taylor]: Taking taylor expansion of (log n) in k 3.721 * [taylor]: Taking taylor expansion of n in k 3.734 * [taylor]: Taking taylor expansion of 0 in k 3.750 * [taylor]: Taking taylor expansion of 0 in k 3.768 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.768 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.768 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.768 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.768 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.768 * [taylor]: Taking taylor expansion of 0.5 in k 3.768 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.768 * [taylor]: Taking taylor expansion of 1.0 in k 3.768 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.768 * [taylor]: Taking taylor expansion of k in k 3.768 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.768 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.768 * [taylor]: Taking taylor expansion of 2.0 in k 3.768 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.768 * [taylor]: Taking taylor expansion of PI in k 3.768 * [taylor]: Taking taylor expansion of n in k 3.769 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.769 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.769 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.769 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.769 * [taylor]: Taking taylor expansion of 0.5 in n 3.769 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.770 * [taylor]: Taking taylor expansion of 1.0 in n 3.770 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.770 * [taylor]: Taking taylor expansion of k in n 3.770 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.770 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.770 * [taylor]: Taking taylor expansion of 2.0 in n 3.770 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.770 * [taylor]: Taking taylor expansion of PI in n 3.770 * [taylor]: Taking taylor expansion of n in n 3.773 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.773 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.773 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.773 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.773 * [taylor]: Taking taylor expansion of 0.5 in n 3.773 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.773 * [taylor]: Taking taylor expansion of 1.0 in n 3.773 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.773 * [taylor]: Taking taylor expansion of k in n 3.773 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.773 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.773 * [taylor]: Taking taylor expansion of 2.0 in n 3.773 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.773 * [taylor]: Taking taylor expansion of PI in n 3.773 * [taylor]: Taking taylor expansion of n in n 3.777 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.777 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.777 * [taylor]: Taking taylor expansion of 0.5 in k 3.777 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.777 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.777 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.777 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.777 * [taylor]: Taking taylor expansion of 2.0 in k 3.777 * [taylor]: Taking taylor expansion of PI in k 3.778 * [taylor]: Taking taylor expansion of (log n) in k 3.778 * [taylor]: Taking taylor expansion of n in k 3.778 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.778 * [taylor]: Taking taylor expansion of 1.0 in k 3.778 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.778 * [taylor]: Taking taylor expansion of k in k 3.787 * [taylor]: Taking taylor expansion of 0 in k 3.794 * [taylor]: Taking taylor expansion of 0 in k 3.803 * [taylor]: Taking taylor expansion of 0 in k 3.804 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.804 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.804 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.804 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.804 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.804 * [taylor]: Taking taylor expansion of 0.5 in k 3.804 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.804 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.804 * [taylor]: Taking taylor expansion of k in k 3.805 * [taylor]: Taking taylor expansion of 1.0 in k 3.805 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.805 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.805 * [taylor]: Taking taylor expansion of -2.0 in k 3.805 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.805 * [taylor]: Taking taylor expansion of PI in k 3.805 * [taylor]: Taking taylor expansion of n in k 3.805 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.805 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.805 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.805 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.806 * [taylor]: Taking taylor expansion of 0.5 in n 3.806 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.806 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.806 * [taylor]: Taking taylor expansion of k in n 3.806 * [taylor]: Taking taylor expansion of 1.0 in n 3.806 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.806 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.806 * [taylor]: Taking taylor expansion of -2.0 in n 3.806 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.806 * [taylor]: Taking taylor expansion of PI in n 3.806 * [taylor]: Taking taylor expansion of n in n 3.809 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.809 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.809 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.809 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.809 * [taylor]: Taking taylor expansion of 0.5 in n 3.809 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.809 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.809 * [taylor]: Taking taylor expansion of k in n 3.809 * [taylor]: Taking taylor expansion of 1.0 in n 3.809 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.809 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.809 * [taylor]: Taking taylor expansion of -2.0 in n 3.809 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.809 * [taylor]: Taking taylor expansion of PI in n 3.809 * [taylor]: Taking taylor expansion of n in n 3.813 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 3.813 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 3.813 * [taylor]: Taking taylor expansion of 0.5 in k 3.813 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 3.813 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.813 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.813 * [taylor]: Taking taylor expansion of k in k 3.813 * [taylor]: Taking taylor expansion of 1.0 in k 3.813 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.813 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.813 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.813 * [taylor]: Taking taylor expansion of -2.0 in k 3.813 * [taylor]: Taking taylor expansion of PI in k 3.814 * [taylor]: Taking taylor expansion of (log n) in k 3.814 * [taylor]: Taking taylor expansion of n in k 3.829 * [taylor]: Taking taylor expansion of 0 in k 3.835 * [taylor]: Taking taylor expansion of 0 in k 3.843 * [taylor]: Taking taylor expansion of 0 in k 3.844 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2) 3.845 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.845 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.845 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.845 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.845 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.845 * [taylor]: Taking taylor expansion of 0.5 in k 3.845 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.845 * [taylor]: Taking taylor expansion of 1.0 in k 3.845 * [taylor]: Taking taylor expansion of k in k 3.845 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.845 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.845 * [taylor]: Taking taylor expansion of 2.0 in k 3.845 * [taylor]: Taking taylor expansion of (* n PI) in k 3.845 * [taylor]: Taking taylor expansion of n in k 3.845 * [taylor]: Taking taylor expansion of PI in k 3.846 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.846 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.846 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.846 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.846 * [taylor]: Taking taylor expansion of 0.5 in n 3.846 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.846 * [taylor]: Taking taylor expansion of 1.0 in n 3.846 * [taylor]: Taking taylor expansion of k in n 3.846 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.846 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.846 * [taylor]: Taking taylor expansion of 2.0 in n 3.846 * [taylor]: Taking taylor expansion of (* n PI) in n 3.846 * [taylor]: Taking taylor expansion of n in n 3.846 * [taylor]: Taking taylor expansion of PI in n 3.851 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.851 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.851 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.851 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.851 * [taylor]: Taking taylor expansion of 0.5 in n 3.851 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.851 * [taylor]: Taking taylor expansion of 1.0 in n 3.851 * [taylor]: Taking taylor expansion of k in n 3.851 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.851 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.851 * [taylor]: Taking taylor expansion of 2.0 in n 3.851 * [taylor]: Taking taylor expansion of (* n PI) in n 3.852 * [taylor]: Taking taylor expansion of n in n 3.852 * [taylor]: Taking taylor expansion of PI in n 3.856 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.856 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.857 * [taylor]: Taking taylor expansion of 0.5 in k 3.857 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.857 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.857 * [taylor]: Taking taylor expansion of 1.0 in k 3.857 * [taylor]: Taking taylor expansion of k in k 3.857 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.857 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.857 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.857 * [taylor]: Taking taylor expansion of 2.0 in k 3.857 * [taylor]: Taking taylor expansion of PI in k 3.858 * [taylor]: Taking taylor expansion of (log n) in k 3.858 * [taylor]: Taking taylor expansion of n in k 3.866 * [taylor]: Taking taylor expansion of 0 in k 3.881 * [taylor]: Taking taylor expansion of 0 in k 3.899 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.899 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.899 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.899 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.899 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.899 * [taylor]: Taking taylor expansion of 0.5 in k 3.899 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.899 * [taylor]: Taking taylor expansion of 1.0 in k 3.899 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.899 * [taylor]: Taking taylor expansion of k in k 3.900 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.900 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.900 * [taylor]: Taking taylor expansion of 2.0 in k 3.900 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.900 * [taylor]: Taking taylor expansion of PI in k 3.900 * [taylor]: Taking taylor expansion of n in k 3.901 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.901 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.901 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.901 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.901 * [taylor]: Taking taylor expansion of 0.5 in n 3.901 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.901 * [taylor]: Taking taylor expansion of 1.0 in n 3.901 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.901 * [taylor]: Taking taylor expansion of k in n 3.901 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.901 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.901 * [taylor]: Taking taylor expansion of 2.0 in n 3.901 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.901 * [taylor]: Taking taylor expansion of PI in n 3.901 * [taylor]: Taking taylor expansion of n in n 3.904 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.904 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.904 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.904 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.904 * [taylor]: Taking taylor expansion of 0.5 in n 3.904 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.904 * [taylor]: Taking taylor expansion of 1.0 in n 3.904 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.904 * [taylor]: Taking taylor expansion of k in n 3.904 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.904 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.904 * [taylor]: Taking taylor expansion of 2.0 in n 3.904 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.904 * [taylor]: Taking taylor expansion of PI in n 3.905 * [taylor]: Taking taylor expansion of n in n 3.908 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.908 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.908 * [taylor]: Taking taylor expansion of 0.5 in k 3.908 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.908 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.908 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.908 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.908 * [taylor]: Taking taylor expansion of 2.0 in k 3.908 * [taylor]: Taking taylor expansion of PI in k 3.909 * [taylor]: Taking taylor expansion of (log n) in k 3.909 * [taylor]: Taking taylor expansion of n in k 3.909 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.909 * [taylor]: Taking taylor expansion of 1.0 in k 3.909 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.909 * [taylor]: Taking taylor expansion of k in k 3.924 * [taylor]: Taking taylor expansion of 0 in k 3.931 * [taylor]: Taking taylor expansion of 0 in k 3.939 * [taylor]: Taking taylor expansion of 0 in k 3.941 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.941 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.941 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.941 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.941 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.941 * [taylor]: Taking taylor expansion of 0.5 in k 3.941 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.941 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.941 * [taylor]: Taking taylor expansion of k in k 3.941 * [taylor]: Taking taylor expansion of 1.0 in k 3.941 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.941 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.941 * [taylor]: Taking taylor expansion of -2.0 in k 3.941 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.941 * [taylor]: Taking taylor expansion of PI in k 3.941 * [taylor]: Taking taylor expansion of n in k 3.942 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.942 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.942 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.942 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.942 * [taylor]: Taking taylor expansion of 0.5 in n 3.942 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.942 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.942 * [taylor]: Taking taylor expansion of k in n 3.942 * [taylor]: Taking taylor expansion of 1.0 in n 3.942 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.942 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.942 * [taylor]: Taking taylor expansion of -2.0 in n 3.942 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.942 * [taylor]: Taking taylor expansion of PI in n 3.942 * [taylor]: Taking taylor expansion of n in n 3.946 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.946 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.946 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.946 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.946 * [taylor]: Taking taylor expansion of 0.5 in n 3.946 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.946 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.946 * [taylor]: Taking taylor expansion of k in n 3.946 * [taylor]: Taking taylor expansion of 1.0 in n 3.946 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.946 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.946 * [taylor]: Taking taylor expansion of -2.0 in n 3.946 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.946 * [taylor]: Taking taylor expansion of PI in n 3.946 * [taylor]: Taking taylor expansion of n in n 3.949 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 3.949 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 3.949 * [taylor]: Taking taylor expansion of 0.5 in k 3.949 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 3.949 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.949 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.949 * [taylor]: Taking taylor expansion of k in k 3.950 * [taylor]: Taking taylor expansion of 1.0 in k 3.950 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.950 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.950 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.950 * [taylor]: Taking taylor expansion of -2.0 in k 3.950 * [taylor]: Taking taylor expansion of PI in k 3.951 * [taylor]: Taking taylor expansion of (log n) in k 3.951 * [taylor]: Taking taylor expansion of n in k 3.959 * [taylor]: Taking taylor expansion of 0 in k 3.966 * [taylor]: Taking taylor expansion of 0 in k 3.975 * [taylor]: Taking taylor expansion of 0 in k 3.975 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 2 1) 3.976 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.976 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.976 * [taylor]: Taking taylor expansion of 2.0 in n 3.976 * [taylor]: Taking taylor expansion of (* n PI) in n 3.976 * [taylor]: Taking taylor expansion of n in n 3.976 * [taylor]: Taking taylor expansion of PI in n 3.976 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.976 * [taylor]: Taking taylor expansion of 2.0 in n 3.976 * [taylor]: Taking taylor expansion of (* n PI) in n 3.976 * [taylor]: Taking taylor expansion of n in n 3.976 * [taylor]: Taking taylor expansion of PI in n 3.988 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.988 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.988 * [taylor]: Taking taylor expansion of 2.0 in n 3.988 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.988 * [taylor]: Taking taylor expansion of PI in n 3.988 * [taylor]: Taking taylor expansion of n in n 3.988 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.988 * [taylor]: Taking taylor expansion of 2.0 in n 3.988 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.988 * [taylor]: Taking taylor expansion of PI in n 3.988 * [taylor]: Taking taylor expansion of n in n 3.997 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.997 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.997 * [taylor]: Taking taylor expansion of -2.0 in n 3.997 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.997 * [taylor]: Taking taylor expansion of PI in n 3.997 * [taylor]: Taking taylor expansion of n in n 3.998 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.998 * [taylor]: Taking taylor expansion of -2.0 in n 3.998 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.998 * [taylor]: Taking taylor expansion of PI in n 3.998 * [taylor]: Taking taylor expansion of n in n 4.012 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 2 1) 4.013 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.013 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.013 * [taylor]: Taking taylor expansion of 2.0 in n 4.013 * [taylor]: Taking taylor expansion of (* n PI) in n 4.013 * [taylor]: Taking taylor expansion of n in n 4.013 * [taylor]: Taking taylor expansion of PI in n 4.013 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.013 * [taylor]: Taking taylor expansion of 2.0 in n 4.013 * [taylor]: Taking taylor expansion of (* n PI) in n 4.013 * [taylor]: Taking taylor expansion of n in n 4.013 * [taylor]: Taking taylor expansion of PI in n 4.025 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.025 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.025 * [taylor]: Taking taylor expansion of 2.0 in n 4.025 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.025 * [taylor]: Taking taylor expansion of PI in n 4.025 * [taylor]: Taking taylor expansion of n in n 4.025 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.025 * [taylor]: Taking taylor expansion of 2.0 in n 4.025 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.025 * [taylor]: Taking taylor expansion of PI in n 4.025 * [taylor]: Taking taylor expansion of n in n 4.034 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.034 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.034 * [taylor]: Taking taylor expansion of -2.0 in n 4.034 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.034 * [taylor]: Taking taylor expansion of PI in n 4.034 * [taylor]: Taking taylor expansion of n in n 4.034 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.034 * [taylor]: Taking taylor expansion of -2.0 in n 4.034 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.034 * [taylor]: Taking taylor expansion of PI in n 4.034 * [taylor]: Taking taylor expansion of n in n 4.043 * * * [progress]: simplifying candidates 4.045 * [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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 4.051 * * [simplify]: iteration 0 : 407 enodes (cost 832 ) 4.058 * * [simplify]: iteration 1 : 1658 enodes (cost 770 ) 4.089 * * [simplify]: iteration 2 : 5001 enodes (cost 732 ) 4.093 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 1/2) (pow (* (* 2.0 PI) n) 1/2) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (expm1 (* (* 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) (+ (+ (* (- (* 0.5 k)) (fma (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI)) (* (pow (* (* 2.0 PI) n) 0.5) (log n)))) (* (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (+ (pow (log (* 2.0 PI)) 2) (pow (log n) 2)))) (fma (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (pow (* (* 2.0 PI) n) 0.5))) (pow (* (* 2.0 PI) n) (* 0.5 (- 1.0 k))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (+ (+ (* (- (* 0.5 k)) (fma (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI)) (* (pow (* (* 2.0 PI) n) 0.5) (log n)))) (* (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (+ (pow (log (* 2.0 PI)) 2) (pow (log n) 2)))) (fma (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (pow (* (* 2.0 PI) n) 0.5))) (pow (* (* 2.0 PI) n) (* 0.5 (- 1.0 k))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) 4.094 * * * [progress]: adding candidates to table 4.509 * [progress]: [Phase 3 of 3] Extracting. 4.509 * * [regime]: Finding splitpoints for: (# # # # # # # #) 4.513 * * * [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) 4.513 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 4.551 * * * * [regimes]: Trying to branch on (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) from (# # # # # # # #) 4.589 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 4.627 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 4.665 * * * [regime]: Found split indices: #