11.515 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.115 * * * [progress]: [2/2] Setting up program. 0.118 * [progress]: [Phase 2 of 3] Improving. 0.118 * [simplify]: Simplifying using # : (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.120 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.122 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.124 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.126 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.132 * * [simplify]: iteration 4 : 1044 enodes (cost 8 ) 0.155 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.155 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.156 * * [progress]: iteration 1 / 4 0.156 * * * [progress]: picking best candidate 0.158 * * * * [pick]: Picked # 0.158 * * * [progress]: localizing error 0.175 * * * [progress]: generating rewritten candidates 0.175 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.184 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.187 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 0.194 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.217 * * * [progress]: generating series expansions 0.217 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.218 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.218 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.218 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.218 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.218 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.218 * [taylor]: Taking taylor expansion of 0.5 in k 0.218 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.218 * [taylor]: Taking taylor expansion of 1.0 in k 0.218 * [taylor]: Taking taylor expansion of k in k 0.218 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.218 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.218 * [taylor]: Taking taylor expansion of 2.0 in k 0.218 * [taylor]: Taking taylor expansion of (* n PI) in k 0.218 * [taylor]: Taking taylor expansion of n in k 0.218 * [taylor]: Taking taylor expansion of PI in k 0.219 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.219 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.219 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.219 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.219 * [taylor]: Taking taylor expansion of 0.5 in n 0.219 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.219 * [taylor]: Taking taylor expansion of 1.0 in n 0.219 * [taylor]: Taking taylor expansion of k in n 0.219 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.219 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.219 * [taylor]: Taking taylor expansion of 2.0 in n 0.219 * [taylor]: Taking taylor expansion of (* n PI) in n 0.219 * [taylor]: Taking taylor expansion of n in n 0.219 * [taylor]: Taking taylor expansion of PI in n 0.224 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.224 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.224 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.224 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.224 * [taylor]: Taking taylor expansion of 0.5 in n 0.224 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.224 * [taylor]: Taking taylor expansion of 1.0 in n 0.224 * [taylor]: Taking taylor expansion of k in n 0.225 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.225 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.225 * [taylor]: Taking taylor expansion of 2.0 in n 0.225 * [taylor]: Taking taylor expansion of (* n PI) in n 0.225 * [taylor]: Taking taylor expansion of n in n 0.225 * [taylor]: Taking taylor expansion of PI in n 0.230 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.230 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.230 * [taylor]: Taking taylor expansion of 0.5 in k 0.230 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.230 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.230 * [taylor]: Taking taylor expansion of 1.0 in k 0.230 * [taylor]: Taking taylor expansion of k in k 0.230 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.230 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.230 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.230 * [taylor]: Taking taylor expansion of 2.0 in k 0.230 * [taylor]: Taking taylor expansion of PI in k 0.231 * [taylor]: Taking taylor expansion of (log n) in k 0.231 * [taylor]: Taking taylor expansion of n in k 0.240 * [taylor]: Taking taylor expansion of 0 in k 0.259 * [taylor]: Taking taylor expansion of 0 in k 0.278 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.278 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.278 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.278 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.278 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.278 * [taylor]: Taking taylor expansion of 0.5 in k 0.278 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.278 * [taylor]: Taking taylor expansion of 1.0 in k 0.278 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.278 * [taylor]: Taking taylor expansion of k in k 0.278 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.278 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.278 * [taylor]: Taking taylor expansion of 2.0 in k 0.278 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.278 * [taylor]: Taking taylor expansion of PI in k 0.278 * [taylor]: Taking taylor expansion of n in k 0.279 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.279 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.279 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.279 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.279 * [taylor]: Taking taylor expansion of 0.5 in n 0.279 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.279 * [taylor]: Taking taylor expansion of 1.0 in n 0.279 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.279 * [taylor]: Taking taylor expansion of k in n 0.280 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.280 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.280 * [taylor]: Taking taylor expansion of 2.0 in n 0.280 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.280 * [taylor]: Taking taylor expansion of PI in n 0.280 * [taylor]: Taking taylor expansion of n in n 0.283 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.283 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.283 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.283 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.283 * [taylor]: Taking taylor expansion of 0.5 in n 0.283 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.283 * [taylor]: Taking taylor expansion of 1.0 in n 0.283 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.283 * [taylor]: Taking taylor expansion of k in n 0.283 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.283 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.283 * [taylor]: Taking taylor expansion of 2.0 in n 0.283 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.283 * [taylor]: Taking taylor expansion of PI in n 0.283 * [taylor]: Taking taylor expansion of n in n 0.287 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.287 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.287 * [taylor]: Taking taylor expansion of 0.5 in k 0.287 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.287 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.287 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.287 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.287 * [taylor]: Taking taylor expansion of 2.0 in k 0.287 * [taylor]: Taking taylor expansion of PI in k 0.288 * [taylor]: Taking taylor expansion of (log n) in k 0.288 * [taylor]: Taking taylor expansion of n in k 0.288 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.288 * [taylor]: Taking taylor expansion of 1.0 in k 0.288 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.288 * [taylor]: Taking taylor expansion of k in k 0.298 * [taylor]: Taking taylor expansion of 0 in k 0.305 * [taylor]: Taking taylor expansion of 0 in k 0.313 * [taylor]: Taking taylor expansion of 0 in k 0.315 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.315 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.315 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.315 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.315 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.315 * [taylor]: Taking taylor expansion of 0.5 in k 0.315 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.315 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.315 * [taylor]: Taking taylor expansion of k in k 0.315 * [taylor]: Taking taylor expansion of 1.0 in k 0.315 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.315 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.315 * [taylor]: Taking taylor expansion of -2.0 in k 0.315 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.315 * [taylor]: Taking taylor expansion of PI in k 0.315 * [taylor]: Taking taylor expansion of n in k 0.316 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.316 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.316 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.316 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.316 * [taylor]: Taking taylor expansion of 0.5 in n 0.316 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.316 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.316 * [taylor]: Taking taylor expansion of k in n 0.316 * [taylor]: Taking taylor expansion of 1.0 in n 0.316 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.316 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.316 * [taylor]: Taking taylor expansion of -2.0 in n 0.316 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.316 * [taylor]: Taking taylor expansion of PI in n 0.316 * [taylor]: Taking taylor expansion of n in n 0.320 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.320 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.320 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.320 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.320 * [taylor]: Taking taylor expansion of 0.5 in n 0.320 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.320 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.320 * [taylor]: Taking taylor expansion of k in n 0.320 * [taylor]: Taking taylor expansion of 1.0 in n 0.320 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.320 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.320 * [taylor]: Taking taylor expansion of -2.0 in n 0.320 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.320 * [taylor]: Taking taylor expansion of PI in n 0.320 * [taylor]: Taking taylor expansion of n in n 0.324 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.324 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.324 * [taylor]: Taking taylor expansion of 0.5 in k 0.324 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.324 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.324 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.324 * [taylor]: Taking taylor expansion of k in k 0.324 * [taylor]: Taking taylor expansion of 1.0 in k 0.324 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.324 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.324 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.324 * [taylor]: Taking taylor expansion of -2.0 in k 0.324 * [taylor]: Taking taylor expansion of PI in k 0.325 * [taylor]: Taking taylor expansion of (log n) in k 0.325 * [taylor]: Taking taylor expansion of n in k 0.339 * [taylor]: Taking taylor expansion of 0 in k 0.346 * [taylor]: Taking taylor expansion of 0 in k 0.354 * [taylor]: Taking taylor expansion of 0 in k 0.355 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.355 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.355 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.355 * [taylor]: Taking taylor expansion of 1.0 in k 0.355 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.355 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.355 * [taylor]: Taking taylor expansion of k in k 0.356 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.356 * [taylor]: Taking taylor expansion of 1.0 in k 0.356 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.356 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.356 * [taylor]: Taking taylor expansion of k in k 0.367 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.367 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.367 * [taylor]: Taking taylor expansion of 1.0 in k 0.367 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.367 * [taylor]: Taking taylor expansion of k in k 0.368 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.368 * [taylor]: Taking taylor expansion of 1.0 in k 0.368 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.368 * [taylor]: Taking taylor expansion of k in k 0.378 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.378 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.378 * [taylor]: Taking taylor expansion of 1.0 in k 0.378 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.378 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.378 * [taylor]: Taking taylor expansion of -1 in k 0.378 * [taylor]: Taking taylor expansion of k in k 0.380 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.380 * [taylor]: Taking taylor expansion of 1.0 in k 0.380 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.380 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.380 * [taylor]: Taking taylor expansion of -1 in k 0.380 * [taylor]: Taking taylor expansion of k in k 0.391 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 0.392 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.392 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.392 * [taylor]: Taking taylor expansion of 2.0 in n 0.392 * [taylor]: Taking taylor expansion of (* n PI) in n 0.392 * [taylor]: Taking taylor expansion of n in n 0.392 * [taylor]: Taking taylor expansion of PI in n 0.392 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.392 * [taylor]: Taking taylor expansion of 2.0 in n 0.392 * [taylor]: Taking taylor expansion of (* n PI) in n 0.392 * [taylor]: Taking taylor expansion of n in n 0.392 * [taylor]: Taking taylor expansion of PI in n 0.403 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.403 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.403 * [taylor]: Taking taylor expansion of 2.0 in n 0.403 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.403 * [taylor]: Taking taylor expansion of PI in n 0.403 * [taylor]: Taking taylor expansion of n in n 0.404 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.404 * [taylor]: Taking taylor expansion of 2.0 in n 0.404 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.404 * [taylor]: Taking taylor expansion of PI in n 0.404 * [taylor]: Taking taylor expansion of n in n 0.418 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.418 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.418 * [taylor]: Taking taylor expansion of -2.0 in n 0.418 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.418 * [taylor]: Taking taylor expansion of PI in n 0.418 * [taylor]: Taking taylor expansion of n in n 0.418 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.418 * [taylor]: Taking taylor expansion of -2.0 in n 0.418 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.418 * [taylor]: Taking taylor expansion of PI in n 0.418 * [taylor]: Taking taylor expansion of n in n 0.426 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.427 * [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 0.427 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.427 * [taylor]: Taking taylor expansion of 1.0 in n 0.427 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.427 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.427 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.427 * [taylor]: Taking taylor expansion of k in n 0.427 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.427 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.427 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.427 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.427 * [taylor]: Taking taylor expansion of 0.5 in n 0.427 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.427 * [taylor]: Taking taylor expansion of 1.0 in n 0.427 * [taylor]: Taking taylor expansion of k in n 0.427 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.427 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.427 * [taylor]: Taking taylor expansion of 2.0 in n 0.427 * [taylor]: Taking taylor expansion of (* n PI) in n 0.427 * [taylor]: Taking taylor expansion of n in n 0.427 * [taylor]: Taking taylor expansion of PI in n 0.433 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.433 * [taylor]: Taking taylor expansion of 1.0 in k 0.433 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.433 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.433 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.433 * [taylor]: Taking taylor expansion of k in k 0.434 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.434 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.434 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.434 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.434 * [taylor]: Taking taylor expansion of 0.5 in k 0.434 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.434 * [taylor]: Taking taylor expansion of 1.0 in k 0.434 * [taylor]: Taking taylor expansion of k in k 0.434 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.434 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.434 * [taylor]: Taking taylor expansion of 2.0 in k 0.434 * [taylor]: Taking taylor expansion of (* n PI) in k 0.434 * [taylor]: Taking taylor expansion of n in k 0.434 * [taylor]: Taking taylor expansion of PI in k 0.435 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.435 * [taylor]: Taking taylor expansion of 1.0 in k 0.435 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.435 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.435 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.435 * [taylor]: Taking taylor expansion of k in k 0.436 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.436 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.436 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.436 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.436 * [taylor]: Taking taylor expansion of 0.5 in k 0.436 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.436 * [taylor]: Taking taylor expansion of 1.0 in k 0.436 * [taylor]: Taking taylor expansion of k in k 0.436 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.436 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.437 * [taylor]: Taking taylor expansion of 2.0 in k 0.437 * [taylor]: Taking taylor expansion of (* n PI) in k 0.437 * [taylor]: Taking taylor expansion of n in k 0.437 * [taylor]: Taking taylor expansion of PI in k 0.438 * [taylor]: Taking taylor expansion of 0 in n 0.443 * [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 0.443 * [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 0.443 * [taylor]: Taking taylor expansion of +nan.0 in n 0.443 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.443 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.443 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.443 * [taylor]: Taking taylor expansion of 0.5 in n 0.443 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.443 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.443 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.443 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.443 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.443 * [taylor]: Taking taylor expansion of 1.0 in n 0.443 * [taylor]: Taking taylor expansion of (log PI) in n 0.443 * [taylor]: Taking taylor expansion of PI in n 0.445 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.445 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.445 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.445 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.445 * [taylor]: Taking taylor expansion of 1.0 in n 0.445 * [taylor]: Taking taylor expansion of (log n) in n 0.445 * [taylor]: Taking taylor expansion of n in n 0.446 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.446 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.446 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.446 * [taylor]: Taking taylor expansion of 1.0 in n 0.446 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.446 * [taylor]: Taking taylor expansion of 2.0 in n 0.464 * [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 0.464 * [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 0.464 * [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 0.464 * [taylor]: Taking taylor expansion of +nan.0 in n 0.464 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.464 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.464 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.464 * [taylor]: Taking taylor expansion of 0.5 in n 0.464 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.465 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.465 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.465 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.465 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.465 * [taylor]: Taking taylor expansion of 1.0 in n 0.465 * [taylor]: Taking taylor expansion of (log PI) in n 0.465 * [taylor]: Taking taylor expansion of PI in n 0.466 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.466 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.466 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.466 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.466 * [taylor]: Taking taylor expansion of 1.0 in n 0.466 * [taylor]: Taking taylor expansion of (log n) in n 0.466 * [taylor]: Taking taylor expansion of n in n 0.467 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.467 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.467 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.467 * [taylor]: Taking taylor expansion of 1.0 in n 0.467 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.467 * [taylor]: Taking taylor expansion of 2.0 in n 0.472 * [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 0.472 * [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 0.472 * [taylor]: Taking taylor expansion of +nan.0 in n 0.472 * [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 0.472 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.472 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.473 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.473 * [taylor]: Taking taylor expansion of 0.5 in n 0.473 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.473 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.473 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.473 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.473 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.473 * [taylor]: Taking taylor expansion of 1.0 in n 0.473 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.473 * [taylor]: Taking taylor expansion of 2.0 in n 0.475 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.475 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.475 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.475 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.475 * [taylor]: Taking taylor expansion of 1.0 in n 0.475 * [taylor]: Taking taylor expansion of (log PI) in n 0.475 * [taylor]: Taking taylor expansion of PI in n 0.476 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.476 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.476 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.476 * [taylor]: Taking taylor expansion of 1.0 in n 0.477 * [taylor]: Taking taylor expansion of (log n) in n 0.477 * [taylor]: Taking taylor expansion of n in n 0.481 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.481 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.481 * [taylor]: Taking taylor expansion of 2.0 in n 0.481 * [taylor]: Taking taylor expansion of (* n PI) in n 0.481 * [taylor]: Taking taylor expansion of n in n 0.481 * [taylor]: Taking taylor expansion of PI in n 0.534 * [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 0.534 * [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 0.534 * [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 0.534 * [taylor]: Taking taylor expansion of +nan.0 in n 0.534 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.534 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.534 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.534 * [taylor]: Taking taylor expansion of 0.5 in n 0.534 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.534 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.534 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.534 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.534 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.534 * [taylor]: Taking taylor expansion of 1.0 in n 0.534 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.534 * [taylor]: Taking taylor expansion of 2.0 in n 0.536 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.536 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.536 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.536 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.536 * [taylor]: Taking taylor expansion of 1.0 in n 0.536 * [taylor]: Taking taylor expansion of (log n) in n 0.536 * [taylor]: Taking taylor expansion of n in n 0.537 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.537 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.537 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.537 * [taylor]: Taking taylor expansion of 1.0 in n 0.537 * [taylor]: Taking taylor expansion of (log PI) in n 0.537 * [taylor]: Taking taylor expansion of PI in n 0.542 * [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 0.542 * [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 0.542 * [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 0.542 * [taylor]: Taking taylor expansion of +nan.0 in n 0.542 * [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 0.542 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.542 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.542 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.542 * [taylor]: Taking taylor expansion of 0.5 in n 0.542 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.542 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.542 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.542 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.542 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.542 * [taylor]: Taking taylor expansion of 1.0 in n 0.542 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.542 * [taylor]: Taking taylor expansion of 2.0 in n 0.544 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.544 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.544 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.544 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.544 * [taylor]: Taking taylor expansion of 1.0 in n 0.544 * [taylor]: Taking taylor expansion of (log PI) in n 0.544 * [taylor]: Taking taylor expansion of PI in n 0.546 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.546 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.546 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.546 * [taylor]: Taking taylor expansion of 1.0 in n 0.546 * [taylor]: Taking taylor expansion of (log n) in n 0.546 * [taylor]: Taking taylor expansion of n in n 0.550 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.550 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.550 * [taylor]: Taking taylor expansion of 2.0 in n 0.550 * [taylor]: Taking taylor expansion of (* n PI) in n 0.550 * [taylor]: Taking taylor expansion of n in n 0.550 * [taylor]: Taking taylor expansion of PI in n 0.553 * [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 0.553 * [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 0.553 * [taylor]: Taking taylor expansion of +nan.0 in n 0.553 * [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 0.553 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.553 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.553 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.553 * [taylor]: Taking taylor expansion of 0.5 in n 0.553 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.553 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.553 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.553 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.553 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.553 * [taylor]: Taking taylor expansion of 1.0 in n 0.553 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.553 * [taylor]: Taking taylor expansion of 2.0 in n 0.555 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.555 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.555 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.555 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.555 * [taylor]: Taking taylor expansion of 1.0 in n 0.555 * [taylor]: Taking taylor expansion of (log PI) in n 0.555 * [taylor]: Taking taylor expansion of PI in n 0.557 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.557 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.557 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.557 * [taylor]: Taking taylor expansion of 1.0 in n 0.557 * [taylor]: Taking taylor expansion of (log n) in n 0.557 * [taylor]: Taking taylor expansion of n in n 0.561 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.561 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.561 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.561 * [taylor]: Taking taylor expansion of 2.0 in n 0.561 * [taylor]: Taking taylor expansion of (* n PI) in n 0.561 * [taylor]: Taking taylor expansion of n in n 0.561 * [taylor]: Taking taylor expansion of PI in n 0.637 * [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 0.637 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.637 * [taylor]: Taking taylor expansion of 1.0 in n 0.637 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.637 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.637 * [taylor]: Taking taylor expansion of k in n 0.637 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.637 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.637 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.637 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.637 * [taylor]: Taking taylor expansion of 0.5 in n 0.637 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.638 * [taylor]: Taking taylor expansion of 1.0 in n 0.638 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.638 * [taylor]: Taking taylor expansion of k in n 0.638 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.638 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.638 * [taylor]: Taking taylor expansion of 2.0 in n 0.638 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.638 * [taylor]: Taking taylor expansion of PI in n 0.638 * [taylor]: Taking taylor expansion of n in n 0.641 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.641 * [taylor]: Taking taylor expansion of 1.0 in k 0.641 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.641 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.641 * [taylor]: Taking taylor expansion of k in k 0.642 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.642 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.642 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.642 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.642 * [taylor]: Taking taylor expansion of 0.5 in k 0.642 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.642 * [taylor]: Taking taylor expansion of 1.0 in k 0.642 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.642 * [taylor]: Taking taylor expansion of k in k 0.643 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.643 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.643 * [taylor]: Taking taylor expansion of 2.0 in k 0.643 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.643 * [taylor]: Taking taylor expansion of PI in k 0.643 * [taylor]: Taking taylor expansion of n in k 0.644 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.644 * [taylor]: Taking taylor expansion of 1.0 in k 0.644 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.644 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.644 * [taylor]: Taking taylor expansion of k in k 0.645 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.645 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.645 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.645 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.645 * [taylor]: Taking taylor expansion of 0.5 in k 0.645 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.645 * [taylor]: Taking taylor expansion of 1.0 in k 0.645 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.645 * [taylor]: Taking taylor expansion of k in k 0.645 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.645 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.645 * [taylor]: Taking taylor expansion of 2.0 in k 0.645 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.645 * [taylor]: Taking taylor expansion of PI in k 0.645 * [taylor]: Taking taylor expansion of n in k 0.647 * [taylor]: Taking taylor expansion of 0 in n 0.647 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.648 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.648 * [taylor]: Taking taylor expansion of +nan.0 in n 0.648 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.648 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.648 * [taylor]: Taking taylor expansion of 0.5 in n 0.648 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.648 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.648 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.648 * [taylor]: Taking taylor expansion of 2.0 in n 0.648 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.648 * [taylor]: Taking taylor expansion of PI in n 0.648 * [taylor]: Taking taylor expansion of n in n 0.649 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.649 * [taylor]: Taking taylor expansion of 1.0 in n 0.649 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.649 * [taylor]: Taking taylor expansion of k in n 0.657 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.657 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.657 * [taylor]: Taking taylor expansion of +nan.0 in n 0.657 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.657 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.657 * [taylor]: Taking taylor expansion of 0.5 in n 0.657 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.657 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.657 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.657 * [taylor]: Taking taylor expansion of 2.0 in n 0.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.657 * [taylor]: Taking taylor expansion of PI in n 0.657 * [taylor]: Taking taylor expansion of n in n 0.659 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.659 * [taylor]: Taking taylor expansion of 1.0 in n 0.659 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.659 * [taylor]: Taking taylor expansion of k in n 0.680 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.680 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.680 * [taylor]: Taking taylor expansion of +nan.0 in n 0.680 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.680 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.680 * [taylor]: Taking taylor expansion of 0.5 in n 0.680 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.680 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.680 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.680 * [taylor]: Taking taylor expansion of 2.0 in n 0.680 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.680 * [taylor]: Taking taylor expansion of PI in n 0.680 * [taylor]: Taking taylor expansion of n in n 0.681 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.681 * [taylor]: Taking taylor expansion of 1.0 in n 0.681 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.681 * [taylor]: Taking taylor expansion of k in n 0.689 * [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 0.689 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.689 * [taylor]: Taking taylor expansion of 1.0 in n 0.690 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.690 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.690 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.690 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.690 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.690 * [taylor]: Taking taylor expansion of 0.5 in n 0.690 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.690 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.690 * [taylor]: Taking taylor expansion of k in n 0.690 * [taylor]: Taking taylor expansion of 1.0 in n 0.690 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.690 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.690 * [taylor]: Taking taylor expansion of -2.0 in n 0.690 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.690 * [taylor]: Taking taylor expansion of PI in n 0.690 * [taylor]: Taking taylor expansion of n in n 0.693 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.693 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.693 * [taylor]: Taking taylor expansion of -1 in n 0.693 * [taylor]: Taking taylor expansion of k in n 0.694 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.694 * [taylor]: Taking taylor expansion of 1.0 in k 0.694 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.694 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.694 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.694 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.694 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.694 * [taylor]: Taking taylor expansion of 0.5 in k 0.694 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.694 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.694 * [taylor]: Taking taylor expansion of k in k 0.695 * [taylor]: Taking taylor expansion of 1.0 in k 0.695 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.695 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.695 * [taylor]: Taking taylor expansion of -2.0 in k 0.695 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.695 * [taylor]: Taking taylor expansion of PI in k 0.695 * [taylor]: Taking taylor expansion of n in k 0.696 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.696 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.696 * [taylor]: Taking taylor expansion of -1 in k 0.696 * [taylor]: Taking taylor expansion of k in k 0.697 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.697 * [taylor]: Taking taylor expansion of 1.0 in k 0.697 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.697 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.697 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.697 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.697 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.697 * [taylor]: Taking taylor expansion of 0.5 in k 0.697 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.697 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.697 * [taylor]: Taking taylor expansion of k in k 0.698 * [taylor]: Taking taylor expansion of 1.0 in k 0.698 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.698 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.698 * [taylor]: Taking taylor expansion of -2.0 in k 0.698 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.698 * [taylor]: Taking taylor expansion of PI in k 0.698 * [taylor]: Taking taylor expansion of n in k 0.698 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.698 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.698 * [taylor]: Taking taylor expansion of -1 in k 0.698 * [taylor]: Taking taylor expansion of k in k 0.700 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.700 * [taylor]: Taking taylor expansion of +nan.0 in n 0.700 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.700 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.700 * [taylor]: Taking taylor expansion of 0.5 in n 0.700 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.700 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.700 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.700 * [taylor]: Taking taylor expansion of k in n 0.700 * [taylor]: Taking taylor expansion of 1.0 in n 0.700 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.700 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.700 * [taylor]: Taking taylor expansion of -2.0 in n 0.700 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.700 * [taylor]: Taking taylor expansion of PI in n 0.700 * [taylor]: Taking taylor expansion of n in n 0.709 * [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 (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 0.726 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.726 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.726 * [taylor]: Taking taylor expansion of +nan.0 in n 0.726 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.726 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.726 * [taylor]: Taking taylor expansion of 0.5 in n 0.726 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.726 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.727 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.727 * [taylor]: Taking taylor expansion of k in n 0.727 * [taylor]: Taking taylor expansion of 1.0 in n 0.727 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.727 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.727 * [taylor]: Taking taylor expansion of -2.0 in n 0.727 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.727 * [taylor]: Taking taylor expansion of PI in n 0.727 * [taylor]: Taking taylor expansion of n in n 0.736 * * * [progress]: simplifying candidates 0.738 * [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 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 (* (* 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)) (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)))))) (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))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (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))))))))) 0.842 * * * [progress]: adding candidates to table 1.271 * * [progress]: iteration 2 / 4 1.271 * * * [progress]: picking best candidate 1.292 * * * * [pick]: Picked # 1.292 * * * [progress]: localizing error 1.307 * * * [progress]: generating rewritten candidates 1.307 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 1.316 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 1.319 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 1.322 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1) 1.333 * * * [progress]: generating series expansions 1.333 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 1.334 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.334 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.334 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.334 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.334 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.334 * [taylor]: Taking taylor expansion of 0.5 in k 1.334 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.334 * [taylor]: Taking taylor expansion of 1.0 in k 1.334 * [taylor]: Taking taylor expansion of k in k 1.334 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.334 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.334 * [taylor]: Taking taylor expansion of 2.0 in k 1.334 * [taylor]: Taking taylor expansion of (* n PI) in k 1.334 * [taylor]: Taking taylor expansion of n in k 1.334 * [taylor]: Taking taylor expansion of PI in k 1.335 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.335 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.335 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.335 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.335 * [taylor]: Taking taylor expansion of 0.5 in n 1.335 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.335 * [taylor]: Taking taylor expansion of 1.0 in n 1.335 * [taylor]: Taking taylor expansion of k in n 1.335 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.335 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.335 * [taylor]: Taking taylor expansion of 2.0 in n 1.335 * [taylor]: Taking taylor expansion of (* n PI) in n 1.335 * [taylor]: Taking taylor expansion of n in n 1.335 * [taylor]: Taking taylor expansion of PI in n 1.344 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.345 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.345 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.345 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.345 * [taylor]: Taking taylor expansion of 0.5 in n 1.345 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.345 * [taylor]: Taking taylor expansion of 1.0 in n 1.345 * [taylor]: Taking taylor expansion of k in n 1.345 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.345 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.345 * [taylor]: Taking taylor expansion of 2.0 in n 1.345 * [taylor]: Taking taylor expansion of (* n PI) in n 1.345 * [taylor]: Taking taylor expansion of n in n 1.345 * [taylor]: Taking taylor expansion of PI in n 1.350 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.350 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.350 * [taylor]: Taking taylor expansion of 0.5 in k 1.350 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.350 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.350 * [taylor]: Taking taylor expansion of 1.0 in k 1.350 * [taylor]: Taking taylor expansion of k in k 1.350 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.350 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.350 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.350 * [taylor]: Taking taylor expansion of 2.0 in k 1.350 * [taylor]: Taking taylor expansion of PI in k 1.351 * [taylor]: Taking taylor expansion of (log n) in k 1.351 * [taylor]: Taking taylor expansion of n in k 1.360 * [taylor]: Taking taylor expansion of 0 in k 1.375 * [taylor]: Taking taylor expansion of 0 in k 1.394 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.394 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.394 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.394 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.394 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.394 * [taylor]: Taking taylor expansion of 0.5 in k 1.394 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.394 * [taylor]: Taking taylor expansion of 1.0 in k 1.394 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.394 * [taylor]: Taking taylor expansion of k in k 1.394 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.394 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.394 * [taylor]: Taking taylor expansion of 2.0 in k 1.394 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.394 * [taylor]: Taking taylor expansion of PI in k 1.394 * [taylor]: Taking taylor expansion of n in k 1.395 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.395 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.395 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.395 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.395 * [taylor]: Taking taylor expansion of 0.5 in n 1.395 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.395 * [taylor]: Taking taylor expansion of 1.0 in n 1.395 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.395 * [taylor]: Taking taylor expansion of k in n 1.395 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.395 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.395 * [taylor]: Taking taylor expansion of 2.0 in n 1.395 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.395 * [taylor]: Taking taylor expansion of PI in n 1.395 * [taylor]: Taking taylor expansion of n in n 1.399 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.399 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.399 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.399 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.399 * [taylor]: Taking taylor expansion of 0.5 in n 1.399 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.399 * [taylor]: Taking taylor expansion of 1.0 in n 1.399 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.399 * [taylor]: Taking taylor expansion of k in n 1.399 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.399 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.399 * [taylor]: Taking taylor expansion of 2.0 in n 1.399 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.399 * [taylor]: Taking taylor expansion of PI in n 1.399 * [taylor]: Taking taylor expansion of n in n 1.403 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.403 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.403 * [taylor]: Taking taylor expansion of 0.5 in k 1.403 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.403 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.403 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.403 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.403 * [taylor]: Taking taylor expansion of 2.0 in k 1.403 * [taylor]: Taking taylor expansion of PI in k 1.404 * [taylor]: Taking taylor expansion of (log n) in k 1.404 * [taylor]: Taking taylor expansion of n in k 1.404 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.404 * [taylor]: Taking taylor expansion of 1.0 in k 1.404 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.404 * [taylor]: Taking taylor expansion of k in k 1.413 * [taylor]: Taking taylor expansion of 0 in k 1.425 * [taylor]: Taking taylor expansion of 0 in k 1.434 * [taylor]: Taking taylor expansion of 0 in k 1.436 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.436 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.436 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.436 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.436 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.436 * [taylor]: Taking taylor expansion of 0.5 in k 1.436 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.436 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.436 * [taylor]: Taking taylor expansion of k in k 1.436 * [taylor]: Taking taylor expansion of 1.0 in k 1.436 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.436 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.436 * [taylor]: Taking taylor expansion of -2.0 in k 1.436 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.436 * [taylor]: Taking taylor expansion of PI in k 1.436 * [taylor]: Taking taylor expansion of n in k 1.437 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.437 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.437 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.437 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.437 * [taylor]: Taking taylor expansion of 0.5 in n 1.437 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.437 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.437 * [taylor]: Taking taylor expansion of k in n 1.437 * [taylor]: Taking taylor expansion of 1.0 in n 1.437 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.437 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.437 * [taylor]: Taking taylor expansion of -2.0 in n 1.437 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.437 * [taylor]: Taking taylor expansion of PI in n 1.437 * [taylor]: Taking taylor expansion of n in n 1.441 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.441 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.441 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.441 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.441 * [taylor]: Taking taylor expansion of 0.5 in n 1.441 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.441 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.441 * [taylor]: Taking taylor expansion of k in n 1.441 * [taylor]: Taking taylor expansion of 1.0 in n 1.441 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.441 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.441 * [taylor]: Taking taylor expansion of -2.0 in n 1.441 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.441 * [taylor]: Taking taylor expansion of PI in n 1.441 * [taylor]: Taking taylor expansion of n in n 1.444 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.445 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.445 * [taylor]: Taking taylor expansion of 0.5 in k 1.445 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.445 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.445 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.445 * [taylor]: Taking taylor expansion of k in k 1.445 * [taylor]: Taking taylor expansion of 1.0 in k 1.445 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.445 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.445 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.445 * [taylor]: Taking taylor expansion of -2.0 in k 1.445 * [taylor]: Taking taylor expansion of PI in k 1.446 * [taylor]: Taking taylor expansion of (log n) in k 1.446 * [taylor]: Taking taylor expansion of n in k 1.454 * [taylor]: Taking taylor expansion of 0 in k 1.461 * [taylor]: Taking taylor expansion of 0 in k 1.469 * [taylor]: Taking taylor expansion of 0 in k 1.470 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 1.470 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.470 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.470 * [taylor]: Taking taylor expansion of 1.0 in k 1.470 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.470 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.470 * [taylor]: Taking taylor expansion of k in k 1.472 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.472 * [taylor]: Taking taylor expansion of 1.0 in k 1.472 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.472 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.472 * [taylor]: Taking taylor expansion of k in k 1.483 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.483 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.483 * [taylor]: Taking taylor expansion of 1.0 in k 1.483 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.483 * [taylor]: Taking taylor expansion of k in k 1.484 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.484 * [taylor]: Taking taylor expansion of 1.0 in k 1.484 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.484 * [taylor]: Taking taylor expansion of k in k 1.494 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.494 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.494 * [taylor]: Taking taylor expansion of 1.0 in k 1.494 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.494 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.494 * [taylor]: Taking taylor expansion of -1 in k 1.494 * [taylor]: Taking taylor expansion of k in k 1.496 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.496 * [taylor]: Taking taylor expansion of 1.0 in k 1.496 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.496 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.496 * [taylor]: Taking taylor expansion of -1 in k 1.496 * [taylor]: Taking taylor expansion of k in k 1.512 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 1.513 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.513 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.513 * [taylor]: Taking taylor expansion of 1.0 in k 1.513 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.513 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.513 * [taylor]: Taking taylor expansion of k in k 1.514 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.514 * [taylor]: Taking taylor expansion of 1.0 in k 1.514 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.514 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.514 * [taylor]: Taking taylor expansion of k in k 1.524 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.525 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.525 * [taylor]: Taking taylor expansion of 1.0 in k 1.525 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.525 * [taylor]: Taking taylor expansion of k in k 1.526 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.526 * [taylor]: Taking taylor expansion of 1.0 in k 1.526 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.526 * [taylor]: Taking taylor expansion of k in k 1.535 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.536 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.536 * [taylor]: Taking taylor expansion of 1.0 in k 1.536 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.536 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.536 * [taylor]: Taking taylor expansion of -1 in k 1.536 * [taylor]: Taking taylor expansion of k in k 1.537 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.537 * [taylor]: Taking taylor expansion of 1.0 in k 1.537 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.537 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.537 * [taylor]: Taking taylor expansion of -1 in k 1.537 * [taylor]: Taking taylor expansion of k in k 1.548 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1) 1.549 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.549 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.549 * [taylor]: Taking taylor expansion of 2.0 in n 1.549 * [taylor]: Taking taylor expansion of (* n PI) in n 1.549 * [taylor]: Taking taylor expansion of n in n 1.549 * [taylor]: Taking taylor expansion of PI in n 1.549 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.549 * [taylor]: Taking taylor expansion of 2.0 in n 1.549 * [taylor]: Taking taylor expansion of (* n PI) in n 1.549 * [taylor]: Taking taylor expansion of n in n 1.549 * [taylor]: Taking taylor expansion of PI 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 1.561 * [taylor]: Taking taylor expansion of 2.0 in n 1.561 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.561 * [taylor]: Taking taylor expansion of PI in n 1.561 * [taylor]: Taking taylor expansion of n in n 1.561 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.561 * [taylor]: Taking taylor expansion of 2.0 in n 1.561 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.561 * [taylor]: Taking taylor expansion of PI in n 1.561 * [taylor]: Taking taylor expansion of n in n 1.570 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.570 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.570 * [taylor]: Taking taylor expansion of -2.0 in n 1.570 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.570 * [taylor]: Taking taylor expansion of PI in n 1.570 * [taylor]: Taking taylor expansion of n in n 1.570 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.570 * [taylor]: Taking taylor expansion of -2.0 in n 1.570 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.570 * [taylor]: Taking taylor expansion of PI in n 1.570 * [taylor]: Taking taylor expansion of n in n 1.578 * * * [progress]: simplifying candidates 1.581 * [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 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) (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)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 1.593 * * [simplify]: iteration 0 : 579 enodes (cost 912 ) 1.603 * * [simplify]: iteration 1 : 2248 enodes (cost 843 ) 1.642 * * [simplify]: iteration 2 : 5001 enodes (cost 807 ) 1.646 * [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 (/ 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) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 1/2) (pow (* (* 2.0 PI) n) 1/2) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (fma (- 0.5) (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)))))) (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))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) 1.647 * * * [progress]: adding candidates to table 2.085 * * [progress]: iteration 3 / 4 2.085 * * * [progress]: picking best candidate 2.101 * * * * [pick]: Picked # 2.101 * * * [progress]: localizing error 2.126 * * * [progress]: generating rewritten candidates 2.127 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 2.136 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1 2 2 1) 2.137 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 1 2 1) 2.137 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1) 2.192 * * * [progress]: generating series expansions 2.192 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 2.192 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.192 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.193 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.193 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.193 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.193 * [taylor]: Taking taylor expansion of 0.5 in k 2.193 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.193 * [taylor]: Taking taylor expansion of 1.0 in k 2.193 * [taylor]: Taking taylor expansion of k in k 2.193 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.193 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.193 * [taylor]: Taking taylor expansion of 2.0 in k 2.193 * [taylor]: Taking taylor expansion of (* n PI) in k 2.193 * [taylor]: Taking taylor expansion of n in k 2.193 * [taylor]: Taking taylor expansion of PI in k 2.194 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.194 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.194 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.194 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.194 * [taylor]: Taking taylor expansion of 0.5 in n 2.194 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.194 * [taylor]: Taking taylor expansion of 1.0 in n 2.194 * [taylor]: Taking taylor expansion of k in n 2.194 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.194 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.194 * [taylor]: Taking taylor expansion of 2.0 in n 2.194 * [taylor]: Taking taylor expansion of (* n PI) in n 2.194 * [taylor]: Taking taylor expansion of n in n 2.194 * [taylor]: Taking taylor expansion of PI in n 2.200 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.200 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.200 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.200 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.200 * [taylor]: Taking taylor expansion of 0.5 in n 2.200 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.200 * [taylor]: Taking taylor expansion of 1.0 in n 2.200 * [taylor]: Taking taylor expansion of k in n 2.200 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.200 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.200 * [taylor]: Taking taylor expansion of 2.0 in n 2.200 * [taylor]: Taking taylor expansion of (* n PI) in n 2.200 * [taylor]: Taking taylor expansion of n in n 2.200 * [taylor]: Taking taylor expansion of PI in n 2.205 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.205 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.205 * [taylor]: Taking taylor expansion of 0.5 in k 2.205 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.205 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.205 * [taylor]: Taking taylor expansion of 1.0 in k 2.205 * [taylor]: Taking taylor expansion of k in k 2.205 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.205 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.205 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.205 * [taylor]: Taking taylor expansion of 2.0 in k 2.205 * [taylor]: Taking taylor expansion of PI in k 2.206 * [taylor]: Taking taylor expansion of (log n) in k 2.206 * [taylor]: Taking taylor expansion of n in k 2.215 * [taylor]: Taking taylor expansion of 0 in k 2.236 * [taylor]: Taking taylor expansion of 0 in k 2.254 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.254 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.254 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.254 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.254 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.254 * [taylor]: Taking taylor expansion of 0.5 in k 2.254 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.254 * [taylor]: Taking taylor expansion of 1.0 in k 2.254 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.254 * [taylor]: Taking taylor expansion of k in k 2.255 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.255 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.255 * [taylor]: Taking taylor expansion of 2.0 in k 2.255 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.255 * [taylor]: Taking taylor expansion of PI in k 2.255 * [taylor]: Taking taylor expansion of n in k 2.256 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.256 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.256 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.256 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.256 * [taylor]: Taking taylor expansion of 0.5 in n 2.256 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.256 * [taylor]: Taking taylor expansion of 1.0 in n 2.256 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.256 * [taylor]: Taking taylor expansion of k in n 2.256 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.256 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.256 * [taylor]: Taking taylor expansion of 2.0 in n 2.256 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.256 * [taylor]: Taking taylor expansion of PI in n 2.256 * [taylor]: Taking taylor expansion of n in n 2.259 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.259 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.259 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.259 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.260 * [taylor]: Taking taylor expansion of 0.5 in n 2.260 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.260 * [taylor]: Taking taylor expansion of 1.0 in n 2.260 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.260 * [taylor]: Taking taylor expansion of k in n 2.260 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.260 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.260 * [taylor]: Taking taylor expansion of 2.0 in n 2.260 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.260 * [taylor]: Taking taylor expansion of PI in n 2.260 * [taylor]: Taking taylor expansion of n in n 2.263 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.263 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.263 * [taylor]: Taking taylor expansion of 0.5 in k 2.263 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.263 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.263 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.263 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.263 * [taylor]: Taking taylor expansion of 2.0 in k 2.263 * [taylor]: Taking taylor expansion of PI in k 2.264 * [taylor]: Taking taylor expansion of (log n) in k 2.264 * [taylor]: Taking taylor expansion of n in k 2.264 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.264 * [taylor]: Taking taylor expansion of 1.0 in k 2.264 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.264 * [taylor]: Taking taylor expansion of k in k 2.274 * [taylor]: Taking taylor expansion of 0 in k 2.281 * [taylor]: Taking taylor expansion of 0 in k 2.290 * [taylor]: Taking taylor expansion of 0 in k 2.291 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.291 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.291 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.291 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.291 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.291 * [taylor]: Taking taylor expansion of 0.5 in k 2.291 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.291 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.291 * [taylor]: Taking taylor expansion of k in k 2.291 * [taylor]: Taking taylor expansion of 1.0 in k 2.291 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.291 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.291 * [taylor]: Taking taylor expansion of -2.0 in k 2.291 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.291 * [taylor]: Taking taylor expansion of PI in k 2.291 * [taylor]: Taking taylor expansion of n in k 2.292 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.292 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.292 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.292 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.292 * [taylor]: Taking taylor expansion of 0.5 in n 2.292 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.292 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.292 * [taylor]: Taking taylor expansion of k in n 2.292 * [taylor]: Taking taylor expansion of 1.0 in n 2.292 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.292 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.292 * [taylor]: Taking taylor expansion of -2.0 in n 2.292 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.292 * [taylor]: Taking taylor expansion of PI in n 2.292 * [taylor]: Taking taylor expansion of n in n 2.296 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.296 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.296 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.296 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.296 * [taylor]: Taking taylor expansion of 0.5 in n 2.296 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.296 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.296 * [taylor]: Taking taylor expansion of k in n 2.296 * [taylor]: Taking taylor expansion of 1.0 in n 2.296 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.296 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.296 * [taylor]: Taking taylor expansion of -2.0 in n 2.296 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.296 * [taylor]: Taking taylor expansion of PI in n 2.296 * [taylor]: Taking taylor expansion of n in n 2.300 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.300 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.300 * [taylor]: Taking taylor expansion of 0.5 in k 2.300 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.300 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.300 * [taylor]: Taking taylor expansion of k in k 2.300 * [taylor]: Taking taylor expansion of 1.0 in k 2.300 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.300 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.300 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.300 * [taylor]: Taking taylor expansion of -2.0 in k 2.300 * [taylor]: Taking taylor expansion of PI in k 2.301 * [taylor]: Taking taylor expansion of (log n) in k 2.301 * [taylor]: Taking taylor expansion of n in k 2.315 * [taylor]: Taking taylor expansion of 0 in k 2.322 * [taylor]: Taking taylor expansion of 0 in k 2.331 * [taylor]: Taking taylor expansion of 0 in k 2.331 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1 2 2 1) 2.332 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 2.332 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 2.332 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 2.332 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 2.332 * [taylor]: Taking taylor expansion of 1/3 in k 2.332 * [taylor]: Taking taylor expansion of (log k) in k 2.332 * [taylor]: Taking taylor expansion of k in k 2.332 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 2.332 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 2.332 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 2.332 * [taylor]: Taking taylor expansion of 1/3 in k 2.332 * [taylor]: Taking taylor expansion of (log k) in k 2.332 * [taylor]: Taking taylor expansion of k in k 2.385 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 2.385 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 2.385 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 2.385 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 2.385 * [taylor]: Taking taylor expansion of 1/3 in k 2.385 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.385 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.385 * [taylor]: Taking taylor expansion of k in k 2.386 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 2.386 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 2.386 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 2.386 * [taylor]: Taking taylor expansion of 1/3 in k 2.386 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.386 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.386 * [taylor]: Taking taylor expansion of k in k 2.436 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in (k) around 0 2.436 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 2.436 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 2.436 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 2.436 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 2.436 * [taylor]: Taking taylor expansion of 1/3 in k 2.436 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.436 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.436 * [taylor]: Taking taylor expansion of k in k 2.437 * [taylor]: Taking taylor expansion of (cbrt -1) in k 2.437 * [taylor]: Taking taylor expansion of -1 in k 2.438 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 2.438 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 2.438 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 2.438 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 2.438 * [taylor]: Taking taylor expansion of 1/3 in k 2.438 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.438 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.438 * [taylor]: Taking taylor expansion of k in k 2.439 * [taylor]: Taking taylor expansion of (cbrt -1) in k 2.439 * [taylor]: Taking taylor expansion of -1 in k 2.503 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 1 2 1) 2.503 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 2.503 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 2.503 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 2.503 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 2.503 * [taylor]: Taking taylor expansion of 1/3 in k 2.503 * [taylor]: Taking taylor expansion of (log k) in k 2.503 * [taylor]: Taking taylor expansion of k in k 2.504 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 2.504 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 2.504 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 2.504 * [taylor]: Taking taylor expansion of 1/3 in k 2.504 * [taylor]: Taking taylor expansion of (log k) in k 2.504 * [taylor]: Taking taylor expansion of k in k 2.555 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 2.556 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 2.556 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 2.556 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 2.556 * [taylor]: Taking taylor expansion of 1/3 in k 2.556 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.556 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.556 * [taylor]: Taking taylor expansion of k in k 2.556 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 2.557 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 2.557 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 2.557 * [taylor]: Taking taylor expansion of 1/3 in k 2.557 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.557 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.557 * [taylor]: Taking taylor expansion of k in k 2.612 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in (k) around 0 2.612 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 2.612 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 2.612 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 2.612 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 2.612 * [taylor]: Taking taylor expansion of 1/3 in k 2.612 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.612 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.612 * [taylor]: Taking taylor expansion of k in k 2.613 * [taylor]: Taking taylor expansion of (cbrt -1) in k 2.613 * [taylor]: Taking taylor expansion of -1 in k 2.614 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 2.614 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 2.614 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 2.614 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 2.614 * [taylor]: Taking taylor expansion of 1/3 in k 2.614 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.614 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.614 * [taylor]: Taking taylor expansion of k in k 2.614 * [taylor]: Taking taylor expansion of (cbrt -1) in k 2.615 * [taylor]: Taking taylor expansion of -1 in k 2.673 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1) 2.674 * [approximate]: Taking taylor expansion of (* (/ (pow (sqrt 1.0) 2) (fabs (pow k 1/3))) (pow (/ 1 k) 1/6)) in (k) around 0 2.674 * [taylor]: Taking taylor expansion of (* (/ (pow (sqrt 1.0) 2) (fabs (pow k 1/3))) (pow (/ 1 k) 1/6)) in k 2.674 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (fabs (pow k 1/3))) in k 2.674 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 2.674 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 2.674 * [taylor]: Taking taylor expansion of 1.0 in k 2.675 * [taylor]: Taking taylor expansion of (fabs (pow k 1/3)) in k 2.676 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/6) in k 2.676 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log (/ 1 k)))) in k 2.676 * [taylor]: Taking taylor expansion of (* 1/6 (log (/ 1 k))) in k 2.676 * [taylor]: Taking taylor expansion of 1/6 in k 2.676 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.676 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.676 * [taylor]: Taking taylor expansion of k in k 2.677 * [taylor]: Taking taylor expansion of (* (/ (pow (sqrt 1.0) 2) (fabs (pow k 1/3))) (pow (/ 1 k) 1/6)) in k 2.677 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (fabs (pow k 1/3))) in k 2.677 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 2.677 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 2.677 * [taylor]: Taking taylor expansion of 1.0 in k 2.678 * [taylor]: Taking taylor expansion of (fabs (pow k 1/3)) in k 2.679 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/6) in k 2.679 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log (/ 1 k)))) in k 2.679 * [taylor]: Taking taylor expansion of (* 1/6 (log (/ 1 k))) in k 2.679 * [taylor]: Taking taylor expansion of 1/6 in k 2.679 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 2.679 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.679 * [taylor]: Taking taylor expansion of k in k 2.764 * [approximate]: Taking taylor expansion of (* (pow k 1/6) (/ (pow (sqrt 1.0) 2) (fabs (pow (/ 1 k) 1/3)))) in (k) around 0 2.764 * [taylor]: Taking taylor expansion of (* (pow k 1/6) (/ (pow (sqrt 1.0) 2) (fabs (pow (/ 1 k) 1/3)))) in k 2.764 * [taylor]: Taking taylor expansion of (pow k 1/6) in k 2.764 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log k))) in k 2.764 * [taylor]: Taking taylor expansion of (* 1/6 (log k)) in k 2.764 * [taylor]: Taking taylor expansion of 1/6 in k 2.764 * [taylor]: Taking taylor expansion of (log k) in k 2.764 * [taylor]: Taking taylor expansion of k in k 2.765 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (fabs (pow (/ 1 k) 1/3))) in k 2.765 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 2.765 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 2.765 * [taylor]: Taking taylor expansion of 1.0 in k 2.765 * [taylor]: Taking taylor expansion of (fabs (pow (/ 1 k) 1/3)) in k 2.767 * [taylor]: Taking taylor expansion of (* (pow k 1/6) (/ (pow (sqrt 1.0) 2) (fabs (pow (/ 1 k) 1/3)))) in k 2.767 * [taylor]: Taking taylor expansion of (pow k 1/6) in k 2.767 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log k))) in k 2.767 * [taylor]: Taking taylor expansion of (* 1/6 (log k)) in k 2.767 * [taylor]: Taking taylor expansion of 1/6 in k 2.767 * [taylor]: Taking taylor expansion of (log k) in k 2.767 * [taylor]: Taking taylor expansion of k in k 2.768 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (fabs (pow (/ 1 k) 1/3))) in k 2.768 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 2.768 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 2.768 * [taylor]: Taking taylor expansion of 1.0 in k 2.769 * [taylor]: Taking taylor expansion of (fabs (pow (/ 1 k) 1/3)) in k 2.847 * [approximate]: Taking taylor expansion of (* (/ (pow (sqrt 1.0) 2) (fabs (* (pow (/ 1 k) 1/3) (cbrt -1)))) (* (sqrt (/ 1 (cbrt -1))) (pow k 1/6))) in (k) around 0 2.847 * [taylor]: Taking taylor expansion of (* (/ (pow (sqrt 1.0) 2) (fabs (* (pow (/ 1 k) 1/3) (cbrt -1)))) (* (sqrt (/ 1 (cbrt -1))) (pow k 1/6))) in k 2.847 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (fabs (* (pow (/ 1 k) 1/3) (cbrt -1)))) in k 2.847 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 2.847 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 2.847 * [taylor]: Taking taylor expansion of 1.0 in k 2.847 * [taylor]: Taking taylor expansion of (fabs (* (pow (/ 1 k) 1/3) (cbrt -1))) in k 2.850 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (cbrt -1))) (pow k 1/6)) in k 2.850 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (cbrt -1))) in k 2.850 * [taylor]: Taking taylor expansion of (/ 1 (cbrt -1)) in k 2.850 * [taylor]: Taking taylor expansion of (cbrt -1) in k 2.850 * [taylor]: Taking taylor expansion of -1 in k 2.853 * [taylor]: Taking taylor expansion of (pow k 1/6) in k 2.853 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log k))) in k 2.853 * [taylor]: Taking taylor expansion of (* 1/6 (log k)) in k 2.853 * [taylor]: Taking taylor expansion of 1/6 in k 2.853 * [taylor]: Taking taylor expansion of (log k) in k 2.853 * [taylor]: Taking taylor expansion of k in k 2.854 * [taylor]: Taking taylor expansion of (* (/ (pow (sqrt 1.0) 2) (fabs (* (pow (/ 1 k) 1/3) (cbrt -1)))) (* (sqrt (/ 1 (cbrt -1))) (pow k 1/6))) in k 2.854 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (fabs (* (pow (/ 1 k) 1/3) (cbrt -1)))) in k 2.854 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 2.854 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 2.854 * [taylor]: Taking taylor expansion of 1.0 in k 2.854 * [taylor]: Taking taylor expansion of (fabs (* (pow (/ 1 k) 1/3) (cbrt -1))) in k 2.856 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (cbrt -1))) (pow k 1/6)) in k 2.856 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (cbrt -1))) in k 2.856 * [taylor]: Taking taylor expansion of (/ 1 (cbrt -1)) in k 2.857 * [taylor]: Taking taylor expansion of (cbrt -1) in k 2.857 * [taylor]: Taking taylor expansion of -1 in k 2.860 * [taylor]: Taking taylor expansion of (pow k 1/6) in k 2.860 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log k))) in k 2.860 * [taylor]: Taking taylor expansion of (* 1/6 (log k)) in k 2.860 * [taylor]: Taking taylor expansion of 1/6 in k 2.860 * [taylor]: Taking taylor expansion of (log k) in k 2.860 * [taylor]: Taking taylor expansion of k in k 2.977 * * * [progress]: simplifying candidates 2.980 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (cbrt k)) (log1p (cbrt k)) (log (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (cbrt k) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) (* (* (cbrt k) (cbrt k)) (cbrt k)) (sqrt (cbrt k)) (sqrt (cbrt k)) (expm1 (cbrt k)) (log1p (cbrt k)) (log (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (cbrt k) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) (* (* (cbrt k) (cbrt k)) (cbrt k)) (sqrt (cbrt k)) (sqrt (cbrt k)) (expm1 (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (log1p (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (+ (- (log (sqrt 1.0)) (log (fabs (cbrt k)))) (- (log (sqrt 1.0)) (log (sqrt (cbrt k))))) (+ (- (log (sqrt 1.0)) (log (fabs (cbrt k)))) (log (/ (sqrt 1.0) (sqrt (cbrt k))))) (+ (log (/ (sqrt 1.0) (fabs (cbrt k)))) (- (log (sqrt 1.0)) (log (sqrt (cbrt k))))) (+ (log (/ (sqrt 1.0) (fabs (cbrt k)))) (log (/ (sqrt 1.0) (sqrt (cbrt k))))) (log (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (exp (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (* (* (sqrt 1.0) (sqrt 1.0)) (sqrt 1.0)) (* (* (fabs (cbrt k)) (fabs (cbrt k))) (fabs (cbrt k)))) (/ (* (* (sqrt 1.0) (sqrt 1.0)) (sqrt 1.0)) (* (* (sqrt (cbrt k)) (sqrt (cbrt k))) (sqrt (cbrt k))))) (* (/ (* (* (sqrt 1.0) (sqrt 1.0)) (sqrt 1.0)) (* (* (fabs (cbrt k)) (fabs (cbrt k))) (fabs (cbrt k)))) (* (* (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (* (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (* (* (sqrt 1.0) (sqrt 1.0)) (sqrt 1.0)) (* (* (sqrt (cbrt k)) (sqrt (cbrt k))) (sqrt (cbrt k))))) (* (* (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt 1.0) (fabs (cbrt k)))) (* (* (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (cbrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (cbrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))))) (cbrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (* (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (sqrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (sqrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (sqrt 1.0) (sqrt 1.0)) (* (fabs (cbrt k)) (sqrt (cbrt k))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (* (cbrt (/ (sqrt 1.0) (sqrt (cbrt k)))) (cbrt (/ (sqrt 1.0) (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt (cbrt (* (cbrt k) (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt (cbrt 1)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt (* (cbrt (cbrt k)) (cbrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt 1))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) 1)) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (* (cbrt 1.0) (cbrt 1.0))) (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (* (cbrt 1.0) (cbrt 1.0))) (sqrt (cbrt (* (cbrt k) (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (* (cbrt 1.0) (cbrt 1.0))) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (* (cbrt 1.0) (cbrt 1.0))) (sqrt (cbrt 1)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (* (cbrt 1.0) (cbrt 1.0))) (sqrt (* (cbrt (cbrt k)) (cbrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (* (cbrt 1.0) (cbrt 1.0))) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (* (cbrt 1.0) (cbrt 1.0))) (sqrt 1))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (* (cbrt 1.0) (cbrt 1.0))) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (* (cbrt 1.0) (cbrt 1.0))) 1)) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (* (cbrt k) (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt 1)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (* (cbrt (cbrt k)) (cbrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt 1))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) 1)) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt (cbrt (* (cbrt k) (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt (cbrt 1)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt (* (cbrt (cbrt k)) (cbrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt 1))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) 1)) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (* (cbrt k) (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt 1)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (* (cbrt (cbrt k)) (cbrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt 1))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) 1)) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ 1 (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ 1 (sqrt (cbrt (* (cbrt k) (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ 1 (sqrt (cbrt (sqrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ 1 (sqrt (cbrt 1)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ 1 (sqrt (* (cbrt (cbrt k)) (cbrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ 1 (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ 1 (sqrt 1))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ 1 (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ 1 1)) (* (/ (sqrt 1.0) (fabs (cbrt k))) 1) (* (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt 1.0)) (* (cbrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (cbrt (sqrt 1.0)) (cbrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (cbrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (cbrt (sqrt 1.0)) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (cbrt 1.0)) (cbrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (cbrt 1.0)) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (sqrt 1.0)) (cbrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (sqrt 1.0)) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt 1.0) (cbrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt 1.0) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (sqrt 1.0)) (cbrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (sqrt 1.0)) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt 1.0) (cbrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt 1.0) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ 1 (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt 1.0)) (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt k)))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) (* (/ (pow (sqrt 1.0) 2) (fabs (pow k 1/3))) (pow (/ 1 k) 1/6)) (* (pow (/ 1 k) 1/6) (/ (pow (sqrt 1.0) 2) (fabs (pow k 1/3)))) (* (pow (/ -1 k) 1/6) (* (sqrt (/ 1 (cbrt -1))) (/ (pow (sqrt 1.0) 2) (fabs (* (pow (* -1 k) 1/3) (cbrt -1)))))) 2.990 * * [simplify]: iteration 0 : 937 enodes (cost 2058 ) 3.006 * * [simplify]: iteration 1 : 4332 enodes (cost 1935 ) 3.074 * * [simplify]: iteration 2 : 5001 enodes (cost 1923 ) 3.082 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (cbrt k)) (log1p (cbrt k)) (log (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (pow k 1/3) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) (pow (pow k 1/3) 3) (sqrt (cbrt k)) (sqrt (cbrt k)) (expm1 (cbrt k)) (log1p (cbrt k)) (log (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (pow k 1/3) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) (pow (pow k 1/3) 3) (sqrt (cbrt k)) (sqrt (cbrt k)) (expm1 (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (log1p (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (/ (/ 1.0 (sqrt (cbrt k))) (fabs (cbrt k))) (- (log (/ 1.0 (fabs (cbrt k)))) (log (sqrt (cbrt k)))) (- (log (/ 1.0 (fabs (cbrt k)))) (log (sqrt (cbrt k)))) (- (log (/ 1.0 (fabs (cbrt k)))) (log (sqrt (cbrt k)))) (- (log (/ 1.0 (fabs (cbrt k)))) (log (sqrt (cbrt k)))) (- (log (/ 1.0 (fabs (cbrt k)))) (log (sqrt (cbrt k)))) (pow (exp 1) (/ (/ 1.0 (sqrt (cbrt k))) (fabs (cbrt k)))) (pow (/ (/ 1.0 (sqrt (cbrt k))) (fabs (cbrt k))) 3) (pow (/ (/ 1.0 (sqrt (cbrt k))) (fabs (cbrt k))) 3) (pow (/ (/ 1.0 (sqrt (cbrt k))) (fabs (cbrt k))) 3) (pow (/ (/ 1.0 (sqrt (cbrt k))) (fabs (cbrt k))) 3) (* (cbrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (cbrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))))) (cbrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (pow (/ (/ 1.0 (sqrt (cbrt k))) (fabs (cbrt k))) 3) (sqrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (sqrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) 1.0 (* (fabs (cbrt k)) (sqrt (cbrt k))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (* (cbrt (/ (sqrt 1.0) (sqrt (cbrt k)))) (cbrt (/ (sqrt 1.0) (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt (cbrt (* (cbrt k) (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt (cbrt 1)))) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0)))) (fabs (cbrt (cbrt k)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt 1))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0))) (sqrt (sqrt (cbrt k))))) (/ (* (sqrt 1.0) (* (cbrt (sqrt 1.0)) (cbrt (sqrt 1.0)))) (fabs (cbrt k))) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (fabs (cbrt 1.0))) (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k))))) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (fabs (cbrt 1.0))) (sqrt (cbrt (* (cbrt k) (cbrt k))))) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (fabs (cbrt 1.0))) (sqrt (cbrt (sqrt k)))) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (fabs (cbrt 1.0))) (sqrt (cbrt 1))) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (fabs (cbrt 1.0))) (fabs (cbrt (cbrt k)))) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (fabs (cbrt 1.0))) (sqrt (sqrt (cbrt k)))) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (fabs (cbrt 1.0))) (sqrt 1)) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (fabs (cbrt 1.0))) (sqrt (sqrt (cbrt k)))) (/ (* (sqrt 1.0) (fabs (cbrt 1.0))) (fabs (cbrt k))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (* (cbrt k) (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt 1)))) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt (sqrt 1.0))) (fabs (cbrt (cbrt k)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt 1))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (/ (* (sqrt 1.0) (sqrt (sqrt 1.0))) (fabs (cbrt k))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt (cbrt (* (cbrt k) (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt (cbrt 1)))) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt 1)) (fabs (cbrt (cbrt k)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt (sqrt (cbrt k))))) (/ (sqrt 1.0) (fabs (cbrt k))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1) (sqrt (sqrt (cbrt k))))) (/ (* (sqrt 1.0) (sqrt 1)) (fabs (cbrt k))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (* (cbrt k) (cbrt k)))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt (sqrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (cbrt 1)))) (/ (* (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt (sqrt 1.0))) (fabs (cbrt (cbrt k)))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt 1))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (cbrt k))))) (/ (* (sqrt 1.0) (sqrt (sqrt 1.0))) (fabs (cbrt k))) (/ (/ (sqrt 1.0) (fabs (cbrt k))) (* (cbrt (sqrt (cbrt k))) (cbrt (sqrt (cbrt k))))) (/ (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt (cbrt (* (cbrt k) (cbrt k))))) (/ (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt (cbrt 1))) (/ (/ (sqrt 1.0) (fabs (cbrt k))) (fabs (cbrt (cbrt k)))) (/ (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt 1)) (/ (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ 1.0 (fabs (cbrt k))) (* (cbrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (cbrt (sqrt 1.0)) (cbrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (cbrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (cbrt (sqrt 1.0)) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (cbrt 1.0)) (cbrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (cbrt 1.0)) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (sqrt 1.0)) (cbrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (sqrt 1.0)) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (/ (/ 1.0 (sqrt (cbrt k))) (cbrt (fabs (cbrt k)))) (/ (/ 1.0 (sqrt (cbrt k))) (sqrt (fabs (cbrt k)))) (/ (/ 1.0 (sqrt (cbrt k))) (fabs (cbrt k))) (* (/ (sqrt (sqrt 1.0)) (cbrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (sqrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (* (/ (sqrt (sqrt 1.0)) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k)))) (/ (/ 1.0 (sqrt (cbrt k))) (cbrt (fabs (cbrt k)))) (/ (/ 1.0 (sqrt (cbrt k))) (sqrt (fabs (cbrt k)))) (/ (/ 1.0 (sqrt (cbrt k))) (fabs (cbrt k))) (/ (/ 1.0 (sqrt (cbrt k))) (fabs (cbrt k))) (/ (/ (sqrt 1.0) (sqrt (cbrt k))) (fabs (pow k 1/3))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (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)))))) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) (/ (* 1.0 (pow (/ 1 k) 1/6)) (fabs (pow k 1/3))) (/ (* 1.0 (pow (/ 1 k) 1/6)) (fabs (pow k 1/3))) (* (/ (* (sqrt (/ 1 (cbrt -1))) 1.0) (fabs (* (pow (* -1 k) 1/3) (cbrt -1)))) (pow (/ -1 k) 1/6)) 3.083 * * * [progress]: adding candidates to table 3.938 * * [progress]: iteration 4 / 4 3.938 * * * [progress]: picking best candidate 3.950 * * * * [pick]: Picked # 3.950 * * * [progress]: localizing error 3.970 * * * [progress]: generating rewritten candidates 3.970 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.983 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 3.997 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 4.000 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 4.018 * * * [progress]: generating series expansions 4.018 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 4.019 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 4.019 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 4.019 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.019 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.019 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 4.019 * [taylor]: Taking taylor expansion of 0.25 in k 4.019 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.019 * [taylor]: Taking taylor expansion of 1.0 in k 4.019 * [taylor]: Taking taylor expansion of k in k 4.019 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.019 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.019 * [taylor]: Taking taylor expansion of 2.0 in k 4.019 * [taylor]: Taking taylor expansion of (* n PI) in k 4.019 * [taylor]: Taking taylor expansion of n in k 4.019 * [taylor]: Taking taylor expansion of PI in k 4.020 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.020 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.020 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.020 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.020 * [taylor]: Taking taylor expansion of 0.25 in n 4.020 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.020 * [taylor]: Taking taylor expansion of 1.0 in n 4.020 * [taylor]: Taking taylor expansion of k in n 4.020 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.020 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.020 * [taylor]: Taking taylor expansion of 2.0 in n 4.020 * [taylor]: Taking taylor expansion of (* n PI) in n 4.020 * [taylor]: Taking taylor expansion of n in n 4.020 * [taylor]: Taking taylor expansion of PI in n 4.026 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.026 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.026 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.026 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.026 * [taylor]: Taking taylor expansion of 0.25 in n 4.026 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.026 * [taylor]: Taking taylor expansion of 1.0 in n 4.026 * [taylor]: Taking taylor expansion of k in n 4.026 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.026 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.026 * [taylor]: Taking taylor expansion of 2.0 in n 4.026 * [taylor]: Taking taylor expansion of (* n PI) in n 4.026 * [taylor]: Taking taylor expansion of n in n 4.026 * [taylor]: Taking taylor expansion of PI in n 4.031 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.031 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.031 * [taylor]: Taking taylor expansion of 0.25 in k 4.031 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.031 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.031 * [taylor]: Taking taylor expansion of 1.0 in k 4.031 * [taylor]: Taking taylor expansion of k in k 4.031 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.031 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.031 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.031 * [taylor]: Taking taylor expansion of 2.0 in k 4.031 * [taylor]: Taking taylor expansion of PI in k 4.032 * [taylor]: Taking taylor expansion of (log n) in k 4.032 * [taylor]: Taking taylor expansion of n in k 4.047 * [taylor]: Taking taylor expansion of 0 in k 4.063 * [taylor]: Taking taylor expansion of 0 in k 4.081 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 4.081 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 4.081 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.081 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.081 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 4.081 * [taylor]: Taking taylor expansion of 0.25 in k 4.081 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.081 * [taylor]: Taking taylor expansion of 1.0 in k 4.081 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.081 * [taylor]: Taking taylor expansion of k in k 4.081 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.081 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.081 * [taylor]: Taking taylor expansion of 2.0 in k 4.081 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.081 * [taylor]: Taking taylor expansion of PI in k 4.081 * [taylor]: Taking taylor expansion of n in k 4.082 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.082 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.082 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.082 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.082 * [taylor]: Taking taylor expansion of 0.25 in n 4.082 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.083 * [taylor]: Taking taylor expansion of 1.0 in n 4.083 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.083 * [taylor]: Taking taylor expansion of k in n 4.083 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.083 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.083 * [taylor]: Taking taylor expansion of 2.0 in n 4.083 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.083 * [taylor]: Taking taylor expansion of PI in n 4.083 * [taylor]: Taking taylor expansion of n in n 4.086 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.086 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.086 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.086 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.086 * [taylor]: Taking taylor expansion of 0.25 in n 4.086 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.087 * [taylor]: Taking taylor expansion of 1.0 in n 4.087 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.087 * [taylor]: Taking taylor expansion of k in n 4.087 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.087 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.087 * [taylor]: Taking taylor expansion of 2.0 in n 4.087 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.087 * [taylor]: Taking taylor expansion of PI in n 4.087 * [taylor]: Taking taylor expansion of n in n 4.091 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.091 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.091 * [taylor]: Taking taylor expansion of 0.25 in k 4.091 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.091 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.091 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.091 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.091 * [taylor]: Taking taylor expansion of 2.0 in k 4.091 * [taylor]: Taking taylor expansion of PI in k 4.092 * [taylor]: Taking taylor expansion of (log n) in k 4.092 * [taylor]: Taking taylor expansion of n in k 4.092 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.092 * [taylor]: Taking taylor expansion of 1.0 in k 4.092 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.092 * [taylor]: Taking taylor expansion of k in k 4.101 * [taylor]: Taking taylor expansion of 0 in k 4.108 * [taylor]: Taking taylor expansion of 0 in k 4.117 * [taylor]: Taking taylor expansion of 0 in k 4.118 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 4.118 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 4.118 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.118 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.118 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 4.118 * [taylor]: Taking taylor expansion of 0.25 in k 4.118 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.118 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.118 * [taylor]: Taking taylor expansion of k in k 4.118 * [taylor]: Taking taylor expansion of 1.0 in k 4.119 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.119 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.119 * [taylor]: Taking taylor expansion of -2.0 in k 4.119 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.119 * [taylor]: Taking taylor expansion of PI in k 4.119 * [taylor]: Taking taylor expansion of n in k 4.119 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.119 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.119 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.119 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.119 * [taylor]: Taking taylor expansion of 0.25 in n 4.119 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.120 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.120 * [taylor]: Taking taylor expansion of k in n 4.120 * [taylor]: Taking taylor expansion of 1.0 in n 4.120 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.120 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.120 * [taylor]: Taking taylor expansion of -2.0 in n 4.120 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.120 * [taylor]: Taking taylor expansion of PI in n 4.120 * [taylor]: Taking taylor expansion of n in n 4.123 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.123 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.123 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.123 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.123 * [taylor]: Taking taylor expansion of 0.25 in n 4.123 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.123 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.123 * [taylor]: Taking taylor expansion of k in n 4.123 * [taylor]: Taking taylor expansion of 1.0 in n 4.123 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.123 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.123 * [taylor]: Taking taylor expansion of -2.0 in n 4.123 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.123 * [taylor]: Taking taylor expansion of PI in n 4.123 * [taylor]: Taking taylor expansion of n in n 4.133 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.133 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.134 * [taylor]: Taking taylor expansion of 0.25 in k 4.134 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.134 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.134 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.134 * [taylor]: Taking taylor expansion of k in k 4.134 * [taylor]: Taking taylor expansion of 1.0 in k 4.134 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.134 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.134 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.135 * [taylor]: Taking taylor expansion of -2.0 in k 4.135 * [taylor]: Taking taylor expansion of PI in k 4.135 * [taylor]: Taking taylor expansion of (log n) in k 4.135 * [taylor]: Taking taylor expansion of n in k 4.144 * [taylor]: Taking taylor expansion of 0 in k 4.151 * [taylor]: Taking taylor expansion of 0 in k 4.159 * [taylor]: Taking taylor expansion of 0 in k 4.160 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 4.161 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 4.161 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 4.161 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.161 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.161 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 4.161 * [taylor]: Taking taylor expansion of 0.25 in k 4.161 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.161 * [taylor]: Taking taylor expansion of 1.0 in k 4.161 * [taylor]: Taking taylor expansion of k in k 4.161 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.161 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.161 * [taylor]: Taking taylor expansion of 2.0 in k 4.161 * [taylor]: Taking taylor expansion of (* n PI) in k 4.161 * [taylor]: Taking taylor expansion of n in k 4.161 * [taylor]: Taking taylor expansion of PI in k 4.162 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.162 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.162 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.162 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.162 * [taylor]: Taking taylor expansion of 0.25 in n 4.162 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.162 * [taylor]: Taking taylor expansion of 1.0 in n 4.162 * [taylor]: Taking taylor expansion of k in n 4.162 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.162 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.162 * [taylor]: Taking taylor expansion of 2.0 in n 4.162 * [taylor]: Taking taylor expansion of (* n PI) in n 4.162 * [taylor]: Taking taylor expansion of n in n 4.162 * [taylor]: Taking taylor expansion of PI in n 4.167 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.167 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.167 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.167 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.167 * [taylor]: Taking taylor expansion of 0.25 in n 4.167 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.167 * [taylor]: Taking taylor expansion of 1.0 in n 4.167 * [taylor]: Taking taylor expansion of k in n 4.167 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.167 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.167 * [taylor]: Taking taylor expansion of 2.0 in n 4.167 * [taylor]: Taking taylor expansion of (* n PI) in n 4.167 * [taylor]: Taking taylor expansion of n in n 4.167 * [taylor]: Taking taylor expansion of PI in n 4.173 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.173 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.173 * [taylor]: Taking taylor expansion of 0.25 in k 4.173 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.173 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.173 * [taylor]: Taking taylor expansion of 1.0 in k 4.173 * [taylor]: Taking taylor expansion of k in k 4.173 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.173 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.173 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.173 * [taylor]: Taking taylor expansion of 2.0 in k 4.173 * [taylor]: Taking taylor expansion of PI in k 4.174 * [taylor]: Taking taylor expansion of (log n) in k 4.174 * [taylor]: Taking taylor expansion of n in k 4.183 * [taylor]: Taking taylor expansion of 0 in k 4.198 * [taylor]: Taking taylor expansion of 0 in k 4.222 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 4.222 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 4.222 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.222 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.222 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 4.222 * [taylor]: Taking taylor expansion of 0.25 in k 4.222 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.222 * [taylor]: Taking taylor expansion of 1.0 in k 4.222 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.222 * [taylor]: Taking taylor expansion of k in k 4.223 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.223 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.223 * [taylor]: Taking taylor expansion of 2.0 in k 4.223 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.223 * [taylor]: Taking taylor expansion of PI in k 4.223 * [taylor]: Taking taylor expansion of n in k 4.224 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.224 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.224 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.224 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.224 * [taylor]: Taking taylor expansion of 0.25 in n 4.224 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.224 * [taylor]: Taking taylor expansion of 1.0 in n 4.224 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.224 * [taylor]: Taking taylor expansion of k in n 4.224 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.224 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.224 * [taylor]: Taking taylor expansion of 2.0 in n 4.224 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.224 * [taylor]: Taking taylor expansion of PI in n 4.224 * [taylor]: Taking taylor expansion of n in n 4.227 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.227 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.227 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.227 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.228 * [taylor]: Taking taylor expansion of 0.25 in n 4.228 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.228 * [taylor]: Taking taylor expansion of 1.0 in n 4.228 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.228 * [taylor]: Taking taylor expansion of k in n 4.228 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.228 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.228 * [taylor]: Taking taylor expansion of 2.0 in n 4.228 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.228 * [taylor]: Taking taylor expansion of PI in n 4.228 * [taylor]: Taking taylor expansion of n in n 4.231 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.231 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.231 * [taylor]: Taking taylor expansion of 0.25 in k 4.231 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.231 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.231 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.231 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.231 * [taylor]: Taking taylor expansion of 2.0 in k 4.231 * [taylor]: Taking taylor expansion of PI in k 4.232 * [taylor]: Taking taylor expansion of (log n) in k 4.232 * [taylor]: Taking taylor expansion of n in k 4.232 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.232 * [taylor]: Taking taylor expansion of 1.0 in k 4.232 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.232 * [taylor]: Taking taylor expansion of k in k 4.242 * [taylor]: Taking taylor expansion of 0 in k 4.248 * [taylor]: Taking taylor expansion of 0 in k 4.257 * [taylor]: Taking taylor expansion of 0 in k 4.259 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 4.259 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 4.259 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.259 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.259 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 4.259 * [taylor]: Taking taylor expansion of 0.25 in k 4.259 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.259 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.259 * [taylor]: Taking taylor expansion of k in k 4.259 * [taylor]: Taking taylor expansion of 1.0 in k 4.259 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.259 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.259 * [taylor]: Taking taylor expansion of -2.0 in k 4.259 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.259 * [taylor]: Taking taylor expansion of PI in k 4.259 * [taylor]: Taking taylor expansion of n in k 4.260 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.260 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.260 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.260 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.260 * [taylor]: Taking taylor expansion of 0.25 in n 4.260 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.260 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.260 * [taylor]: Taking taylor expansion of k in n 4.260 * [taylor]: Taking taylor expansion of 1.0 in n 4.260 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.260 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.260 * [taylor]: Taking taylor expansion of -2.0 in n 4.260 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.260 * [taylor]: Taking taylor expansion of PI in n 4.260 * [taylor]: Taking taylor expansion of n in n 4.264 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.264 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.264 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.264 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.264 * [taylor]: Taking taylor expansion of 0.25 in n 4.264 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.264 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.264 * [taylor]: Taking taylor expansion of k in n 4.264 * [taylor]: Taking taylor expansion of 1.0 in n 4.264 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.264 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.264 * [taylor]: Taking taylor expansion of -2.0 in n 4.264 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.264 * [taylor]: Taking taylor expansion of PI in n 4.264 * [taylor]: Taking taylor expansion of n in n 4.268 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.268 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.268 * [taylor]: Taking taylor expansion of 0.25 in k 4.268 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.268 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.268 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.268 * [taylor]: Taking taylor expansion of k in k 4.268 * [taylor]: Taking taylor expansion of 1.0 in k 4.268 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.268 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.268 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.268 * [taylor]: Taking taylor expansion of -2.0 in k 4.268 * [taylor]: Taking taylor expansion of PI in k 4.269 * [taylor]: Taking taylor expansion of (log n) in k 4.269 * [taylor]: Taking taylor expansion of n in k 4.278 * [taylor]: Taking taylor expansion of 0 in k 4.285 * [taylor]: Taking taylor expansion of 0 in k 4.293 * [taylor]: Taking taylor expansion of 0 in k 4.300 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 4.300 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.300 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.300 * [taylor]: Taking taylor expansion of 1.0 in k 4.300 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.300 * [taylor]: Taking taylor expansion of k in k 4.302 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.302 * [taylor]: Taking taylor expansion of 1.0 in k 4.302 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.302 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.302 * [taylor]: Taking taylor expansion of k in k 4.313 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.313 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.313 * [taylor]: Taking taylor expansion of 1.0 in k 4.313 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.313 * [taylor]: Taking taylor expansion of k in k 4.314 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.314 * [taylor]: Taking taylor expansion of 1.0 in k 4.314 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.314 * [taylor]: Taking taylor expansion of k in k 4.324 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.324 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.324 * [taylor]: Taking taylor expansion of 1.0 in k 4.324 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.324 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.324 * [taylor]: Taking taylor expansion of -1 in k 4.324 * [taylor]: Taking taylor expansion of k in k 4.325 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.325 * [taylor]: Taking taylor expansion of 1.0 in k 4.325 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.325 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.325 * [taylor]: Taking taylor expansion of -1 in k 4.325 * [taylor]: Taking taylor expansion of k in k 4.337 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 4.337 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.337 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.337 * [taylor]: Taking taylor expansion of 2.0 in n 4.337 * [taylor]: Taking taylor expansion of (* n PI) in n 4.337 * [taylor]: Taking taylor expansion of n in n 4.337 * [taylor]: Taking taylor expansion of PI in n 4.337 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.337 * [taylor]: Taking taylor expansion of 2.0 in n 4.337 * [taylor]: Taking taylor expansion of (* n PI) in n 4.337 * [taylor]: Taking taylor expansion of n in n 4.337 * [taylor]: Taking taylor expansion of PI in n 4.349 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.349 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.349 * [taylor]: Taking taylor expansion of 2.0 in n 4.349 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.349 * [taylor]: Taking taylor expansion of PI in n 4.349 * [taylor]: Taking taylor expansion of n in n 4.349 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.349 * [taylor]: Taking taylor expansion of 2.0 in n 4.349 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.349 * [taylor]: Taking taylor expansion of PI in n 4.349 * [taylor]: Taking taylor expansion of n in n 4.358 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.358 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.358 * [taylor]: Taking taylor expansion of -2.0 in n 4.358 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.358 * [taylor]: Taking taylor expansion of PI in n 4.358 * [taylor]: Taking taylor expansion of n in n 4.358 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.358 * [taylor]: Taking taylor expansion of -2.0 in n 4.358 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.358 * [taylor]: Taking taylor expansion of PI in n 4.358 * [taylor]: Taking taylor expansion of n in n 4.367 * * * [progress]: simplifying candidates 4.370 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* 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(- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (expm1 (/ 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)) 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(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)) (/ 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 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 1/2) (pow (* (* 2.0 PI) n) 1/2) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (fma (- 0.25) (fma (* k (log (* 2.0 PI))) (pow (exp 0.25) (log (* (* 2.0 PI) n))) (* (* k (pow (exp 0.25) (log (* (* 2.0 PI) n)))) (log n))) (fma (* (* 0.03125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.25)) (pow (log (* 2.0 PI)) 2) (fma (* 0.0625 (pow k 2)) (* (* (log (* 2.0 PI)) (log n)) (pow (* (* 2.0 PI) n) 0.25)) (+ (* (* (* (pow k 2) (pow (exp 0.25) (log (* (* 2.0 PI) n)))) (pow (log n) 2)) 0.03125) (pow (* (* 2.0 PI) n) 0.25))))) (pow (* (* 2.0 PI) n) (* 0.25 (- 1.0 k))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- 0.25) (fma (* k (log (* 2.0 PI))) (pow (exp 0.25) (log (* (* 2.0 PI) n))) (* (* k (pow (exp 0.25) (log (* (* 2.0 PI) n)))) (log n))) (fma (* (* 0.03125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.25)) (pow (log (* 2.0 PI)) 2) (fma (* 0.0625 (pow k 2)) (* (* (log (* 2.0 PI)) (log n)) (pow (* (* 2.0 PI) n) 0.25)) (+ (* (* (* (pow k 2) (pow (exp 0.25) (log (* (* 2.0 PI) n)))) (pow (log n) 2)) 0.03125) (pow (* (* 2.0 PI) n) 0.25))))) (pow (* (* 2.0 PI) n) (* 0.25 (- 1.0 k))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (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))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) 4.463 * * * [progress]: adding candidates to table 5.199 * [progress]: [Phase 3 of 3] Extracting. 5.199 * * [regime]: Finding splitpoints for: (# # # # # #) 5.205 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 5.205 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # #) 5.233 * * * * [regimes]: Trying to branch on n from (# # # # # #) 5.263 * * * * [regimes]: Trying to branch on k from (# # # # # #) 5.289 * * * [regime]: Found split indices: #