53.310 * [progress]: [Phase 1 of 3] Setting up. 0.003 * * * [progress]: [1/2] Preparing points 0.228 * * * [progress]: [2/2] Setting up program. 0.232 * [progress]: [Phase 2 of 3] Improving. 0.233 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.233 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.233 * * [simplify]: iteration 0: 13 enodes 0.237 * * [simplify]: iteration 1: 31 enodes 0.243 * * [simplify]: iteration 2: 62 enodes 0.255 * * [simplify]: iteration 3: 124 enodes 0.335 * * [simplify]: iteration 4: 328 enodes 0.939 * * [simplify]: iteration 5: 970 enodes 1.344 * * [simplify]: iteration complete: 2000 enodes 1.344 * * [simplify]: Extracting #0: cost 1 inf + 0 1.345 * * [simplify]: Extracting #1: cost 86 inf + 0 1.346 * * [simplify]: Extracting #2: cost 302 inf + 1 1.353 * * [simplify]: Extracting #3: cost 426 inf + 46 1.357 * * [simplify]: Extracting #4: cost 394 inf + 4201 1.369 * * [simplify]: Extracting #5: cost 275 inf + 34222 1.410 * * [simplify]: Extracting #6: cost 82 inf + 177969 1.454 * * [simplify]: Extracting #7: cost 7 inf + 250233 1.521 * * [simplify]: Extracting #8: cost 0 inf + 255820 1.585 * * [simplify]: Extracting #9: cost 0 inf + 255818 1.629 * * [simplify]: Extracting #10: cost 0 inf + 255564 1.673 * [simplify]: Simplified to: (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1.677 * * [progress]: iteration 1 / 4 1.677 * * * [progress]: picking best candidate 1.683 * * * * [pick]: Picked # 1.683 * * * [progress]: localizing error 1.710 * * * [progress]: generating rewritten candidates 1.710 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1) 1.732 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 1.747 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 1.786 * * * [progress]: generating series expansions 1.786 * * * * [progress]: [ 1 / 3 ] generating series at (2 1) 1.787 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1.787 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1.787 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1.787 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1.787 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1.787 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.787 * [taylor]: Taking taylor expansion of 1/2 in k 1.787 * [backup-simplify]: Simplify 1/2 into 1/2 1.787 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.787 * [taylor]: Taking taylor expansion of 1/2 in k 1.787 * [backup-simplify]: Simplify 1/2 into 1/2 1.787 * [taylor]: Taking taylor expansion of k in k 1.787 * [backup-simplify]: Simplify 0 into 0 1.787 * [backup-simplify]: Simplify 1 into 1 1.787 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.787 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.787 * [taylor]: Taking taylor expansion of 2 in k 1.787 * [backup-simplify]: Simplify 2 into 2 1.787 * [taylor]: Taking taylor expansion of (* n PI) in k 1.787 * [taylor]: Taking taylor expansion of n in k 1.787 * [backup-simplify]: Simplify n into n 1.787 * [taylor]: Taking taylor expansion of PI in k 1.787 * [backup-simplify]: Simplify PI into PI 1.787 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.787 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1.787 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1.788 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.788 * [backup-simplify]: Simplify (- 0) into 0 1.788 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.788 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1.788 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1.788 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.788 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.788 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.788 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.788 * [taylor]: Taking taylor expansion of 1/2 in n 1.788 * [backup-simplify]: Simplify 1/2 into 1/2 1.788 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.788 * [taylor]: Taking taylor expansion of 1/2 in n 1.788 * [backup-simplify]: Simplify 1/2 into 1/2 1.788 * [taylor]: Taking taylor expansion of k in n 1.788 * [backup-simplify]: Simplify k into k 1.788 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.788 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.789 * [taylor]: Taking taylor expansion of 2 in n 1.789 * [backup-simplify]: Simplify 2 into 2 1.789 * [taylor]: Taking taylor expansion of (* n PI) in n 1.789 * [taylor]: Taking taylor expansion of n in n 1.789 * [backup-simplify]: Simplify 0 into 0 1.789 * [backup-simplify]: Simplify 1 into 1 1.789 * [taylor]: Taking taylor expansion of PI in n 1.789 * [backup-simplify]: Simplify PI into PI 1.789 * [backup-simplify]: Simplify (* 0 PI) into 0 1.789 * [backup-simplify]: Simplify (* 2 0) into 0 1.790 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.791 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.792 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.792 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.798 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.798 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.800 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.801 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.802 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1.802 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.802 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.802 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.802 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.802 * [taylor]: Taking taylor expansion of 1/2 in n 1.802 * [backup-simplify]: Simplify 1/2 into 1/2 1.803 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.803 * [taylor]: Taking taylor expansion of 1/2 in n 1.803 * [backup-simplify]: Simplify 1/2 into 1/2 1.803 * [taylor]: Taking taylor expansion of k in n 1.803 * [backup-simplify]: Simplify k into k 1.803 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.803 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.803 * [taylor]: Taking taylor expansion of 2 in n 1.803 * [backup-simplify]: Simplify 2 into 2 1.803 * [taylor]: Taking taylor expansion of (* n PI) in n 1.803 * [taylor]: Taking taylor expansion of n in n 1.803 * [backup-simplify]: Simplify 0 into 0 1.803 * [backup-simplify]: Simplify 1 into 1 1.803 * [taylor]: Taking taylor expansion of PI in n 1.803 * [backup-simplify]: Simplify PI into PI 1.803 * [backup-simplify]: Simplify (* 0 PI) into 0 1.804 * [backup-simplify]: Simplify (* 2 0) into 0 1.805 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.807 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.808 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.808 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.808 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.808 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.810 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.811 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.812 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1.812 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1.812 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1.812 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.812 * [taylor]: Taking taylor expansion of 1/2 in k 1.812 * [backup-simplify]: Simplify 1/2 into 1/2 1.813 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.813 * [taylor]: Taking taylor expansion of 1/2 in k 1.813 * [backup-simplify]: Simplify 1/2 into 1/2 1.813 * [taylor]: Taking taylor expansion of k in k 1.813 * [backup-simplify]: Simplify 0 into 0 1.813 * [backup-simplify]: Simplify 1 into 1 1.813 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1.813 * [taylor]: Taking taylor expansion of (log n) in k 1.813 * [taylor]: Taking taylor expansion of n in k 1.813 * [backup-simplify]: Simplify n into n 1.813 * [backup-simplify]: Simplify (log n) into (log n) 1.813 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.813 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.813 * [taylor]: Taking taylor expansion of 2 in k 1.813 * [backup-simplify]: Simplify 2 into 2 1.813 * [taylor]: Taking taylor expansion of PI in k 1.813 * [backup-simplify]: Simplify PI into PI 1.813 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.814 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.815 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.815 * [backup-simplify]: Simplify (- 0) into 0 1.816 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.817 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.818 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1.819 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.820 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.821 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.822 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1.824 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.825 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1.825 * [backup-simplify]: Simplify (- 0) into 0 1.826 * [backup-simplify]: Simplify (+ 0 0) into 0 1.828 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.829 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1.831 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.831 * [taylor]: Taking taylor expansion of 0 in k 1.831 * [backup-simplify]: Simplify 0 into 0 1.831 * [backup-simplify]: Simplify 0 into 0 1.832 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.832 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.834 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.835 * [backup-simplify]: Simplify (+ 0 0) into 0 1.835 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1.836 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.836 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.838 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1.841 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1.844 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1.845 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.846 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.848 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1.848 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1.848 * [backup-simplify]: Simplify (- 0) into 0 1.849 * [backup-simplify]: Simplify (+ 0 0) into 0 1.850 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.851 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.852 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.852 * [taylor]: Taking taylor expansion of 0 in k 1.852 * [backup-simplify]: Simplify 0 into 0 1.852 * [backup-simplify]: Simplify 0 into 0 1.852 * [backup-simplify]: Simplify 0 into 0 1.853 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.854 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1.856 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1.856 * [backup-simplify]: Simplify (+ 0 0) into 0 1.857 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1.857 * [backup-simplify]: Simplify (- 0) into 0 1.857 * [backup-simplify]: Simplify (+ 0 0) into 0 1.859 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.861 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1.864 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1.871 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1.871 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1.871 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1.871 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1.871 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1.871 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1.871 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1.871 * [taylor]: Taking taylor expansion of 1/2 in k 1.871 * [backup-simplify]: Simplify 1/2 into 1/2 1.871 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.871 * [taylor]: Taking taylor expansion of 1/2 in k 1.871 * [backup-simplify]: Simplify 1/2 into 1/2 1.871 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.871 * [taylor]: Taking taylor expansion of k in k 1.871 * [backup-simplify]: Simplify 0 into 0 1.871 * [backup-simplify]: Simplify 1 into 1 1.872 * [backup-simplify]: Simplify (/ 1 1) into 1 1.872 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1.872 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 1.872 * [taylor]: Taking taylor expansion of 2 in k 1.872 * [backup-simplify]: Simplify 2 into 2 1.872 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.872 * [taylor]: Taking taylor expansion of PI in k 1.872 * [backup-simplify]: Simplify PI into PI 1.872 * [taylor]: Taking taylor expansion of n in k 1.872 * [backup-simplify]: Simplify n into n 1.872 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.872 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1.872 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1.872 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.873 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.873 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.873 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1.873 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1.873 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1.873 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1.873 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1.873 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1.873 * [taylor]: Taking taylor expansion of 1/2 in n 1.873 * [backup-simplify]: Simplify 1/2 into 1/2 1.873 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.873 * [taylor]: Taking taylor expansion of 1/2 in n 1.873 * [backup-simplify]: Simplify 1/2 into 1/2 1.873 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.873 * [taylor]: Taking taylor expansion of k in n 1.873 * [backup-simplify]: Simplify k into k 1.873 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.873 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.873 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.873 * [taylor]: Taking taylor expansion of 2 in n 1.873 * [backup-simplify]: Simplify 2 into 2 1.873 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.873 * [taylor]: Taking taylor expansion of PI in n 1.873 * [backup-simplify]: Simplify PI into PI 1.873 * [taylor]: Taking taylor expansion of n in n 1.873 * [backup-simplify]: Simplify 0 into 0 1.873 * [backup-simplify]: Simplify 1 into 1 1.874 * [backup-simplify]: Simplify (/ PI 1) into PI 1.874 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.875 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.875 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.875 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1.875 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1.876 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.877 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1.878 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1.878 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1.878 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1.878 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1.879 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1.879 * [taylor]: Taking taylor expansion of 1/2 in n 1.879 * [backup-simplify]: Simplify 1/2 into 1/2 1.879 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.879 * [taylor]: Taking taylor expansion of 1/2 in n 1.879 * [backup-simplify]: Simplify 1/2 into 1/2 1.879 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.879 * [taylor]: Taking taylor expansion of k in n 1.879 * [backup-simplify]: Simplify k into k 1.879 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.879 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.879 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.879 * [taylor]: Taking taylor expansion of 2 in n 1.879 * [backup-simplify]: Simplify 2 into 2 1.879 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.879 * [taylor]: Taking taylor expansion of PI in n 1.879 * [backup-simplify]: Simplify PI into PI 1.879 * [taylor]: Taking taylor expansion of n in n 1.879 * [backup-simplify]: Simplify 0 into 0 1.879 * [backup-simplify]: Simplify 1 into 1 1.880 * [backup-simplify]: Simplify (/ PI 1) into PI 1.880 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.881 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.881 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.881 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1.881 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1.883 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.884 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1.885 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1.886 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1.886 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1.886 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1.886 * [taylor]: Taking taylor expansion of 1/2 in k 1.886 * [backup-simplify]: Simplify 1/2 into 1/2 1.886 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.886 * [taylor]: Taking taylor expansion of 1/2 in k 1.886 * [backup-simplify]: Simplify 1/2 into 1/2 1.886 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.886 * [taylor]: Taking taylor expansion of k in k 1.886 * [backup-simplify]: Simplify 0 into 0 1.886 * [backup-simplify]: Simplify 1 into 1 1.887 * [backup-simplify]: Simplify (/ 1 1) into 1 1.887 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1.887 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.887 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.887 * [taylor]: Taking taylor expansion of 2 in k 1.887 * [backup-simplify]: Simplify 2 into 2 1.887 * [taylor]: Taking taylor expansion of PI in k 1.887 * [backup-simplify]: Simplify PI into PI 1.887 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.888 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.888 * [taylor]: Taking taylor expansion of (log n) in k 1.888 * [taylor]: Taking taylor expansion of n in k 1.889 * [backup-simplify]: Simplify n into n 1.889 * [backup-simplify]: Simplify (log n) into (log n) 1.889 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.889 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.890 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.890 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.891 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1.892 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1.893 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1.895 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1.896 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.896 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.898 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.898 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.899 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1.899 * [backup-simplify]: Simplify (- 0) into 0 1.900 * [backup-simplify]: Simplify (+ 0 0) into 0 1.901 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.902 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1.904 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1.904 * [taylor]: Taking taylor expansion of 0 in k 1.904 * [backup-simplify]: Simplify 0 into 0 1.905 * [backup-simplify]: Simplify 0 into 0 1.905 * [backup-simplify]: Simplify 0 into 0 1.906 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.907 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1.910 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1.910 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.911 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1.912 * [backup-simplify]: Simplify (- 0) into 0 1.912 * [backup-simplify]: Simplify (+ 0 0) into 0 1.913 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.915 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1.917 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.917 * [taylor]: Taking taylor expansion of 0 in k 1.917 * [backup-simplify]: Simplify 0 into 0 1.918 * [backup-simplify]: Simplify 0 into 0 1.918 * [backup-simplify]: Simplify 0 into 0 1.918 * [backup-simplify]: Simplify 0 into 0 1.919 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.920 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.928 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1.929 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.930 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1.931 * [backup-simplify]: Simplify (- 0) into 0 1.931 * [backup-simplify]: Simplify (+ 0 0) into 0 1.933 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.935 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1.938 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.938 * [taylor]: Taking taylor expansion of 0 in k 1.938 * [backup-simplify]: Simplify 0 into 0 1.938 * [backup-simplify]: Simplify 0 into 0 1.940 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1.940 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1.940 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1.940 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1.941 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1.941 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1.941 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1.941 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.941 * [taylor]: Taking taylor expansion of 1/2 in k 1.941 * [backup-simplify]: Simplify 1/2 into 1/2 1.941 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.941 * [taylor]: Taking taylor expansion of k in k 1.941 * [backup-simplify]: Simplify 0 into 0 1.941 * [backup-simplify]: Simplify 1 into 1 1.941 * [backup-simplify]: Simplify (/ 1 1) into 1 1.941 * [taylor]: Taking taylor expansion of 1/2 in k 1.941 * [backup-simplify]: Simplify 1/2 into 1/2 1.941 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1.941 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 1.941 * [taylor]: Taking taylor expansion of -2 in k 1.941 * [backup-simplify]: Simplify -2 into -2 1.941 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.941 * [taylor]: Taking taylor expansion of PI in k 1.941 * [backup-simplify]: Simplify PI into PI 1.941 * [taylor]: Taking taylor expansion of n in k 1.941 * [backup-simplify]: Simplify n into n 1.941 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.942 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1.942 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1.942 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.942 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.943 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1.943 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1.943 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1.943 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1.943 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1.943 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1.943 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.943 * [taylor]: Taking taylor expansion of 1/2 in n 1.943 * [backup-simplify]: Simplify 1/2 into 1/2 1.943 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.943 * [taylor]: Taking taylor expansion of k in n 1.943 * [backup-simplify]: Simplify k into k 1.943 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.943 * [taylor]: Taking taylor expansion of 1/2 in n 1.943 * [backup-simplify]: Simplify 1/2 into 1/2 1.943 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.943 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.943 * [taylor]: Taking taylor expansion of -2 in n 1.943 * [backup-simplify]: Simplify -2 into -2 1.943 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.943 * [taylor]: Taking taylor expansion of PI in n 1.943 * [backup-simplify]: Simplify PI into PI 1.943 * [taylor]: Taking taylor expansion of n in n 1.943 * [backup-simplify]: Simplify 0 into 0 1.943 * [backup-simplify]: Simplify 1 into 1 1.944 * [backup-simplify]: Simplify (/ PI 1) into PI 1.944 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 1.946 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1.946 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.946 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1.947 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1.948 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1.950 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1.950 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1.950 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1.950 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1.950 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1.950 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.950 * [taylor]: Taking taylor expansion of 1/2 in n 1.950 * [backup-simplify]: Simplify 1/2 into 1/2 1.950 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.950 * [taylor]: Taking taylor expansion of k in n 1.950 * [backup-simplify]: Simplify k into k 1.950 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.950 * [taylor]: Taking taylor expansion of 1/2 in n 1.950 * [backup-simplify]: Simplify 1/2 into 1/2 1.950 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.950 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.950 * [taylor]: Taking taylor expansion of -2 in n 1.950 * [backup-simplify]: Simplify -2 into -2 1.950 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.950 * [taylor]: Taking taylor expansion of PI in n 1.950 * [backup-simplify]: Simplify PI into PI 1.950 * [taylor]: Taking taylor expansion of n in n 1.950 * [backup-simplify]: Simplify 0 into 0 1.950 * [backup-simplify]: Simplify 1 into 1 1.951 * [backup-simplify]: Simplify (/ PI 1) into PI 1.951 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 1.952 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1.953 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.953 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1.954 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1.955 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1.956 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1.957 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1.957 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1.957 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1.957 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.957 * [taylor]: Taking taylor expansion of 1/2 in k 1.957 * [backup-simplify]: Simplify 1/2 into 1/2 1.957 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.957 * [taylor]: Taking taylor expansion of k in k 1.957 * [backup-simplify]: Simplify 0 into 0 1.957 * [backup-simplify]: Simplify 1 into 1 1.957 * [backup-simplify]: Simplify (/ 1 1) into 1 1.957 * [taylor]: Taking taylor expansion of 1/2 in k 1.957 * [backup-simplify]: Simplify 1/2 into 1/2 1.957 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1.957 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 1.957 * [taylor]: Taking taylor expansion of (* -2 PI) in k 1.957 * [taylor]: Taking taylor expansion of -2 in k 1.957 * [backup-simplify]: Simplify -2 into -2 1.957 * [taylor]: Taking taylor expansion of PI in k 1.957 * [backup-simplify]: Simplify PI into PI 1.958 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 1.959 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1.959 * [taylor]: Taking taylor expansion of (log n) in k 1.959 * [taylor]: Taking taylor expansion of n in k 1.959 * [backup-simplify]: Simplify n into n 1.959 * [backup-simplify]: Simplify (log n) into (log n) 1.960 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.960 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.960 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.962 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1.963 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1.964 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1.965 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1.966 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.967 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 1.969 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1.969 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.969 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1.970 * [backup-simplify]: Simplify (+ 0 0) into 0 1.971 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1.973 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1.974 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1.975 * [taylor]: Taking taylor expansion of 0 in k 1.975 * [backup-simplify]: Simplify 0 into 0 1.975 * [backup-simplify]: Simplify 0 into 0 1.975 * [backup-simplify]: Simplify 0 into 0 1.976 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.977 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1.980 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1.981 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.981 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1.982 * [backup-simplify]: Simplify (+ 0 0) into 0 1.983 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1.985 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1.988 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.988 * [taylor]: Taking taylor expansion of 0 in k 1.988 * [backup-simplify]: Simplify 0 into 0 1.988 * [backup-simplify]: Simplify 0 into 0 1.988 * [backup-simplify]: Simplify 0 into 0 1.988 * [backup-simplify]: Simplify 0 into 0 1.989 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.990 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.996 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1.996 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.998 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1.998 * [backup-simplify]: Simplify (+ 0 0) into 0 2.000 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.002 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 2.004 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.004 * [taylor]: Taking taylor expansion of 0 in k 2.004 * [backup-simplify]: Simplify 0 into 0 2.004 * [backup-simplify]: Simplify 0 into 0 2.005 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 2.005 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 2.005 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 2.005 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 2.006 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.006 * [taylor]: Taking taylor expansion of 2 in n 2.006 * [backup-simplify]: Simplify 2 into 2 2.006 * [taylor]: Taking taylor expansion of (* n PI) in n 2.006 * [taylor]: Taking taylor expansion of n in n 2.006 * [backup-simplify]: Simplify 0 into 0 2.006 * [backup-simplify]: Simplify 1 into 1 2.006 * [taylor]: Taking taylor expansion of PI in n 2.006 * [backup-simplify]: Simplify PI into PI 2.006 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.006 * [taylor]: Taking taylor expansion of 2 in n 2.006 * [backup-simplify]: Simplify 2 into 2 2.006 * [taylor]: Taking taylor expansion of (* n PI) in n 2.006 * [taylor]: Taking taylor expansion of n in n 2.006 * [backup-simplify]: Simplify 0 into 0 2.006 * [backup-simplify]: Simplify 1 into 1 2.006 * [taylor]: Taking taylor expansion of PI in n 2.006 * [backup-simplify]: Simplify PI into PI 2.006 * [backup-simplify]: Simplify (* 0 PI) into 0 2.006 * [backup-simplify]: Simplify (* 2 0) into 0 2.006 * [backup-simplify]: Simplify 0 into 0 2.007 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.008 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.009 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.009 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.010 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.010 * [backup-simplify]: Simplify 0 into 0 2.011 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.011 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.011 * [backup-simplify]: Simplify 0 into 0 2.012 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.013 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.013 * [backup-simplify]: Simplify 0 into 0 2.014 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.015 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.015 * [backup-simplify]: Simplify 0 into 0 2.016 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.016 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.017 * [backup-simplify]: Simplify 0 into 0 2.018 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.019 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.019 * [backup-simplify]: Simplify 0 into 0 2.019 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 2.019 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 2.020 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 2.020 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.020 * [taylor]: Taking taylor expansion of 2 in n 2.020 * [backup-simplify]: Simplify 2 into 2 2.020 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.020 * [taylor]: Taking taylor expansion of PI in n 2.020 * [backup-simplify]: Simplify PI into PI 2.020 * [taylor]: Taking taylor expansion of n in n 2.020 * [backup-simplify]: Simplify 0 into 0 2.020 * [backup-simplify]: Simplify 1 into 1 2.020 * [backup-simplify]: Simplify (/ PI 1) into PI 2.020 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.020 * [taylor]: Taking taylor expansion of 2 in n 2.020 * [backup-simplify]: Simplify 2 into 2 2.020 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.020 * [taylor]: Taking taylor expansion of PI in n 2.020 * [backup-simplify]: Simplify PI into PI 2.020 * [taylor]: Taking taylor expansion of n in n 2.020 * [backup-simplify]: Simplify 0 into 0 2.020 * [backup-simplify]: Simplify 1 into 1 2.020 * [backup-simplify]: Simplify (/ PI 1) into PI 2.021 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.021 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.022 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.022 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.022 * [backup-simplify]: Simplify 0 into 0 2.023 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.023 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.023 * [backup-simplify]: Simplify 0 into 0 2.024 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.025 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.025 * [backup-simplify]: Simplify 0 into 0 2.025 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.026 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.026 * [backup-simplify]: Simplify 0 into 0 2.027 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.028 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.028 * [backup-simplify]: Simplify 0 into 0 2.028 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.029 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.029 * [backup-simplify]: Simplify 0 into 0 2.030 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 2.030 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 2.030 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 2.030 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.030 * [taylor]: Taking taylor expansion of -2 in n 2.030 * [backup-simplify]: Simplify -2 into -2 2.030 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.030 * [taylor]: Taking taylor expansion of PI in n 2.030 * [backup-simplify]: Simplify PI into PI 2.030 * [taylor]: Taking taylor expansion of n in n 2.030 * [backup-simplify]: Simplify 0 into 0 2.030 * [backup-simplify]: Simplify 1 into 1 2.031 * [backup-simplify]: Simplify (/ PI 1) into PI 2.031 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.031 * [taylor]: Taking taylor expansion of -2 in n 2.031 * [backup-simplify]: Simplify -2 into -2 2.031 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.031 * [taylor]: Taking taylor expansion of PI in n 2.031 * [backup-simplify]: Simplify PI into PI 2.031 * [taylor]: Taking taylor expansion of n in n 2.031 * [backup-simplify]: Simplify 0 into 0 2.031 * [backup-simplify]: Simplify 1 into 1 2.031 * [backup-simplify]: Simplify (/ PI 1) into PI 2.031 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.032 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.032 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.033 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.033 * [backup-simplify]: Simplify 0 into 0 2.033 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.034 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.034 * [backup-simplify]: Simplify 0 into 0 2.035 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.035 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.035 * [backup-simplify]: Simplify 0 into 0 2.036 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.037 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.037 * [backup-simplify]: Simplify 0 into 0 2.038 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.038 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.038 * [backup-simplify]: Simplify 0 into 0 2.039 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.041 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.041 * [backup-simplify]: Simplify 0 into 0 2.041 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 2.042 * * * * [progress]: [ 3 / 3 ] generating series at (2) 2.042 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 2.042 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 2.042 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 2.042 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.042 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.042 * [taylor]: Taking taylor expansion of k in k 2.042 * [backup-simplify]: Simplify 0 into 0 2.042 * [backup-simplify]: Simplify 1 into 1 2.043 * [backup-simplify]: Simplify (/ 1 1) into 1 2.043 * [backup-simplify]: Simplify (sqrt 0) into 0 2.045 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.045 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.045 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.045 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.045 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.045 * [taylor]: Taking taylor expansion of 1/2 in k 2.045 * [backup-simplify]: Simplify 1/2 into 1/2 2.045 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.045 * [taylor]: Taking taylor expansion of 1/2 in k 2.045 * [backup-simplify]: Simplify 1/2 into 1/2 2.045 * [taylor]: Taking taylor expansion of k in k 2.045 * [backup-simplify]: Simplify 0 into 0 2.045 * [backup-simplify]: Simplify 1 into 1 2.045 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.045 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.045 * [taylor]: Taking taylor expansion of 2 in k 2.046 * [backup-simplify]: Simplify 2 into 2 2.046 * [taylor]: Taking taylor expansion of (* n PI) in k 2.046 * [taylor]: Taking taylor expansion of n in k 2.046 * [backup-simplify]: Simplify n into n 2.046 * [taylor]: Taking taylor expansion of PI in k 2.046 * [backup-simplify]: Simplify PI into PI 2.046 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.046 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.046 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.046 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.047 * [backup-simplify]: Simplify (- 0) into 0 2.047 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.047 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.047 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.047 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.047 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.047 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.047 * [taylor]: Taking taylor expansion of k in n 2.047 * [backup-simplify]: Simplify k into k 2.047 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.048 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.048 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.048 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.048 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.048 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.048 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.048 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.048 * [taylor]: Taking taylor expansion of 1/2 in n 2.048 * [backup-simplify]: Simplify 1/2 into 1/2 2.048 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.048 * [taylor]: Taking taylor expansion of 1/2 in n 2.048 * [backup-simplify]: Simplify 1/2 into 1/2 2.048 * [taylor]: Taking taylor expansion of k in n 2.048 * [backup-simplify]: Simplify k into k 2.048 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.048 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.048 * [taylor]: Taking taylor expansion of 2 in n 2.048 * [backup-simplify]: Simplify 2 into 2 2.048 * [taylor]: Taking taylor expansion of (* n PI) in n 2.048 * [taylor]: Taking taylor expansion of n in n 2.048 * [backup-simplify]: Simplify 0 into 0 2.048 * [backup-simplify]: Simplify 1 into 1 2.048 * [taylor]: Taking taylor expansion of PI in n 2.048 * [backup-simplify]: Simplify PI into PI 2.049 * [backup-simplify]: Simplify (* 0 PI) into 0 2.049 * [backup-simplify]: Simplify (* 2 0) into 0 2.051 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.056 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.057 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.057 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.057 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.057 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.058 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.060 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.061 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 2.061 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.061 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.061 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.061 * [taylor]: Taking taylor expansion of k in n 2.061 * [backup-simplify]: Simplify k into k 2.061 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.061 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.061 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.061 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.061 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.061 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.061 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.061 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.061 * [taylor]: Taking taylor expansion of 1/2 in n 2.061 * [backup-simplify]: Simplify 1/2 into 1/2 2.062 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.062 * [taylor]: Taking taylor expansion of 1/2 in n 2.062 * [backup-simplify]: Simplify 1/2 into 1/2 2.062 * [taylor]: Taking taylor expansion of k in n 2.062 * [backup-simplify]: Simplify k into k 2.062 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.062 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.062 * [taylor]: Taking taylor expansion of 2 in n 2.062 * [backup-simplify]: Simplify 2 into 2 2.062 * [taylor]: Taking taylor expansion of (* n PI) in n 2.062 * [taylor]: Taking taylor expansion of n in n 2.062 * [backup-simplify]: Simplify 0 into 0 2.062 * [backup-simplify]: Simplify 1 into 1 2.062 * [taylor]: Taking taylor expansion of PI in n 2.062 * [backup-simplify]: Simplify PI into PI 2.062 * [backup-simplify]: Simplify (* 0 PI) into 0 2.063 * [backup-simplify]: Simplify (* 2 0) into 0 2.064 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.066 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.067 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.067 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.067 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.067 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.068 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.070 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.071 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 2.072 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) 2.072 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 2.072 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.072 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.072 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.072 * [taylor]: Taking taylor expansion of 1/2 in k 2.072 * [backup-simplify]: Simplify 1/2 into 1/2 2.072 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.072 * [taylor]: Taking taylor expansion of 1/2 in k 2.072 * [backup-simplify]: Simplify 1/2 into 1/2 2.072 * [taylor]: Taking taylor expansion of k in k 2.072 * [backup-simplify]: Simplify 0 into 0 2.072 * [backup-simplify]: Simplify 1 into 1 2.072 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.072 * [taylor]: Taking taylor expansion of (log n) in k 2.073 * [taylor]: Taking taylor expansion of n in k 2.073 * [backup-simplify]: Simplify n into n 2.073 * [backup-simplify]: Simplify (log n) into (log n) 2.073 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.073 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.073 * [taylor]: Taking taylor expansion of 2 in k 2.073 * [backup-simplify]: Simplify 2 into 2 2.073 * [taylor]: Taking taylor expansion of PI in k 2.073 * [backup-simplify]: Simplify PI into PI 2.073 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.074 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.075 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.075 * [backup-simplify]: Simplify (- 0) into 0 2.075 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.077 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.078 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.079 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.079 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.079 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.079 * [taylor]: Taking taylor expansion of k in k 2.079 * [backup-simplify]: Simplify 0 into 0 2.079 * [backup-simplify]: Simplify 1 into 1 2.079 * [backup-simplify]: Simplify (/ 1 1) into 1 2.079 * [backup-simplify]: Simplify (sqrt 0) into 0 2.081 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.082 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 2.082 * [backup-simplify]: Simplify 0 into 0 2.083 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.084 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.085 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.085 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.085 * [backup-simplify]: Simplify (- 0) into 0 2.086 * [backup-simplify]: Simplify (+ 0 0) into 0 2.087 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.087 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.088 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.089 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 2.089 * [taylor]: Taking taylor expansion of 0 in k 2.089 * [backup-simplify]: Simplify 0 into 0 2.090 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.090 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.091 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.091 * [backup-simplify]: Simplify (+ 0 0) into 0 2.092 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.092 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.092 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.093 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.095 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.098 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.099 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.099 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.100 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.102 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 2.102 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.103 * [backup-simplify]: Simplify (- 0) into 0 2.103 * [backup-simplify]: Simplify (+ 0 0) into 0 2.104 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.105 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.106 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.106 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.107 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 2.108 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 2.108 * [taylor]: Taking taylor expansion of 0 in k 2.108 * [backup-simplify]: Simplify 0 into 0 2.108 * [backup-simplify]: Simplify 0 into 0 2.108 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.110 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.111 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.112 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.114 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 2.114 * [backup-simplify]: Simplify (+ 0 0) into 0 2.114 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.115 * [backup-simplify]: Simplify (- 0) into 0 2.115 * [backup-simplify]: Simplify (+ 0 0) into 0 2.116 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.120 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 2.130 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 2.135 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 2.137 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.138 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.144 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.145 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 2.146 * [backup-simplify]: Simplify (- 0) into 0 2.146 * [backup-simplify]: Simplify (+ 0 0) into 0 2.148 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.150 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.153 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.153 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.154 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 2.156 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 2.156 * [taylor]: Taking taylor expansion of 0 in k 2.156 * [backup-simplify]: Simplify 0 into 0 2.156 * [backup-simplify]: Simplify 0 into 0 2.156 * [backup-simplify]: Simplify 0 into 0 2.157 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.161 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.164 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 2.165 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.171 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.172 * [backup-simplify]: Simplify (+ 0 0) into 0 2.175 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 2.176 * [backup-simplify]: Simplify (- 0) into 0 2.176 * [backup-simplify]: Simplify (+ 0 0) into 0 2.178 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.182 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.193 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 2.204 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 2.224 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 2.225 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 2.225 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 2.225 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 2.225 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.225 * [taylor]: Taking taylor expansion of k in k 2.226 * [backup-simplify]: Simplify 0 into 0 2.226 * [backup-simplify]: Simplify 1 into 1 2.226 * [backup-simplify]: Simplify (sqrt 0) into 0 2.227 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.227 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.227 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.228 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.228 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.228 * [taylor]: Taking taylor expansion of 1/2 in k 2.228 * [backup-simplify]: Simplify 1/2 into 1/2 2.228 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.228 * [taylor]: Taking taylor expansion of 1/2 in k 2.228 * [backup-simplify]: Simplify 1/2 into 1/2 2.228 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.228 * [taylor]: Taking taylor expansion of k in k 2.228 * [backup-simplify]: Simplify 0 into 0 2.228 * [backup-simplify]: Simplify 1 into 1 2.228 * [backup-simplify]: Simplify (/ 1 1) into 1 2.228 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.228 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.228 * [taylor]: Taking taylor expansion of 2 in k 2.228 * [backup-simplify]: Simplify 2 into 2 2.228 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.228 * [taylor]: Taking taylor expansion of PI in k 2.228 * [backup-simplify]: Simplify PI into PI 2.228 * [taylor]: Taking taylor expansion of n in k 2.228 * [backup-simplify]: Simplify n into n 2.228 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.229 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.229 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.229 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.230 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.230 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.230 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.230 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 2.230 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.230 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.230 * [taylor]: Taking taylor expansion of k in n 2.230 * [backup-simplify]: Simplify k into k 2.230 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.230 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.231 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.231 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.231 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.231 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.231 * [taylor]: Taking taylor expansion of 1/2 in n 2.231 * [backup-simplify]: Simplify 1/2 into 1/2 2.231 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.231 * [taylor]: Taking taylor expansion of 1/2 in n 2.231 * [backup-simplify]: Simplify 1/2 into 1/2 2.231 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.231 * [taylor]: Taking taylor expansion of k in n 2.231 * [backup-simplify]: Simplify k into k 2.231 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.231 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.231 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.231 * [taylor]: Taking taylor expansion of 2 in n 2.231 * [backup-simplify]: Simplify 2 into 2 2.231 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.231 * [taylor]: Taking taylor expansion of PI in n 2.231 * [backup-simplify]: Simplify PI into PI 2.231 * [taylor]: Taking taylor expansion of n in n 2.231 * [backup-simplify]: Simplify 0 into 0 2.231 * [backup-simplify]: Simplify 1 into 1 2.232 * [backup-simplify]: Simplify (/ PI 1) into PI 2.232 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.233 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.233 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.233 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.233 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.235 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.236 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.237 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.237 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.237 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.237 * [taylor]: Taking taylor expansion of k in n 2.237 * [backup-simplify]: Simplify k into k 2.237 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.237 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.237 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.237 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.238 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.238 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.238 * [taylor]: Taking taylor expansion of 1/2 in n 2.238 * [backup-simplify]: Simplify 1/2 into 1/2 2.238 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.238 * [taylor]: Taking taylor expansion of 1/2 in n 2.238 * [backup-simplify]: Simplify 1/2 into 1/2 2.238 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.238 * [taylor]: Taking taylor expansion of k in n 2.238 * [backup-simplify]: Simplify k into k 2.238 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.238 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.238 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.238 * [taylor]: Taking taylor expansion of 2 in n 2.238 * [backup-simplify]: Simplify 2 into 2 2.238 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.238 * [taylor]: Taking taylor expansion of PI in n 2.238 * [backup-simplify]: Simplify PI into PI 2.238 * [taylor]: Taking taylor expansion of n in n 2.238 * [backup-simplify]: Simplify 0 into 0 2.238 * [backup-simplify]: Simplify 1 into 1 2.239 * [backup-simplify]: Simplify (/ PI 1) into PI 2.239 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.240 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.240 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.240 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.240 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.242 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.243 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.244 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.246 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 2.246 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 2.246 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.246 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.246 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.246 * [taylor]: Taking taylor expansion of 1/2 in k 2.246 * [backup-simplify]: Simplify 1/2 into 1/2 2.246 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.246 * [taylor]: Taking taylor expansion of 1/2 in k 2.246 * [backup-simplify]: Simplify 1/2 into 1/2 2.246 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.246 * [taylor]: Taking taylor expansion of k in k 2.246 * [backup-simplify]: Simplify 0 into 0 2.246 * [backup-simplify]: Simplify 1 into 1 2.246 * [backup-simplify]: Simplify (/ 1 1) into 1 2.246 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.246 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.246 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.246 * [taylor]: Taking taylor expansion of 2 in k 2.246 * [backup-simplify]: Simplify 2 into 2 2.246 * [taylor]: Taking taylor expansion of PI in k 2.247 * [backup-simplify]: Simplify PI into PI 2.247 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.248 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.248 * [taylor]: Taking taylor expansion of (log n) in k 2.248 * [taylor]: Taking taylor expansion of n in k 2.248 * [backup-simplify]: Simplify n into n 2.248 * [backup-simplify]: Simplify (log n) into (log n) 2.249 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.249 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.249 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.249 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.250 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.252 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.253 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.253 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.253 * [taylor]: Taking taylor expansion of k in k 2.253 * [backup-simplify]: Simplify 0 into 0 2.253 * [backup-simplify]: Simplify 1 into 1 2.253 * [backup-simplify]: Simplify (sqrt 0) into 0 2.255 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.256 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 2.256 * [backup-simplify]: Simplify 0 into 0 2.257 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.257 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.259 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.259 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.260 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.260 * [backup-simplify]: Simplify (- 0) into 0 2.261 * [backup-simplify]: Simplify (+ 0 0) into 0 2.262 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.263 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.265 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.266 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 2.266 * [taylor]: Taking taylor expansion of 0 in k 2.266 * [backup-simplify]: Simplify 0 into 0 2.266 * [backup-simplify]: Simplify 0 into 0 2.268 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.269 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.271 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.272 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.275 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 2.275 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.276 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.277 * [backup-simplify]: Simplify (- 0) into 0 2.277 * [backup-simplify]: Simplify (+ 0 0) into 0 2.279 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.281 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.283 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.284 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 2.286 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 2.286 * [taylor]: Taking taylor expansion of 0 in k 2.286 * [backup-simplify]: Simplify 0 into 0 2.286 * [backup-simplify]: Simplify 0 into 0 2.286 * [backup-simplify]: Simplify 0 into 0 2.289 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.291 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.292 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.294 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.295 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.300 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.301 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.302 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.305 * [backup-simplify]: Simplify (- 0) into 0 2.306 * [backup-simplify]: Simplify (+ 0 0) into 0 2.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.309 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.312 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.313 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 2.314 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 2.315 * [taylor]: Taking taylor expansion of 0 in k 2.315 * [backup-simplify]: Simplify 0 into 0 2.315 * [backup-simplify]: Simplify 0 into 0 2.315 * [backup-simplify]: Simplify 0 into 0 2.315 * [backup-simplify]: Simplify 0 into 0 2.318 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.320 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.321 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.323 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 2.324 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 2.324 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 2.324 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 2.324 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.324 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.324 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.324 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.324 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.324 * [taylor]: Taking taylor expansion of 1/2 in k 2.324 * [backup-simplify]: Simplify 1/2 into 1/2 2.324 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.324 * [taylor]: Taking taylor expansion of k in k 2.324 * [backup-simplify]: Simplify 0 into 0 2.324 * [backup-simplify]: Simplify 1 into 1 2.324 * [backup-simplify]: Simplify (/ 1 1) into 1 2.324 * [taylor]: Taking taylor expansion of 1/2 in k 2.324 * [backup-simplify]: Simplify 1/2 into 1/2 2.324 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.324 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.324 * [taylor]: Taking taylor expansion of -2 in k 2.324 * [backup-simplify]: Simplify -2 into -2 2.324 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.324 * [taylor]: Taking taylor expansion of PI in k 2.324 * [backup-simplify]: Simplify PI into PI 2.324 * [taylor]: Taking taylor expansion of n in k 2.324 * [backup-simplify]: Simplify n into n 2.325 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.325 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.325 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.325 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.325 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.325 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.325 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 2.325 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.325 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.325 * [taylor]: Taking taylor expansion of -1 in k 2.325 * [backup-simplify]: Simplify -1 into -1 2.325 * [taylor]: Taking taylor expansion of k in k 2.325 * [backup-simplify]: Simplify 0 into 0 2.325 * [backup-simplify]: Simplify 1 into 1 2.326 * [backup-simplify]: Simplify (/ -1 1) into -1 2.326 * [backup-simplify]: Simplify (sqrt 0) into 0 2.327 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.327 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 2.327 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.327 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.327 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.327 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.327 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.327 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.327 * [taylor]: Taking taylor expansion of 1/2 in n 2.327 * [backup-simplify]: Simplify 1/2 into 1/2 2.327 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.327 * [taylor]: Taking taylor expansion of k in n 2.327 * [backup-simplify]: Simplify k into k 2.327 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.327 * [taylor]: Taking taylor expansion of 1/2 in n 2.327 * [backup-simplify]: Simplify 1/2 into 1/2 2.327 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.327 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.327 * [taylor]: Taking taylor expansion of -2 in n 2.327 * [backup-simplify]: Simplify -2 into -2 2.327 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.327 * [taylor]: Taking taylor expansion of PI in n 2.327 * [backup-simplify]: Simplify PI into PI 2.327 * [taylor]: Taking taylor expansion of n in n 2.327 * [backup-simplify]: Simplify 0 into 0 2.327 * [backup-simplify]: Simplify 1 into 1 2.328 * [backup-simplify]: Simplify (/ PI 1) into PI 2.328 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.329 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.329 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.329 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.330 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.330 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.331 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.331 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.331 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.331 * [taylor]: Taking taylor expansion of -1 in n 2.331 * [backup-simplify]: Simplify -1 into -1 2.331 * [taylor]: Taking taylor expansion of k in n 2.331 * [backup-simplify]: Simplify k into k 2.331 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.331 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.331 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.331 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.332 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 2.332 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.332 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.332 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.332 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.332 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.332 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.332 * [taylor]: Taking taylor expansion of 1/2 in n 2.332 * [backup-simplify]: Simplify 1/2 into 1/2 2.332 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.332 * [taylor]: Taking taylor expansion of k in n 2.332 * [backup-simplify]: Simplify k into k 2.332 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.332 * [taylor]: Taking taylor expansion of 1/2 in n 2.332 * [backup-simplify]: Simplify 1/2 into 1/2 2.332 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.332 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.332 * [taylor]: Taking taylor expansion of -2 in n 2.332 * [backup-simplify]: Simplify -2 into -2 2.332 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.332 * [taylor]: Taking taylor expansion of PI in n 2.332 * [backup-simplify]: Simplify PI into PI 2.332 * [taylor]: Taking taylor expansion of n in n 2.332 * [backup-simplify]: Simplify 0 into 0 2.332 * [backup-simplify]: Simplify 1 into 1 2.333 * [backup-simplify]: Simplify (/ PI 1) into PI 2.333 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.334 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.334 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.334 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.335 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.336 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.336 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.336 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.336 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.336 * [taylor]: Taking taylor expansion of -1 in n 2.336 * [backup-simplify]: Simplify -1 into -1 2.336 * [taylor]: Taking taylor expansion of k in n 2.336 * [backup-simplify]: Simplify k into k 2.336 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.336 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.337 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.337 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.337 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 2.337 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 2.337 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.337 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.338 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.338 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.338 * [taylor]: Taking taylor expansion of 1/2 in k 2.338 * [backup-simplify]: Simplify 1/2 into 1/2 2.338 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.338 * [taylor]: Taking taylor expansion of k in k 2.338 * [backup-simplify]: Simplify 0 into 0 2.338 * [backup-simplify]: Simplify 1 into 1 2.338 * [backup-simplify]: Simplify (/ 1 1) into 1 2.338 * [taylor]: Taking taylor expansion of 1/2 in k 2.338 * [backup-simplify]: Simplify 1/2 into 1/2 2.338 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.338 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.338 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.338 * [taylor]: Taking taylor expansion of -2 in k 2.338 * [backup-simplify]: Simplify -2 into -2 2.338 * [taylor]: Taking taylor expansion of PI in k 2.338 * [backup-simplify]: Simplify PI into PI 2.338 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.339 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.339 * [taylor]: Taking taylor expansion of (log n) in k 2.339 * [taylor]: Taking taylor expansion of n in k 2.339 * [backup-simplify]: Simplify n into n 2.339 * [backup-simplify]: Simplify (log n) into (log n) 2.340 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.340 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.340 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.341 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.341 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.342 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.342 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.342 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.342 * [taylor]: Taking taylor expansion of -1 in k 2.342 * [backup-simplify]: Simplify -1 into -1 2.342 * [taylor]: Taking taylor expansion of k in k 2.342 * [backup-simplify]: Simplify 0 into 0 2.342 * [backup-simplify]: Simplify 1 into 1 2.342 * [backup-simplify]: Simplify (/ -1 1) into -1 2.343 * [backup-simplify]: Simplify (sqrt 0) into 0 2.343 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.344 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2.345 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2.345 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.346 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.347 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.347 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.347 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.348 * [backup-simplify]: Simplify (+ 0 0) into 0 2.349 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.349 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.351 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.351 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 2.351 * [taylor]: Taking taylor expansion of 0 in k 2.351 * [backup-simplify]: Simplify 0 into 0 2.351 * [backup-simplify]: Simplify 0 into 0 2.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.354 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.355 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.356 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.358 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.361 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 2.362 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.362 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.363 * [backup-simplify]: Simplify (+ 0 0) into 0 2.364 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.366 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.368 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.369 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.370 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 2.372 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 2.372 * [taylor]: Taking taylor expansion of 0 in k 2.372 * [backup-simplify]: Simplify 0 into 0 2.372 * [backup-simplify]: Simplify 0 into 0 2.372 * [backup-simplify]: Simplify 0 into 0 2.373 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.377 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.381 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.382 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.386 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 2.386 * * * [progress]: simplifying candidates 2.387 * * * * [progress]: [ 1 / 445 ] simplifiying candidate # 2.387 * * * * [progress]: [ 2 / 445 ] simplifiying candidate # 2.387 * * * * [progress]: [ 3 / 445 ] simplifiying candidate # 2.387 * * * * [progress]: [ 4 / 445 ] simplifiying candidate # 2.387 * * * * [progress]: [ 5 / 445 ] simplifiying candidate # 2.387 * * * * [progress]: [ 6 / 445 ] simplifiying candidate # 2.387 * * * * [progress]: [ 7 / 445 ] simplifiying candidate # 2.387 * * * * [progress]: [ 8 / 445 ] simplifiying candidate # 2.387 * * * * [progress]: [ 9 / 445 ] simplifiying candidate # 2.387 * * * * [progress]: [ 10 / 445 ] simplifiying candidate # 2.387 * 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candidate # 2.391 * * * * [progress]: [ 58 / 445 ] simplifiying candidate # 2.391 * * * * [progress]: [ 59 / 445 ] simplifiying candidate # 2.392 * * * * [progress]: [ 60 / 445 ] simplifiying candidate # 2.392 * * * * [progress]: [ 61 / 445 ] simplifiying candidate # 2.392 * * * * [progress]: [ 62 / 445 ] simplifiying candidate # 2.392 * * * * [progress]: [ 63 / 445 ] simplifiying candidate # 2.392 * * * * [progress]: [ 64 / 445 ] simplifiying candidate # 2.392 * * * * [progress]: [ 65 / 445 ] simplifiying candidate # 2.392 * * * * [progress]: [ 66 / 445 ] simplifiying candidate # 2.392 * * * * [progress]: [ 67 / 445 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))> 2.392 * * * * [progress]: [ 68 / 445 ] simplifiying candidate # 2.392 * * * * [progress]: [ 69 / 445 ] simplifiying candidate # 2.392 * * * * [progress]: [ 70 / 445 ] simplifiying candidate # 2.392 * * * * [progress]: [ 71 / 445 ] simplifiying candidate # 2.392 * * * * 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candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))> 2.393 * * * * [progress]: [ 88 / 445 ] simplifiying candidate # 2.393 * * * * [progress]: [ 89 / 445 ] simplifiying candidate # 2.393 * * * * [progress]: [ 90 / 445 ] simplifiying candidate # 2.393 * * * * [progress]: [ 91 / 445 ] simplifiying candidate # 2.394 * * * * [progress]: [ 92 / 445 ] simplifiying candidate # 2.394 * * * * [progress]: [ 93 / 445 ] simplifiying candidate # 2.394 * * * * [progress]: [ 94 / 445 ] simplifiying candidate # 2.394 * * * * [progress]: [ 95 / 445 ] simplifiying candidate # 2.394 * * * * [progress]: [ 96 / 445 ] simplifiying candidate # 2.394 * * * * [progress]: [ 97 / 445 ] simplifiying candidate # 2.394 * * * * [progress]: [ 98 / 445 ] simplifiying candidate # 2.394 * * * * [progress]: [ 99 / 445 ] simplifiying candidate # 2.394 * * * * [progress]: [ 100 / 445 ] simplifiying candidate # 2.394 * * * * [progress]: [ 101 / 445 ] simplifiying candidate # 2.394 * * * * [progress]: 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(sqrt (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt 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(* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 2.453 * * [simplify]: iteration 0: 695 enodes 2.731 * * [simplify]: iteration 1: 1526 enodes 3.224 * * [simplify]: iteration complete: 2001 enodes 3.225 * * [simplify]: Extracting #0: cost 233 inf + 0 3.227 * * [simplify]: Extracting #1: cost 515 inf + 1 3.231 * * [simplify]: Extracting #2: cost 739 inf + 1881 3.238 * * [simplify]: Extracting #3: cost 804 inf + 11914 3.260 * * [simplify]: Extracting #4: cost 562 inf + 88070 3.300 * * [simplify]: Extracting #5: cost 346 inf + 180910 3.351 * * [simplify]: Extracting #6: cost 193 inf + 273665 3.411 * * [simplify]: Extracting #7: cost 60 inf + 356856 3.478 * * [simplify]: Extracting #8: cost 23 inf + 387667 3.543 * * [simplify]: Extracting #9: cost 23 inf + 390493 3.630 * * [simplify]: Extracting #10: cost 15 inf + 395110 3.711 * * [simplify]: Extracting #11: cost 10 inf + 400340 3.782 * * [simplify]: Extracting #12: cost 4 inf + 408621 3.899 * * [simplify]: Extracting #13: cost 0 inf + 415390 3.986 * * [simplify]: Extracting #14: cost 0 inf + 415265 4.072 * * [simplify]: Extracting #15: cost 0 inf + 415190 4.198 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (log1p (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (/ k 2)) (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2)))) (* (* PI 2) n) (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* (* 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k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k)) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (fabs (cbrt k))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k)) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1 (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1 (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)) (/ (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (fabs (cbrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))) (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))) (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))) (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (cbrt 2))) (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (sqrt 2)) (sqrt 2))) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma -1/2 k (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))) (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))) (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))) (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (cbrt 2))) (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (sqrt 2)) (sqrt 2))) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma -1/2 k (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))) (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))) (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))) (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (cbrt 2))) (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (sqrt 2)) (sqrt 2))) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma -1/2 k (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (/ (- k) 2))) (/ (sqrt k) (pow (* (* PI 2) n) (/ (- k) 2))) (/ (sqrt k) (pow (* PI 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2))) (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (real->posit16 (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))) (fma (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) (* (* k k) (log n))) 1/4 (- (fma (* (* (* (log n) (log n)) (* k k)) (exp (* 1/2 (log (* (* PI 2) n))))) 1/8 (fma 1/8 (* (* (* (log (* PI 2)) (log (* PI 2))) (exp (* 1/2 (log (* (* PI 2) n))))) (* k k)) (exp (* 1/2 (log (* (* PI 2) n)))))) (* 1/2 (fma (* k (log n)) (exp (* 1/2 (log (* (* PI 2) n)))) (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) k))))) (exp (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))) (exp (* (- 1/2 (/ k 2)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (- (- (* +nan.0 (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) (* (* k k) (log n)))) (fma (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) (* k k)) +nan.0 (- (fma (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (* (* (log n) (log n)) (* k k)) (- (fma (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) k (- (- (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (- (* +nan.0 (* (* (* (log (* PI 2)) (log (* PI 2))) (exp (* 1/2 (log (* (* PI 2) n))))) (* k k))) (- (* (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (* (* k k) (log n))) (- (* (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (* k k)) (- (* (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) k) +nan.0) (* +nan.0 (* (exp (* 1/2 (log (* (* PI 2) n)))) (* k (log n))))))))))))))))) (+ (- (* +nan.0 (/ (exp (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))) (* (* k k) k)))) (- (/ (* +nan.0 (exp (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))))) k) (* (/ (exp (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))) (* k k)) +nan.0))) (+ (- (/ (* (exp (* (- 1/2 (/ k 2)) (- (log (* -2 PI)) (log (/ -1 n))))) +nan.0) k)) (- (/ (* (exp (* (- 1/2 (/ k 2)) (- (log (* -2 PI)) (log (/ -1 n))))) +nan.0) (* k k)) (* (exp (* (- 1/2 (/ k 2)) (- (log (* -2 PI)) (log (/ -1 n))))) +nan.0))) 4.344 * * * [progress]: adding candidates to table 7.348 * * [progress]: iteration 2 / 4 7.348 * * * [progress]: picking best candidate 7.386 * * * * [pick]: Picked # 7.386 * * * [progress]: localizing error 7.426 * * * [progress]: generating rewritten candidates 7.426 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 7.459 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 7.485 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 7.510 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 7.660 * * * [progress]: generating series expansions 7.660 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 7.661 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 7.661 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 7.661 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 7.661 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 7.661 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 7.661 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 7.661 * [taylor]: Taking taylor expansion of 1/2 in k 7.661 * [backup-simplify]: Simplify 1/2 into 1/2 7.661 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 7.661 * [taylor]: Taking taylor expansion of 1/2 in k 7.661 * [backup-simplify]: Simplify 1/2 into 1/2 7.661 * [taylor]: Taking taylor expansion of k in k 7.661 * [backup-simplify]: Simplify 0 into 0 7.661 * [backup-simplify]: Simplify 1 into 1 7.661 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 7.661 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 7.661 * [taylor]: Taking taylor expansion of 2 in k 7.661 * [backup-simplify]: Simplify 2 into 2 7.661 * [taylor]: Taking taylor expansion of (* n PI) in k 7.661 * [taylor]: Taking taylor expansion of n in k 7.661 * [backup-simplify]: Simplify n into n 7.661 * [taylor]: Taking taylor expansion of PI in k 7.661 * [backup-simplify]: Simplify PI into PI 7.661 * [backup-simplify]: Simplify (* n PI) into (* n PI) 7.661 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 7.661 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 7.662 * [backup-simplify]: Simplify (* 1/2 0) into 0 7.662 * [backup-simplify]: Simplify (- 0) into 0 7.663 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 7.663 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 7.663 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 7.663 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 7.663 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 7.663 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 7.663 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 7.663 * [taylor]: Taking taylor expansion of 1/2 in n 7.663 * [backup-simplify]: Simplify 1/2 into 1/2 7.663 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 7.663 * [taylor]: Taking taylor expansion of 1/2 in n 7.663 * [backup-simplify]: Simplify 1/2 into 1/2 7.663 * [taylor]: Taking taylor expansion of k in n 7.663 * [backup-simplify]: Simplify k into k 7.663 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 7.663 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.663 * [taylor]: Taking taylor expansion of 2 in n 7.663 * [backup-simplify]: Simplify 2 into 2 7.663 * [taylor]: Taking taylor expansion of (* n PI) in n 7.663 * [taylor]: Taking taylor expansion of n in n 7.663 * [backup-simplify]: Simplify 0 into 0 7.663 * [backup-simplify]: Simplify 1 into 1 7.663 * [taylor]: Taking taylor expansion of PI in n 7.663 * [backup-simplify]: Simplify PI into PI 7.664 * [backup-simplify]: Simplify (* 0 PI) into 0 7.664 * [backup-simplify]: Simplify (* 2 0) into 0 7.666 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.667 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 7.668 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.668 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 7.668 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 7.668 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 7.669 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.670 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 7.671 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 7.671 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 7.671 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 7.672 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 7.672 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 7.672 * [taylor]: Taking taylor expansion of 1/2 in n 7.672 * [backup-simplify]: Simplify 1/2 into 1/2 7.672 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 7.672 * [taylor]: Taking taylor expansion of 1/2 in n 7.672 * [backup-simplify]: Simplify 1/2 into 1/2 7.672 * [taylor]: Taking taylor expansion of k in n 7.672 * [backup-simplify]: Simplify k into k 7.672 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 7.672 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.672 * [taylor]: Taking taylor expansion of 2 in n 7.672 * [backup-simplify]: Simplify 2 into 2 7.672 * [taylor]: Taking taylor expansion of (* n PI) in n 7.672 * [taylor]: Taking taylor expansion of n in n 7.672 * [backup-simplify]: Simplify 0 into 0 7.672 * [backup-simplify]: Simplify 1 into 1 7.672 * [taylor]: Taking taylor expansion of PI in n 7.672 * [backup-simplify]: Simplify PI into PI 7.672 * [backup-simplify]: Simplify (* 0 PI) into 0 7.673 * [backup-simplify]: Simplify (* 2 0) into 0 7.675 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.677 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 7.678 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.678 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 7.678 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 7.678 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 7.679 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.681 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 7.682 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 7.682 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 7.682 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 7.682 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 7.682 * [taylor]: Taking taylor expansion of 1/2 in k 7.682 * [backup-simplify]: Simplify 1/2 into 1/2 7.682 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 7.682 * [taylor]: Taking taylor expansion of 1/2 in k 7.682 * [backup-simplify]: Simplify 1/2 into 1/2 7.682 * [taylor]: Taking taylor expansion of k in k 7.682 * [backup-simplify]: Simplify 0 into 0 7.682 * [backup-simplify]: Simplify 1 into 1 7.682 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 7.682 * [taylor]: Taking taylor expansion of (log n) in k 7.682 * [taylor]: Taking taylor expansion of n in k 7.682 * [backup-simplify]: Simplify n into n 7.682 * [backup-simplify]: Simplify (log n) into (log n) 7.683 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 7.683 * [taylor]: Taking taylor expansion of (* 2 PI) in k 7.683 * [taylor]: Taking taylor expansion of 2 in k 7.683 * [backup-simplify]: Simplify 2 into 2 7.683 * [taylor]: Taking taylor expansion of PI in k 7.683 * [backup-simplify]: Simplify PI into PI 7.683 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.684 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.685 * [backup-simplify]: Simplify (* 1/2 0) into 0 7.685 * [backup-simplify]: Simplify (- 0) into 0 7.685 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 7.686 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.688 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 7.688 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 7.689 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 7.690 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 7.690 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 7.691 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 7.692 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 7.692 * [backup-simplify]: Simplify (- 0) into 0 7.692 * [backup-simplify]: Simplify (+ 0 0) into 0 7.693 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.694 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 7.695 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.695 * [taylor]: Taking taylor expansion of 0 in k 7.695 * [backup-simplify]: Simplify 0 into 0 7.695 * [backup-simplify]: Simplify 0 into 0 7.695 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 7.696 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 7.697 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 7.697 * [backup-simplify]: Simplify (+ 0 0) into 0 7.709 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 7.710 * [backup-simplify]: Simplify (- 1/2) into -1/2 7.710 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 7.711 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 7.713 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 7.715 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 7.716 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 7.716 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 7.718 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 7.719 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 7.719 * [backup-simplify]: Simplify (- 0) into 0 7.719 * [backup-simplify]: Simplify (+ 0 0) into 0 7.720 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.722 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 7.724 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 7.725 * [taylor]: Taking taylor expansion of 0 in k 7.725 * [backup-simplify]: Simplify 0 into 0 7.725 * [backup-simplify]: Simplify 0 into 0 7.725 * [backup-simplify]: Simplify 0 into 0 7.726 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 7.727 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 7.731 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 7.731 * [backup-simplify]: Simplify (+ 0 0) into 0 7.732 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 7.732 * [backup-simplify]: Simplify (- 0) into 0 7.733 * [backup-simplify]: Simplify (+ 0 0) into 0 7.735 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 7.739 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 7.744 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 7.752 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 7.752 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 7.752 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 7.752 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 7.752 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 7.752 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 7.752 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 7.752 * [taylor]: Taking taylor expansion of 1/2 in k 7.752 * [backup-simplify]: Simplify 1/2 into 1/2 7.752 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 7.752 * [taylor]: Taking taylor expansion of 1/2 in k 7.752 * [backup-simplify]: Simplify 1/2 into 1/2 7.752 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.752 * [taylor]: Taking taylor expansion of k in k 7.752 * [backup-simplify]: Simplify 0 into 0 7.752 * [backup-simplify]: Simplify 1 into 1 7.753 * [backup-simplify]: Simplify (/ 1 1) into 1 7.753 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 7.753 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 7.753 * [taylor]: Taking taylor expansion of 2 in k 7.753 * [backup-simplify]: Simplify 2 into 2 7.753 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.753 * [taylor]: Taking taylor expansion of PI in k 7.753 * [backup-simplify]: Simplify PI into PI 7.753 * [taylor]: Taking taylor expansion of n in k 7.753 * [backup-simplify]: Simplify n into n 7.753 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.753 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 7.753 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 7.753 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 7.753 * [backup-simplify]: Simplify (- 1/2) into -1/2 7.754 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 7.754 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 7.754 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 7.754 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 7.754 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 7.754 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 7.754 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 7.754 * [taylor]: Taking taylor expansion of 1/2 in n 7.754 * [backup-simplify]: Simplify 1/2 into 1/2 7.754 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 7.754 * [taylor]: Taking taylor expansion of 1/2 in n 7.754 * [backup-simplify]: Simplify 1/2 into 1/2 7.754 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.754 * [taylor]: Taking taylor expansion of k in n 7.754 * [backup-simplify]: Simplify k into k 7.754 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.754 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 7.754 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 7.754 * [taylor]: Taking taylor expansion of 2 in n 7.754 * [backup-simplify]: Simplify 2 into 2 7.754 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.754 * [taylor]: Taking taylor expansion of PI in n 7.754 * [backup-simplify]: Simplify PI into PI 7.754 * [taylor]: Taking taylor expansion of n in n 7.754 * [backup-simplify]: Simplify 0 into 0 7.754 * [backup-simplify]: Simplify 1 into 1 7.755 * [backup-simplify]: Simplify (/ PI 1) into PI 7.755 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.756 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.756 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 7.756 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 7.756 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 7.757 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 7.757 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 7.758 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 7.758 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 7.758 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 7.758 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 7.758 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 7.758 * [taylor]: Taking taylor expansion of 1/2 in n 7.758 * [backup-simplify]: Simplify 1/2 into 1/2 7.758 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 7.758 * [taylor]: Taking taylor expansion of 1/2 in n 7.758 * [backup-simplify]: Simplify 1/2 into 1/2 7.758 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.758 * [taylor]: Taking taylor expansion of k in n 7.758 * [backup-simplify]: Simplify k into k 7.758 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.758 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 7.758 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 7.758 * [taylor]: Taking taylor expansion of 2 in n 7.758 * [backup-simplify]: Simplify 2 into 2 7.758 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.758 * [taylor]: Taking taylor expansion of PI in n 7.758 * [backup-simplify]: Simplify PI into PI 7.758 * [taylor]: Taking taylor expansion of n in n 7.758 * [backup-simplify]: Simplify 0 into 0 7.758 * [backup-simplify]: Simplify 1 into 1 7.759 * [backup-simplify]: Simplify (/ PI 1) into PI 7.759 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.760 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.760 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 7.760 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 7.760 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 7.761 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 7.762 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 7.762 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 7.762 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 7.762 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 7.762 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 7.762 * [taylor]: Taking taylor expansion of 1/2 in k 7.762 * [backup-simplify]: Simplify 1/2 into 1/2 7.762 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 7.762 * [taylor]: Taking taylor expansion of 1/2 in k 7.762 * [backup-simplify]: Simplify 1/2 into 1/2 7.762 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.763 * [taylor]: Taking taylor expansion of k in k 7.763 * [backup-simplify]: Simplify 0 into 0 7.763 * [backup-simplify]: Simplify 1 into 1 7.763 * [backup-simplify]: Simplify (/ 1 1) into 1 7.763 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 7.763 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 7.763 * [taylor]: Taking taylor expansion of (* 2 PI) in k 7.763 * [taylor]: Taking taylor expansion of 2 in k 7.763 * [backup-simplify]: Simplify 2 into 2 7.763 * [taylor]: Taking taylor expansion of PI in k 7.763 * [backup-simplify]: Simplify PI into PI 7.763 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.764 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.764 * [taylor]: Taking taylor expansion of (log n) in k 7.764 * [taylor]: Taking taylor expansion of n in k 7.764 * [backup-simplify]: Simplify n into n 7.764 * [backup-simplify]: Simplify (log n) into (log n) 7.764 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 7.765 * [backup-simplify]: Simplify (- 1/2) into -1/2 7.765 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 7.765 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 7.766 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 7.766 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 7.767 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 7.768 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 7.768 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.769 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 7.770 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 7.770 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 7.770 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 7.770 * [backup-simplify]: Simplify (- 0) into 0 7.771 * [backup-simplify]: Simplify (+ 0 0) into 0 7.772 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 7.772 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 7.773 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 7.773 * [taylor]: Taking taylor expansion of 0 in k 7.773 * [backup-simplify]: Simplify 0 into 0 7.774 * [backup-simplify]: Simplify 0 into 0 7.774 * [backup-simplify]: Simplify 0 into 0 7.774 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.775 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 7.777 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 7.777 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.778 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 7.778 * [backup-simplify]: Simplify (- 0) into 0 7.778 * [backup-simplify]: Simplify (+ 0 0) into 0 7.779 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 7.780 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 7.783 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 7.783 * [taylor]: Taking taylor expansion of 0 in k 7.783 * [backup-simplify]: Simplify 0 into 0 7.783 * [backup-simplify]: Simplify 0 into 0 7.783 * [backup-simplify]: Simplify 0 into 0 7.783 * [backup-simplify]: Simplify 0 into 0 7.784 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.785 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.791 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 7.792 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.793 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 7.794 * [backup-simplify]: Simplify (- 0) into 0 7.794 * [backup-simplify]: Simplify (+ 0 0) into 0 7.796 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 7.798 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 7.801 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 7.801 * [taylor]: Taking taylor expansion of 0 in k 7.801 * [backup-simplify]: Simplify 0 into 0 7.801 * [backup-simplify]: Simplify 0 into 0 7.802 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 7.803 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 7.803 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 7.803 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 7.803 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 7.803 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 7.803 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 7.803 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 7.803 * [taylor]: Taking taylor expansion of 1/2 in k 7.803 * [backup-simplify]: Simplify 1/2 into 1/2 7.803 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.803 * [taylor]: Taking taylor expansion of k in k 7.803 * [backup-simplify]: Simplify 0 into 0 7.803 * [backup-simplify]: Simplify 1 into 1 7.804 * [backup-simplify]: Simplify (/ 1 1) into 1 7.804 * [taylor]: Taking taylor expansion of 1/2 in k 7.804 * [backup-simplify]: Simplify 1/2 into 1/2 7.804 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 7.804 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 7.804 * [taylor]: Taking taylor expansion of -2 in k 7.804 * [backup-simplify]: Simplify -2 into -2 7.804 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.804 * [taylor]: Taking taylor expansion of PI in k 7.804 * [backup-simplify]: Simplify PI into PI 7.804 * [taylor]: Taking taylor expansion of n in k 7.804 * [backup-simplify]: Simplify n into n 7.804 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.804 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 7.804 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 7.805 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 7.805 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 7.805 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 7.805 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 7.805 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 7.805 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 7.805 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 7.805 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 7.805 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 7.805 * [taylor]: Taking taylor expansion of 1/2 in n 7.806 * [backup-simplify]: Simplify 1/2 into 1/2 7.806 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.806 * [taylor]: Taking taylor expansion of k in n 7.806 * [backup-simplify]: Simplify k into k 7.806 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.806 * [taylor]: Taking taylor expansion of 1/2 in n 7.806 * [backup-simplify]: Simplify 1/2 into 1/2 7.806 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 7.806 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 7.806 * [taylor]: Taking taylor expansion of -2 in n 7.806 * [backup-simplify]: Simplify -2 into -2 7.806 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.806 * [taylor]: Taking taylor expansion of PI in n 7.806 * [backup-simplify]: Simplify PI into PI 7.806 * [taylor]: Taking taylor expansion of n in n 7.806 * [backup-simplify]: Simplify 0 into 0 7.806 * [backup-simplify]: Simplify 1 into 1 7.806 * [backup-simplify]: Simplify (/ PI 1) into PI 7.807 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 7.808 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 7.808 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 7.808 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 7.810 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 7.811 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 7.812 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 7.812 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 7.812 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 7.812 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 7.812 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 7.812 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 7.812 * [taylor]: Taking taylor expansion of 1/2 in n 7.812 * [backup-simplify]: Simplify 1/2 into 1/2 7.812 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.812 * [taylor]: Taking taylor expansion of k in n 7.812 * [backup-simplify]: Simplify k into k 7.812 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.812 * [taylor]: Taking taylor expansion of 1/2 in n 7.812 * [backup-simplify]: Simplify 1/2 into 1/2 7.812 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 7.812 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 7.812 * [taylor]: Taking taylor expansion of -2 in n 7.813 * [backup-simplify]: Simplify -2 into -2 7.813 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.813 * [taylor]: Taking taylor expansion of PI in n 7.813 * [backup-simplify]: Simplify PI into PI 7.813 * [taylor]: Taking taylor expansion of n in n 7.813 * [backup-simplify]: Simplify 0 into 0 7.813 * [backup-simplify]: Simplify 1 into 1 7.813 * [backup-simplify]: Simplify (/ PI 1) into PI 7.814 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 7.815 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 7.815 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 7.815 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 7.817 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 7.818 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 7.819 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 7.819 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 7.819 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 7.819 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 7.819 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 7.819 * [taylor]: Taking taylor expansion of 1/2 in k 7.820 * [backup-simplify]: Simplify 1/2 into 1/2 7.820 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.820 * [taylor]: Taking taylor expansion of k in k 7.820 * [backup-simplify]: Simplify 0 into 0 7.820 * [backup-simplify]: Simplify 1 into 1 7.820 * [backup-simplify]: Simplify (/ 1 1) into 1 7.820 * [taylor]: Taking taylor expansion of 1/2 in k 7.820 * [backup-simplify]: Simplify 1/2 into 1/2 7.820 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 7.820 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 7.820 * [taylor]: Taking taylor expansion of (* -2 PI) in k 7.820 * [taylor]: Taking taylor expansion of -2 in k 7.820 * [backup-simplify]: Simplify -2 into -2 7.820 * [taylor]: Taking taylor expansion of PI in k 7.820 * [backup-simplify]: Simplify PI into PI 7.821 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 7.822 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 7.822 * [taylor]: Taking taylor expansion of (log n) in k 7.822 * [taylor]: Taking taylor expansion of n in k 7.822 * [backup-simplify]: Simplify n into n 7.822 * [backup-simplify]: Simplify (log n) into (log n) 7.822 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 7.823 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 7.823 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 7.824 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 7.827 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 7.828 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 7.829 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 7.829 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.830 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 7.831 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 7.831 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 7.831 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 7.832 * [backup-simplify]: Simplify (+ 0 0) into 0 7.833 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 7.834 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 7.835 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 7.835 * [taylor]: Taking taylor expansion of 0 in k 7.835 * [backup-simplify]: Simplify 0 into 0 7.835 * [backup-simplify]: Simplify 0 into 0 7.835 * [backup-simplify]: Simplify 0 into 0 7.836 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.836 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 7.838 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 7.838 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.839 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 7.839 * [backup-simplify]: Simplify (+ 0 0) into 0 7.840 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 7.841 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 7.842 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 7.842 * [taylor]: Taking taylor expansion of 0 in k 7.842 * [backup-simplify]: Simplify 0 into 0 7.842 * [backup-simplify]: Simplify 0 into 0 7.843 * [backup-simplify]: Simplify 0 into 0 7.843 * [backup-simplify]: Simplify 0 into 0 7.843 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.844 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.847 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 7.847 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.848 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 7.848 * [backup-simplify]: Simplify (+ 0 0) into 0 7.849 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 7.850 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 7.852 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 7.852 * [taylor]: Taking taylor expansion of 0 in k 7.852 * [backup-simplify]: Simplify 0 into 0 7.852 * [backup-simplify]: Simplify 0 into 0 7.853 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 7.853 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 7.853 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 7.853 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 7.853 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.853 * [taylor]: Taking taylor expansion of 2 in n 7.853 * [backup-simplify]: Simplify 2 into 2 7.853 * [taylor]: Taking taylor expansion of (* n PI) in n 7.853 * [taylor]: Taking taylor expansion of n in n 7.853 * [backup-simplify]: Simplify 0 into 0 7.853 * [backup-simplify]: Simplify 1 into 1 7.853 * [taylor]: Taking taylor expansion of PI in n 7.853 * [backup-simplify]: Simplify PI into PI 7.853 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.854 * [taylor]: Taking taylor expansion of 2 in n 7.854 * [backup-simplify]: Simplify 2 into 2 7.854 * [taylor]: Taking taylor expansion of (* n PI) in n 7.854 * [taylor]: Taking taylor expansion of n in n 7.854 * [backup-simplify]: Simplify 0 into 0 7.854 * [backup-simplify]: Simplify 1 into 1 7.854 * [taylor]: Taking taylor expansion of PI in n 7.854 * [backup-simplify]: Simplify PI into PI 7.854 * [backup-simplify]: Simplify (* 0 PI) into 0 7.854 * [backup-simplify]: Simplify (* 2 0) into 0 7.854 * [backup-simplify]: Simplify 0 into 0 7.855 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.856 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 7.857 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.857 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 7.858 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 7.858 * [backup-simplify]: Simplify 0 into 0 7.858 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 7.859 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 7.859 * [backup-simplify]: Simplify 0 into 0 7.860 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 7.861 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 7.861 * [backup-simplify]: Simplify 0 into 0 7.862 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 7.863 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 7.863 * [backup-simplify]: Simplify 0 into 0 7.864 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 7.865 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 7.865 * [backup-simplify]: Simplify 0 into 0 7.867 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 7.870 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 7.870 * [backup-simplify]: Simplify 0 into 0 7.870 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 7.871 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 7.871 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 7.871 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 7.871 * [taylor]: Taking taylor expansion of 2 in n 7.871 * [backup-simplify]: Simplify 2 into 2 7.871 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.871 * [taylor]: Taking taylor expansion of PI in n 7.871 * [backup-simplify]: Simplify PI into PI 7.871 * [taylor]: Taking taylor expansion of n in n 7.871 * [backup-simplify]: Simplify 0 into 0 7.871 * [backup-simplify]: Simplify 1 into 1 7.872 * [backup-simplify]: Simplify (/ PI 1) into PI 7.872 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 7.872 * [taylor]: Taking taylor expansion of 2 in n 7.872 * [backup-simplify]: Simplify 2 into 2 7.872 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.872 * [taylor]: Taking taylor expansion of PI in n 7.872 * [backup-simplify]: Simplify PI into PI 7.872 * [taylor]: Taking taylor expansion of n in n 7.872 * [backup-simplify]: Simplify 0 into 0 7.872 * [backup-simplify]: Simplify 1 into 1 7.872 * [backup-simplify]: Simplify (/ PI 1) into PI 7.873 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.873 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.874 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.875 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 7.875 * [backup-simplify]: Simplify 0 into 0 7.876 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.877 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 7.877 * [backup-simplify]: Simplify 0 into 0 7.878 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.880 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.880 * [backup-simplify]: Simplify 0 into 0 7.881 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.882 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 7.882 * [backup-simplify]: Simplify 0 into 0 7.883 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.885 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 7.885 * [backup-simplify]: Simplify 0 into 0 7.886 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.888 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 7.888 * [backup-simplify]: Simplify 0 into 0 7.889 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 7.889 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 7.889 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 7.889 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 7.889 * [taylor]: Taking taylor expansion of -2 in n 7.889 * [backup-simplify]: Simplify -2 into -2 7.889 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.889 * [taylor]: Taking taylor expansion of PI in n 7.889 * [backup-simplify]: Simplify PI into PI 7.889 * [taylor]: Taking taylor expansion of n in n 7.889 * [backup-simplify]: Simplify 0 into 0 7.889 * [backup-simplify]: Simplify 1 into 1 7.890 * [backup-simplify]: Simplify (/ PI 1) into PI 7.890 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 7.890 * [taylor]: Taking taylor expansion of -2 in n 7.890 * [backup-simplify]: Simplify -2 into -2 7.890 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.890 * [taylor]: Taking taylor expansion of PI in n 7.890 * [backup-simplify]: Simplify PI into PI 7.890 * [taylor]: Taking taylor expansion of n in n 7.890 * [backup-simplify]: Simplify 0 into 0 7.890 * [backup-simplify]: Simplify 1 into 1 7.891 * [backup-simplify]: Simplify (/ PI 1) into PI 7.891 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 7.892 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 7.893 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.894 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 7.894 * [backup-simplify]: Simplify 0 into 0 7.895 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.896 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 7.896 * [backup-simplify]: Simplify 0 into 0 7.897 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.898 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.898 * [backup-simplify]: Simplify 0 into 0 7.899 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.901 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 7.901 * [backup-simplify]: Simplify 0 into 0 7.902 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.903 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 7.903 * [backup-simplify]: Simplify 0 into 0 7.905 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.907 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 7.907 * [backup-simplify]: Simplify 0 into 0 7.907 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 7.907 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 7.908 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 7.908 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 7.908 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 7.908 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 7.908 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 7.908 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 7.908 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 7.908 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 7.908 * [taylor]: Taking taylor expansion of 1/2 in n 7.908 * [backup-simplify]: Simplify 1/2 into 1/2 7.908 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 7.908 * [taylor]: Taking taylor expansion of 1/2 in n 7.908 * [backup-simplify]: Simplify 1/2 into 1/2 7.908 * [taylor]: Taking taylor expansion of k in n 7.908 * [backup-simplify]: Simplify k into k 7.908 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 7.909 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.909 * [taylor]: Taking taylor expansion of 2 in n 7.909 * [backup-simplify]: Simplify 2 into 2 7.909 * [taylor]: Taking taylor expansion of (* n PI) in n 7.909 * [taylor]: Taking taylor expansion of n in n 7.909 * [backup-simplify]: Simplify 0 into 0 7.909 * [backup-simplify]: Simplify 1 into 1 7.909 * [taylor]: Taking taylor expansion of PI in n 7.909 * [backup-simplify]: Simplify PI into PI 7.909 * [backup-simplify]: Simplify (* 0 PI) into 0 7.910 * [backup-simplify]: Simplify (* 2 0) into 0 7.911 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.913 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 7.914 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.914 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 7.914 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 7.914 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 7.916 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.917 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 7.918 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 7.920 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 7.920 * [taylor]: Taking taylor expansion of (sqrt k) in n 7.920 * [taylor]: Taking taylor expansion of k in n 7.920 * [backup-simplify]: Simplify k into k 7.920 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 7.920 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 7.920 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 7.920 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 7.920 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 7.920 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 7.920 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 7.920 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 7.920 * [taylor]: Taking taylor expansion of 1/2 in k 7.920 * [backup-simplify]: Simplify 1/2 into 1/2 7.920 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 7.920 * [taylor]: Taking taylor expansion of 1/2 in k 7.920 * [backup-simplify]: Simplify 1/2 into 1/2 7.920 * [taylor]: Taking taylor expansion of k in k 7.920 * [backup-simplify]: Simplify 0 into 0 7.920 * [backup-simplify]: Simplify 1 into 1 7.920 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 7.920 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 7.920 * [taylor]: Taking taylor expansion of 2 in k 7.920 * [backup-simplify]: Simplify 2 into 2 7.920 * [taylor]: Taking taylor expansion of (* n PI) in k 7.920 * [taylor]: Taking taylor expansion of n in k 7.920 * [backup-simplify]: Simplify n into n 7.920 * [taylor]: Taking taylor expansion of PI in k 7.920 * [backup-simplify]: Simplify PI into PI 7.920 * [backup-simplify]: Simplify (* n PI) into (* n PI) 7.920 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 7.920 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 7.921 * [backup-simplify]: Simplify (* 1/2 0) into 0 7.921 * [backup-simplify]: Simplify (- 0) into 0 7.922 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 7.922 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 7.922 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 7.922 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 7.922 * [taylor]: Taking taylor expansion of (sqrt k) in k 7.922 * [taylor]: Taking taylor expansion of k in k 7.922 * [backup-simplify]: Simplify 0 into 0 7.922 * [backup-simplify]: Simplify 1 into 1 7.923 * [backup-simplify]: Simplify (sqrt 0) into 0 7.924 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 7.924 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 7.924 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 7.924 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 7.924 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 7.924 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 7.924 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 7.924 * [taylor]: Taking taylor expansion of 1/2 in k 7.924 * [backup-simplify]: Simplify 1/2 into 1/2 7.924 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 7.924 * [taylor]: Taking taylor expansion of 1/2 in k 7.924 * [backup-simplify]: Simplify 1/2 into 1/2 7.924 * [taylor]: Taking taylor expansion of k in k 7.924 * [backup-simplify]: Simplify 0 into 0 7.925 * [backup-simplify]: Simplify 1 into 1 7.925 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 7.925 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 7.925 * [taylor]: Taking taylor expansion of 2 in k 7.925 * [backup-simplify]: Simplify 2 into 2 7.925 * [taylor]: Taking taylor expansion of (* n PI) in k 7.925 * [taylor]: Taking taylor expansion of n in k 7.925 * [backup-simplify]: Simplify n into n 7.925 * [taylor]: Taking taylor expansion of PI in k 7.925 * [backup-simplify]: Simplify PI into PI 7.925 * [backup-simplify]: Simplify (* n PI) into (* n PI) 7.925 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 7.925 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 7.925 * [backup-simplify]: Simplify (* 1/2 0) into 0 7.926 * [backup-simplify]: Simplify (- 0) into 0 7.926 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 7.926 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 7.926 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 7.927 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 7.927 * [taylor]: Taking taylor expansion of (sqrt k) in k 7.927 * [taylor]: Taking taylor expansion of k in k 7.927 * [backup-simplify]: Simplify 0 into 0 7.927 * [backup-simplify]: Simplify 1 into 1 7.927 * [backup-simplify]: Simplify (sqrt 0) into 0 7.928 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 7.929 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 7.929 * [taylor]: Taking taylor expansion of 0 in n 7.929 * [backup-simplify]: Simplify 0 into 0 7.929 * [backup-simplify]: Simplify 0 into 0 7.929 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 7.930 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 7.931 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 7.931 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 7.932 * [backup-simplify]: Simplify (- 1/2) into -1/2 7.932 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 7.933 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 7.933 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 7.934 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 7.936 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 7.936 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 7.936 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 7.936 * [taylor]: Taking taylor expansion of +nan.0 in n 7.936 * [backup-simplify]: Simplify +nan.0 into +nan.0 7.936 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 7.936 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 7.936 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 7.937 * [taylor]: Taking taylor expansion of (* n PI) in n 7.937 * [taylor]: Taking taylor expansion of n in n 7.937 * [backup-simplify]: Simplify 0 into 0 7.937 * [backup-simplify]: Simplify 1 into 1 7.937 * [taylor]: Taking taylor expansion of PI in n 7.937 * [backup-simplify]: Simplify PI into PI 7.937 * [backup-simplify]: Simplify (* 0 PI) into 0 7.939 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.939 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 7.940 * [backup-simplify]: Simplify (sqrt 0) into 0 7.942 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 7.942 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 7.942 * [taylor]: Taking taylor expansion of 1/2 in n 7.942 * [backup-simplify]: Simplify 1/2 into 1/2 7.942 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 7.943 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 7.945 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 7.946 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 7.951 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 7.954 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 7.955 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 7.955 * [backup-simplify]: Simplify 0 into 0 7.957 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 7.958 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 7.958 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 7.960 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 7.960 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 7.961 * [backup-simplify]: Simplify (- 0) into 0 7.961 * [backup-simplify]: Simplify (+ 0 0) into 0 7.961 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 7.962 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 7.964 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 7.968 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 7.968 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 7.968 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 7.968 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 7.968 * [taylor]: Taking taylor expansion of +nan.0 in n 7.968 * [backup-simplify]: Simplify +nan.0 into +nan.0 7.968 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 7.968 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 7.968 * [taylor]: Taking taylor expansion of (sqrt 2) in n 7.968 * [taylor]: Taking taylor expansion of 2 in n 7.968 * [backup-simplify]: Simplify 2 into 2 7.968 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 7.969 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 7.969 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 7.969 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 7.969 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.969 * [taylor]: Taking taylor expansion of 2 in n 7.969 * [backup-simplify]: Simplify 2 into 2 7.969 * [taylor]: Taking taylor expansion of (* n PI) in n 7.969 * [taylor]: Taking taylor expansion of n in n 7.969 * [backup-simplify]: Simplify 0 into 0 7.969 * [backup-simplify]: Simplify 1 into 1 7.969 * [taylor]: Taking taylor expansion of PI in n 7.969 * [backup-simplify]: Simplify PI into PI 7.969 * [backup-simplify]: Simplify (* 0 PI) into 0 7.969 * [backup-simplify]: Simplify (* 2 0) into 0 7.970 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.971 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 7.972 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.972 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 7.972 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 7.972 * [taylor]: Taking taylor expansion of 1/2 in n 7.972 * [backup-simplify]: Simplify 1/2 into 1/2 7.972 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 7.973 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 7.973 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 7.973 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 7.973 * [taylor]: Taking taylor expansion of (* n PI) in n 7.973 * [taylor]: Taking taylor expansion of n in n 7.973 * [backup-simplify]: Simplify 0 into 0 7.973 * [backup-simplify]: Simplify 1 into 1 7.973 * [taylor]: Taking taylor expansion of PI in n 7.973 * [backup-simplify]: Simplify PI into PI 7.973 * [backup-simplify]: Simplify (* 0 PI) into 0 7.974 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.974 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 7.975 * [backup-simplify]: Simplify (sqrt 0) into 0 7.976 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 7.976 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 7.976 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 7.976 * [taylor]: Taking taylor expansion of +nan.0 in n 7.976 * [backup-simplify]: Simplify +nan.0 into +nan.0 7.976 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 7.976 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 7.976 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 7.976 * [taylor]: Taking taylor expansion of (* n PI) in n 7.976 * [taylor]: Taking taylor expansion of n in n 7.976 * [backup-simplify]: Simplify 0 into 0 7.976 * [backup-simplify]: Simplify 1 into 1 7.976 * [taylor]: Taking taylor expansion of PI in n 7.976 * [backup-simplify]: Simplify PI into PI 7.976 * [backup-simplify]: Simplify (* 0 PI) into 0 7.977 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.978 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 7.978 * [backup-simplify]: Simplify (sqrt 0) into 0 7.979 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 7.979 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 7.979 * [taylor]: Taking taylor expansion of 1/2 in n 7.979 * [backup-simplify]: Simplify 1/2 into 1/2 7.979 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 7.980 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 7.981 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.981 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 7.983 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 7.984 * [backup-simplify]: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 7.985 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.985 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 7.986 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 7.987 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 7.988 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 7.989 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 7.990 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 7.993 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 7.994 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 8.002 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 8.004 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 8.005 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 8.011 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 8.015 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 8.031 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 8.043 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 8.057 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 8.058 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 8.059 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.059 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 8.062 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 8.066 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 8.074 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 8.079 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 8.083 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 8.110 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 8.111 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 8.111 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 8.111 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 8.111 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.111 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.111 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.111 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.111 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.111 * [taylor]: Taking taylor expansion of 1/2 in n 8.111 * [backup-simplify]: Simplify 1/2 into 1/2 8.111 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.111 * [taylor]: Taking taylor expansion of 1/2 in n 8.111 * [backup-simplify]: Simplify 1/2 into 1/2 8.111 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.111 * [taylor]: Taking taylor expansion of k in n 8.111 * [backup-simplify]: Simplify k into k 8.111 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.111 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.111 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.111 * [taylor]: Taking taylor expansion of 2 in n 8.111 * [backup-simplify]: Simplify 2 into 2 8.111 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.111 * [taylor]: Taking taylor expansion of PI in n 8.111 * [backup-simplify]: Simplify PI into PI 8.111 * [taylor]: Taking taylor expansion of n in n 8.111 * [backup-simplify]: Simplify 0 into 0 8.111 * [backup-simplify]: Simplify 1 into 1 8.112 * [backup-simplify]: Simplify (/ PI 1) into PI 8.112 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.113 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.113 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.113 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.113 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.114 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.115 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.115 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.116 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.116 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 8.116 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.116 * [taylor]: Taking taylor expansion of k in n 8.116 * [backup-simplify]: Simplify k into k 8.116 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.116 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 8.116 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.116 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 8.117 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 8.117 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 8.117 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 8.117 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 8.117 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 8.117 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 8.117 * [taylor]: Taking taylor expansion of 1/2 in k 8.117 * [backup-simplify]: Simplify 1/2 into 1/2 8.117 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.117 * [taylor]: Taking taylor expansion of 1/2 in k 8.117 * [backup-simplify]: Simplify 1/2 into 1/2 8.117 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.117 * [taylor]: Taking taylor expansion of k in k 8.117 * [backup-simplify]: Simplify 0 into 0 8.117 * [backup-simplify]: Simplify 1 into 1 8.117 * [backup-simplify]: Simplify (/ 1 1) into 1 8.117 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 8.117 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 8.117 * [taylor]: Taking taylor expansion of 2 in k 8.117 * [backup-simplify]: Simplify 2 into 2 8.117 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.117 * [taylor]: Taking taylor expansion of PI in k 8.117 * [backup-simplify]: Simplify PI into PI 8.117 * [taylor]: Taking taylor expansion of n in k 8.117 * [backup-simplify]: Simplify n into n 8.117 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.117 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 8.117 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 8.118 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.118 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.118 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.118 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 8.118 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 8.118 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 8.118 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.118 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.118 * [taylor]: Taking taylor expansion of k in k 8.118 * [backup-simplify]: Simplify 0 into 0 8.118 * [backup-simplify]: Simplify 1 into 1 8.119 * [backup-simplify]: Simplify (/ 1 1) into 1 8.119 * [backup-simplify]: Simplify (sqrt 0) into 0 8.120 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.120 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 8.120 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 8.120 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 8.120 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 8.120 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 8.120 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 8.120 * [taylor]: Taking taylor expansion of 1/2 in k 8.120 * [backup-simplify]: Simplify 1/2 into 1/2 8.120 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.120 * [taylor]: Taking taylor expansion of 1/2 in k 8.120 * [backup-simplify]: Simplify 1/2 into 1/2 8.120 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.120 * [taylor]: Taking taylor expansion of k in k 8.120 * [backup-simplify]: Simplify 0 into 0 8.120 * [backup-simplify]: Simplify 1 into 1 8.120 * [backup-simplify]: Simplify (/ 1 1) into 1 8.120 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 8.120 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 8.120 * [taylor]: Taking taylor expansion of 2 in k 8.120 * [backup-simplify]: Simplify 2 into 2 8.121 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.121 * [taylor]: Taking taylor expansion of PI in k 8.121 * [backup-simplify]: Simplify PI into PI 8.121 * [taylor]: Taking taylor expansion of n in k 8.121 * [backup-simplify]: Simplify n into n 8.121 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.121 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 8.121 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 8.121 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.121 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.121 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.122 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 8.122 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 8.122 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 8.122 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.122 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.122 * [taylor]: Taking taylor expansion of k in k 8.122 * [backup-simplify]: Simplify 0 into 0 8.122 * [backup-simplify]: Simplify 1 into 1 8.122 * [backup-simplify]: Simplify (/ 1 1) into 1 8.122 * [backup-simplify]: Simplify (sqrt 0) into 0 8.123 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.123 * [backup-simplify]: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 8.123 * [taylor]: Taking taylor expansion of 0 in n 8.123 * [backup-simplify]: Simplify 0 into 0 8.123 * [backup-simplify]: Simplify 0 into 0 8.124 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 8.124 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 8.124 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 8.124 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.124 * [taylor]: Taking taylor expansion of +nan.0 in n 8.124 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.124 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.124 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.124 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.124 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.124 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.124 * [taylor]: Taking taylor expansion of 1/2 in n 8.124 * [backup-simplify]: Simplify 1/2 into 1/2 8.124 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.124 * [taylor]: Taking taylor expansion of 1/2 in n 8.124 * [backup-simplify]: Simplify 1/2 into 1/2 8.124 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.124 * [taylor]: Taking taylor expansion of k in n 8.124 * [backup-simplify]: Simplify k into k 8.124 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.124 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.124 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.124 * [taylor]: Taking taylor expansion of 2 in n 8.124 * [backup-simplify]: Simplify 2 into 2 8.124 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.124 * [taylor]: Taking taylor expansion of PI in n 8.124 * [backup-simplify]: Simplify PI into PI 8.125 * [taylor]: Taking taylor expansion of n in n 8.125 * [backup-simplify]: Simplify 0 into 0 8.125 * [backup-simplify]: Simplify 1 into 1 8.125 * [backup-simplify]: Simplify (/ PI 1) into PI 8.125 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.126 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.126 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.126 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.126 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.127 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.128 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.128 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.130 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.131 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.131 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.132 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.132 * [backup-simplify]: Simplify 0 into 0 8.133 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.135 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.135 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 8.135 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 8.135 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 8.136 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.136 * [taylor]: Taking taylor expansion of +nan.0 in n 8.136 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.136 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.136 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.136 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.136 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.136 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.136 * [taylor]: Taking taylor expansion of 1/2 in n 8.136 * [backup-simplify]: Simplify 1/2 into 1/2 8.136 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.136 * [taylor]: Taking taylor expansion of 1/2 in n 8.136 * [backup-simplify]: Simplify 1/2 into 1/2 8.136 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.136 * [taylor]: Taking taylor expansion of k in n 8.136 * [backup-simplify]: Simplify k into k 8.136 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.136 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.136 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.136 * [taylor]: Taking taylor expansion of 2 in n 8.136 * [backup-simplify]: Simplify 2 into 2 8.136 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.136 * [taylor]: Taking taylor expansion of PI in n 8.136 * [backup-simplify]: Simplify PI into PI 8.136 * [taylor]: Taking taylor expansion of n in n 8.136 * [backup-simplify]: Simplify 0 into 0 8.136 * [backup-simplify]: Simplify 1 into 1 8.136 * [backup-simplify]: Simplify (/ PI 1) into PI 8.137 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.137 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.137 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.137 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.137 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.138 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.139 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.140 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.141 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.141 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.142 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.143 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.143 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.144 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 8.145 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 8.145 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.145 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 8.146 * [backup-simplify]: Simplify (- 0) into 0 8.146 * [backup-simplify]: Simplify (+ 0 0) into 0 8.147 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.148 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 8.149 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.150 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 8.151 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 8.152 * [backup-simplify]: Simplify (- 0) into 0 8.152 * [backup-simplify]: Simplify 0 into 0 8.152 * [backup-simplify]: Simplify 0 into 0 8.155 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.158 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.158 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 8.159 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 8.159 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 8.159 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.159 * [taylor]: Taking taylor expansion of +nan.0 in n 8.159 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.159 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.159 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.159 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.159 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.159 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.159 * [taylor]: Taking taylor expansion of 1/2 in n 8.159 * [backup-simplify]: Simplify 1/2 into 1/2 8.159 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.159 * [taylor]: Taking taylor expansion of 1/2 in n 8.159 * [backup-simplify]: Simplify 1/2 into 1/2 8.159 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.159 * [taylor]: Taking taylor expansion of k in n 8.159 * [backup-simplify]: Simplify k into k 8.159 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.159 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.159 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.159 * [taylor]: Taking taylor expansion of 2 in n 8.159 * [backup-simplify]: Simplify 2 into 2 8.159 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.159 * [taylor]: Taking taylor expansion of PI in n 8.159 * [backup-simplify]: Simplify PI into PI 8.159 * [taylor]: Taking taylor expansion of n in n 8.159 * [backup-simplify]: Simplify 0 into 0 8.159 * [backup-simplify]: Simplify 1 into 1 8.159 * [backup-simplify]: Simplify (/ PI 1) into PI 8.160 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.161 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.161 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.161 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.161 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.163 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.164 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.165 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.167 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.168 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.170 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.171 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.176 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 8.177 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 8.177 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 8.177 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.177 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 8.177 * [taylor]: Taking taylor expansion of (/ -1 k) in n 8.177 * [taylor]: Taking taylor expansion of -1 in n 8.177 * [backup-simplify]: Simplify -1 into -1 8.177 * [taylor]: Taking taylor expansion of k in n 8.177 * [backup-simplify]: Simplify k into k 8.177 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 8.177 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 8.177 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 8.177 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 8.177 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.177 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 8.177 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 8.177 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.177 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.178 * [taylor]: Taking taylor expansion of 1/2 in n 8.178 * [backup-simplify]: Simplify 1/2 into 1/2 8.178 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.178 * [taylor]: Taking taylor expansion of k in n 8.178 * [backup-simplify]: Simplify k into k 8.178 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.178 * [taylor]: Taking taylor expansion of 1/2 in n 8.178 * [backup-simplify]: Simplify 1/2 into 1/2 8.178 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.178 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.178 * [taylor]: Taking taylor expansion of -2 in n 8.178 * [backup-simplify]: Simplify -2 into -2 8.178 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.178 * [taylor]: Taking taylor expansion of PI in n 8.178 * [backup-simplify]: Simplify PI into PI 8.178 * [taylor]: Taking taylor expansion of n in n 8.178 * [backup-simplify]: Simplify 0 into 0 8.178 * [backup-simplify]: Simplify 1 into 1 8.179 * [backup-simplify]: Simplify (/ PI 1) into PI 8.179 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.180 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.180 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.180 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.182 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.183 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.185 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.186 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.186 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 8.186 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.186 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.186 * [taylor]: Taking taylor expansion of -1 in k 8.186 * [backup-simplify]: Simplify -1 into -1 8.186 * [taylor]: Taking taylor expansion of k in k 8.186 * [backup-simplify]: Simplify 0 into 0 8.186 * [backup-simplify]: Simplify 1 into 1 8.187 * [backup-simplify]: Simplify (/ -1 1) into -1 8.187 * [backup-simplify]: Simplify (sqrt 0) into 0 8.188 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.188 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 8.188 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 8.188 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 8.188 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 8.188 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.188 * [taylor]: Taking taylor expansion of 1/2 in k 8.188 * [backup-simplify]: Simplify 1/2 into 1/2 8.188 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.188 * [taylor]: Taking taylor expansion of k in k 8.188 * [backup-simplify]: Simplify 0 into 0 8.188 * [backup-simplify]: Simplify 1 into 1 8.189 * [backup-simplify]: Simplify (/ 1 1) into 1 8.189 * [taylor]: Taking taylor expansion of 1/2 in k 8.189 * [backup-simplify]: Simplify 1/2 into 1/2 8.189 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 8.189 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 8.189 * [taylor]: Taking taylor expansion of -2 in k 8.189 * [backup-simplify]: Simplify -2 into -2 8.189 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.189 * [taylor]: Taking taylor expansion of PI in k 8.189 * [backup-simplify]: Simplify PI into PI 8.189 * [taylor]: Taking taylor expansion of n in k 8.189 * [backup-simplify]: Simplify n into n 8.189 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.189 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 8.189 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 8.189 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.190 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.190 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 8.190 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 8.190 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 8.190 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 8.190 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.190 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.190 * [taylor]: Taking taylor expansion of -1 in k 8.190 * [backup-simplify]: Simplify -1 into -1 8.190 * [taylor]: Taking taylor expansion of k in k 8.190 * [backup-simplify]: Simplify 0 into 0 8.190 * [backup-simplify]: Simplify 1 into 1 8.190 * [backup-simplify]: Simplify (/ -1 1) into -1 8.191 * [backup-simplify]: Simplify (sqrt 0) into 0 8.191 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.191 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 8.191 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 8.191 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 8.192 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 8.192 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.192 * [taylor]: Taking taylor expansion of 1/2 in k 8.192 * [backup-simplify]: Simplify 1/2 into 1/2 8.192 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.192 * [taylor]: Taking taylor expansion of k in k 8.192 * [backup-simplify]: Simplify 0 into 0 8.192 * [backup-simplify]: Simplify 1 into 1 8.192 * [backup-simplify]: Simplify (/ 1 1) into 1 8.192 * [taylor]: Taking taylor expansion of 1/2 in k 8.192 * [backup-simplify]: Simplify 1/2 into 1/2 8.192 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 8.192 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 8.192 * [taylor]: Taking taylor expansion of -2 in k 8.192 * [backup-simplify]: Simplify -2 into -2 8.192 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.192 * [taylor]: Taking taylor expansion of PI in k 8.192 * [backup-simplify]: Simplify PI into PI 8.192 * [taylor]: Taking taylor expansion of n in k 8.192 * [backup-simplify]: Simplify n into n 8.192 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.192 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 8.192 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 8.192 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.193 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.193 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 8.193 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 8.193 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 8.193 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.193 * [taylor]: Taking taylor expansion of +nan.0 in n 8.193 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.193 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.193 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.193 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.193 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.193 * [taylor]: Taking taylor expansion of -2 in n 8.193 * [backup-simplify]: Simplify -2 into -2 8.193 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.193 * [taylor]: Taking taylor expansion of PI in n 8.193 * [backup-simplify]: Simplify PI into PI 8.193 * [taylor]: Taking taylor expansion of n in n 8.193 * [backup-simplify]: Simplify 0 into 0 8.193 * [backup-simplify]: Simplify 1 into 1 8.194 * [backup-simplify]: Simplify (/ PI 1) into PI 8.194 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.195 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.195 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.195 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.195 * [taylor]: Taking taylor expansion of 1/2 in n 8.195 * [backup-simplify]: Simplify 1/2 into 1/2 8.195 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.195 * [taylor]: Taking taylor expansion of k in n 8.195 * [backup-simplify]: Simplify k into k 8.195 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.195 * [taylor]: Taking taylor expansion of 1/2 in n 8.195 * [backup-simplify]: Simplify 1/2 into 1/2 8.196 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.196 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.196 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.197 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.197 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.198 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.199 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.200 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.202 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.202 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 8.202 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 8.202 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 8.202 * [taylor]: Taking taylor expansion of +nan.0 in n 8.202 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.202 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.202 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.202 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.202 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.202 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.202 * [taylor]: Taking taylor expansion of -2 in n 8.202 * [backup-simplify]: Simplify -2 into -2 8.202 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.202 * [taylor]: Taking taylor expansion of PI in n 8.202 * [backup-simplify]: Simplify PI into PI 8.202 * [taylor]: Taking taylor expansion of n in n 8.202 * [backup-simplify]: Simplify 0 into 0 8.202 * [backup-simplify]: Simplify 1 into 1 8.203 * [backup-simplify]: Simplify (/ PI 1) into PI 8.203 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.204 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.204 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.204 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.204 * [taylor]: Taking taylor expansion of 1/2 in n 8.204 * [backup-simplify]: Simplify 1/2 into 1/2 8.204 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.204 * [taylor]: Taking taylor expansion of k in n 8.204 * [backup-simplify]: Simplify k into k 8.204 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.204 * [taylor]: Taking taylor expansion of 1/2 in n 8.204 * [backup-simplify]: Simplify 1/2 into 1/2 8.205 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.205 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.205 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.205 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.206 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.207 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.208 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.209 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 8.209 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 8.210 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.210 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.211 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 8.211 * [backup-simplify]: Simplify (+ 0 0) into 0 8.212 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.212 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 8.213 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 8.214 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 8.215 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.217 * [backup-simplify]: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 8.217 * [backup-simplify]: Simplify 0 into 0 8.218 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.221 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.222 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 8.222 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 8.222 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 8.222 * [taylor]: Taking taylor expansion of +nan.0 in n 8.222 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.222 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.222 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.222 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.222 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.222 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.222 * [taylor]: Taking taylor expansion of -2 in n 8.222 * [backup-simplify]: Simplify -2 into -2 8.222 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.222 * [taylor]: Taking taylor expansion of PI in n 8.222 * [backup-simplify]: Simplify PI into PI 8.222 * [taylor]: Taking taylor expansion of n in n 8.222 * [backup-simplify]: Simplify 0 into 0 8.222 * [backup-simplify]: Simplify 1 into 1 8.223 * [backup-simplify]: Simplify (/ PI 1) into PI 8.224 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.225 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.225 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.225 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.225 * [taylor]: Taking taylor expansion of 1/2 in n 8.225 * [backup-simplify]: Simplify 1/2 into 1/2 8.225 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.225 * [taylor]: Taking taylor expansion of k in n 8.225 * [backup-simplify]: Simplify k into k 8.225 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.225 * [taylor]: Taking taylor expansion of 1/2 in n 8.225 * [backup-simplify]: Simplify 1/2 into 1/2 8.227 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.227 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.227 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.229 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.230 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.231 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.233 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.234 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 8.235 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 8.240 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 8.240 * * * * [progress]: [ 4 / 4 ] generating series at (2) 8.241 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 8.241 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 8.241 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 8.241 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 8.241 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.241 * [taylor]: Taking taylor expansion of k in n 8.241 * [backup-simplify]: Simplify k into k 8.241 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.241 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 8.241 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.241 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 8.241 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 8.241 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 8.241 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 8.242 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 8.242 * [taylor]: Taking taylor expansion of 1/2 in n 8.242 * [backup-simplify]: Simplify 1/2 into 1/2 8.242 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 8.242 * [taylor]: Taking taylor expansion of 1/2 in n 8.242 * [backup-simplify]: Simplify 1/2 into 1/2 8.242 * [taylor]: Taking taylor expansion of k in n 8.242 * [backup-simplify]: Simplify k into k 8.242 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.242 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.242 * [taylor]: Taking taylor expansion of 2 in n 8.242 * [backup-simplify]: Simplify 2 into 2 8.242 * [taylor]: Taking taylor expansion of (* n PI) in n 8.242 * [taylor]: Taking taylor expansion of n in n 8.242 * [backup-simplify]: Simplify 0 into 0 8.242 * [backup-simplify]: Simplify 1 into 1 8.242 * [taylor]: Taking taylor expansion of PI in n 8.242 * [backup-simplify]: Simplify PI into PI 8.243 * [backup-simplify]: Simplify (* 0 PI) into 0 8.243 * [backup-simplify]: Simplify (* 2 0) into 0 8.245 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.246 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.248 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.248 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 8.248 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 8.248 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 8.249 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.249 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 8.250 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 8.250 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 8.250 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.250 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.250 * [taylor]: Taking taylor expansion of k in k 8.250 * [backup-simplify]: Simplify 0 into 0 8.250 * [backup-simplify]: Simplify 1 into 1 8.250 * [backup-simplify]: Simplify (/ 1 1) into 1 8.251 * [backup-simplify]: Simplify (sqrt 0) into 0 8.252 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.252 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 8.252 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 8.252 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 8.252 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 8.252 * [taylor]: Taking taylor expansion of 1/2 in k 8.252 * [backup-simplify]: Simplify 1/2 into 1/2 8.252 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 8.252 * [taylor]: Taking taylor expansion of 1/2 in k 8.252 * [backup-simplify]: Simplify 1/2 into 1/2 8.252 * [taylor]: Taking taylor expansion of k in k 8.252 * [backup-simplify]: Simplify 0 into 0 8.252 * [backup-simplify]: Simplify 1 into 1 8.252 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 8.252 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 8.252 * [taylor]: Taking taylor expansion of 2 in k 8.252 * [backup-simplify]: Simplify 2 into 2 8.252 * [taylor]: Taking taylor expansion of (* n PI) in k 8.252 * [taylor]: Taking taylor expansion of n in k 8.252 * [backup-simplify]: Simplify n into n 8.252 * [taylor]: Taking taylor expansion of PI in k 8.252 * [backup-simplify]: Simplify PI into PI 8.252 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.252 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 8.252 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 8.252 * [backup-simplify]: Simplify (* 1/2 0) into 0 8.252 * [backup-simplify]: Simplify (- 0) into 0 8.253 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.253 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 8.253 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 8.253 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 8.253 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.253 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.253 * [taylor]: Taking taylor expansion of k in k 8.253 * [backup-simplify]: Simplify 0 into 0 8.253 * [backup-simplify]: Simplify 1 into 1 8.253 * [backup-simplify]: Simplify (/ 1 1) into 1 8.253 * [backup-simplify]: Simplify (sqrt 0) into 0 8.254 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.254 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 8.254 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 8.254 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 8.254 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 8.254 * [taylor]: Taking taylor expansion of 1/2 in k 8.254 * [backup-simplify]: Simplify 1/2 into 1/2 8.254 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 8.254 * [taylor]: Taking taylor expansion of 1/2 in k 8.254 * [backup-simplify]: Simplify 1/2 into 1/2 8.254 * [taylor]: Taking taylor expansion of k in k 8.254 * [backup-simplify]: Simplify 0 into 0 8.254 * [backup-simplify]: Simplify 1 into 1 8.255 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 8.255 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 8.255 * [taylor]: Taking taylor expansion of 2 in k 8.255 * [backup-simplify]: Simplify 2 into 2 8.255 * [taylor]: Taking taylor expansion of (* n PI) in k 8.255 * [taylor]: Taking taylor expansion of n in k 8.255 * [backup-simplify]: Simplify n into n 8.255 * [taylor]: Taking taylor expansion of PI in k 8.255 * [backup-simplify]: Simplify PI into PI 8.255 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.255 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 8.255 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 8.255 * [backup-simplify]: Simplify (* 1/2 0) into 0 8.255 * [backup-simplify]: Simplify (- 0) into 0 8.256 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.256 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 8.256 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 8.256 * [backup-simplify]: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 8.256 * [taylor]: Taking taylor expansion of 0 in n 8.256 * [backup-simplify]: Simplify 0 into 0 8.256 * [backup-simplify]: Simplify 0 into 0 8.256 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 8.257 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 8.257 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 8.257 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 8.258 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.258 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.258 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 8.258 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 8.259 * [backup-simplify]: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 8.259 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 8.259 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 8.259 * [taylor]: Taking taylor expansion of +nan.0 in n 8.259 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.259 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 8.259 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.259 * [taylor]: Taking taylor expansion of 2 in n 8.259 * [backup-simplify]: Simplify 2 into 2 8.259 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.259 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.260 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.260 * [taylor]: Taking taylor expansion of (* n PI) in n 8.260 * [taylor]: Taking taylor expansion of n in n 8.260 * [backup-simplify]: Simplify 0 into 0 8.260 * [backup-simplify]: Simplify 1 into 1 8.260 * [taylor]: Taking taylor expansion of PI in n 8.260 * [backup-simplify]: Simplify PI into PI 8.260 * [backup-simplify]: Simplify (* 0 PI) into 0 8.261 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.261 * [backup-simplify]: Simplify (sqrt 0) into 0 8.262 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.262 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 8.263 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.263 * [backup-simplify]: Simplify (- 0) into 0 8.263 * [backup-simplify]: Simplify 0 into 0 8.263 * [backup-simplify]: Simplify 0 into 0 8.263 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 8.264 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 8.265 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 8.265 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 8.266 * [backup-simplify]: Simplify (- 0) into 0 8.266 * [backup-simplify]: Simplify (+ 0 0) into 0 8.269 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 8.270 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 8.270 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.272 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.273 * [backup-simplify]: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 8.273 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 8.273 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 8.273 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 8.273 * [taylor]: Taking taylor expansion of +nan.0 in n 8.273 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.273 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 8.273 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 8.273 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.273 * [taylor]: Taking taylor expansion of 2 in n 8.273 * [backup-simplify]: Simplify 2 into 2 8.273 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.273 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.273 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.273 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.273 * [taylor]: Taking taylor expansion of 2 in n 8.274 * [backup-simplify]: Simplify 2 into 2 8.274 * [taylor]: Taking taylor expansion of (* n PI) in n 8.274 * [taylor]: Taking taylor expansion of n in n 8.274 * [backup-simplify]: Simplify 0 into 0 8.274 * [backup-simplify]: Simplify 1 into 1 8.274 * [taylor]: Taking taylor expansion of PI in n 8.274 * [backup-simplify]: Simplify PI into PI 8.274 * [backup-simplify]: Simplify (* 0 PI) into 0 8.274 * [backup-simplify]: Simplify (* 2 0) into 0 8.275 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.276 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.278 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.278 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.278 * [taylor]: Taking taylor expansion of (* n PI) in n 8.278 * [taylor]: Taking taylor expansion of n in n 8.278 * [backup-simplify]: Simplify 0 into 0 8.278 * [backup-simplify]: Simplify 1 into 1 8.278 * [taylor]: Taking taylor expansion of PI in n 8.278 * [backup-simplify]: Simplify PI into PI 8.278 * [backup-simplify]: Simplify (* 0 PI) into 0 8.280 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.281 * [backup-simplify]: Simplify (sqrt 0) into 0 8.282 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.282 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 8.282 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 8.282 * [taylor]: Taking taylor expansion of +nan.0 in n 8.282 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.282 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 8.282 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.282 * [taylor]: Taking taylor expansion of 2 in n 8.282 * [backup-simplify]: Simplify 2 into 2 8.283 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.284 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.284 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.284 * [taylor]: Taking taylor expansion of (* n PI) in n 8.284 * [taylor]: Taking taylor expansion of n in n 8.284 * [backup-simplify]: Simplify 0 into 0 8.284 * [backup-simplify]: Simplify 1 into 1 8.284 * [taylor]: Taking taylor expansion of PI in n 8.284 * [backup-simplify]: Simplify PI into PI 8.284 * [backup-simplify]: Simplify (* 0 PI) into 0 8.286 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.286 * [backup-simplify]: Simplify (sqrt 0) into 0 8.288 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.289 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.291 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 8.292 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 8.293 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.293 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 8.294 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.294 * [backup-simplify]: Simplify (- 0) into 0 8.295 * [backup-simplify]: Simplify (+ 0 0) into 0 8.295 * [backup-simplify]: Simplify (- 0) into 0 8.295 * [backup-simplify]: Simplify 0 into 0 8.299 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.305 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.309 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 8.312 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 8.312 * [backup-simplify]: Simplify 0 into 0 8.312 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.313 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 8.315 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 8.316 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 8.316 * [backup-simplify]: Simplify (- 0) into 0 8.316 * [backup-simplify]: Simplify (+ 0 0) into 0 8.317 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 8.318 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 8.318 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.321 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.322 * [backup-simplify]: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 8.322 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 8.322 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 8.322 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 8.322 * [taylor]: Taking taylor expansion of +nan.0 in n 8.322 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.322 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 8.322 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 8.322 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.322 * [taylor]: Taking taylor expansion of 2 in n 8.322 * [backup-simplify]: Simplify 2 into 2 8.322 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.322 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.322 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.322 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.323 * [taylor]: Taking taylor expansion of 2 in n 8.323 * [backup-simplify]: Simplify 2 into 2 8.323 * [taylor]: Taking taylor expansion of (* n PI) in n 8.323 * [taylor]: Taking taylor expansion of n in n 8.323 * [backup-simplify]: Simplify 0 into 0 8.323 * [backup-simplify]: Simplify 1 into 1 8.323 * [taylor]: Taking taylor expansion of PI in n 8.323 * [backup-simplify]: Simplify PI into PI 8.323 * [backup-simplify]: Simplify (* 0 PI) into 0 8.323 * [backup-simplify]: Simplify (* 2 0) into 0 8.324 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.325 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.326 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.326 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.326 * [taylor]: Taking taylor expansion of (* n PI) in n 8.326 * [taylor]: Taking taylor expansion of n in n 8.326 * [backup-simplify]: Simplify 0 into 0 8.326 * [backup-simplify]: Simplify 1 into 1 8.326 * [taylor]: Taking taylor expansion of PI in n 8.326 * [backup-simplify]: Simplify PI into PI 8.326 * [backup-simplify]: Simplify (* 0 PI) into 0 8.327 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.327 * [backup-simplify]: Simplify (sqrt 0) into 0 8.328 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.328 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 8.328 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 8.328 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 8.328 * [taylor]: Taking taylor expansion of +nan.0 in n 8.328 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.328 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 8.328 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 8.328 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.328 * [taylor]: Taking taylor expansion of 2 in n 8.328 * [backup-simplify]: Simplify 2 into 2 8.329 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.329 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.329 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 8.329 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.329 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.329 * [taylor]: Taking taylor expansion of 2 in n 8.329 * [backup-simplify]: Simplify 2 into 2 8.329 * [taylor]: Taking taylor expansion of (* n PI) in n 8.329 * [taylor]: Taking taylor expansion of n in n 8.329 * [backup-simplify]: Simplify 0 into 0 8.329 * [backup-simplify]: Simplify 1 into 1 8.329 * [taylor]: Taking taylor expansion of PI in n 8.329 * [backup-simplify]: Simplify PI into PI 8.330 * [backup-simplify]: Simplify (* 0 PI) into 0 8.330 * [backup-simplify]: Simplify (* 2 0) into 0 8.331 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.332 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.332 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.333 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.333 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.333 * [taylor]: Taking taylor expansion of (* n PI) in n 8.333 * [taylor]: Taking taylor expansion of n in n 8.333 * [backup-simplify]: Simplify 0 into 0 8.333 * [backup-simplify]: Simplify 1 into 1 8.333 * [taylor]: Taking taylor expansion of PI in n 8.333 * [backup-simplify]: Simplify PI into PI 8.334 * [backup-simplify]: Simplify (* 0 PI) into 0 8.335 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.335 * [backup-simplify]: Simplify (sqrt 0) into 0 8.336 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.336 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 8.336 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 8.336 * [taylor]: Taking taylor expansion of +nan.0 in n 8.336 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.336 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 8.336 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.336 * [taylor]: Taking taylor expansion of 2 in n 8.336 * [backup-simplify]: Simplify 2 into 2 8.336 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.336 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.336 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.337 * [taylor]: Taking taylor expansion of (* n PI) in n 8.337 * [taylor]: Taking taylor expansion of n in n 8.337 * [backup-simplify]: Simplify 0 into 0 8.337 * [backup-simplify]: Simplify 1 into 1 8.337 * [taylor]: Taking taylor expansion of PI in n 8.337 * [backup-simplify]: Simplify PI into PI 8.337 * [backup-simplify]: Simplify (* 0 PI) into 0 8.338 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.338 * [backup-simplify]: Simplify (sqrt 0) into 0 8.339 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.340 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.341 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 8.342 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 8.342 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.343 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.344 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.347 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 8.348 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 8.350 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 8.350 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.351 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 8.351 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.352 * [backup-simplify]: Simplify (- 0) into 0 8.352 * [backup-simplify]: Simplify (+ 0 0) into 0 8.352 * [backup-simplify]: Simplify (- 0) into 0 8.353 * [backup-simplify]: Simplify (+ 0 0) into 0 8.353 * [backup-simplify]: Simplify (- 0) into 0 8.353 * [backup-simplify]: Simplify 0 into 0 8.354 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.355 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 8.357 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 8.357 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.358 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 8.360 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 8.364 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 8.366 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.369 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.371 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 8.380 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 8.384 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 8.389 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 8.390 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.393 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 8.394 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 8.397 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.402 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.404 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.407 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.415 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 8.416 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 8.416 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 8.416 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.416 * [taylor]: Taking taylor expansion of (sqrt k) in n 8.416 * [taylor]: Taking taylor expansion of k in n 8.416 * [backup-simplify]: Simplify k into k 8.416 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 8.416 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 8.416 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.416 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.416 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.416 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.416 * [taylor]: Taking taylor expansion of 1/2 in n 8.416 * [backup-simplify]: Simplify 1/2 into 1/2 8.416 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.416 * [taylor]: Taking taylor expansion of 1/2 in n 8.416 * [backup-simplify]: Simplify 1/2 into 1/2 8.416 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.416 * [taylor]: Taking taylor expansion of k in n 8.416 * [backup-simplify]: Simplify k into k 8.416 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.416 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.416 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.416 * [taylor]: Taking taylor expansion of 2 in n 8.416 * [backup-simplify]: Simplify 2 into 2 8.416 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.416 * [taylor]: Taking taylor expansion of PI in n 8.416 * [backup-simplify]: Simplify PI into PI 8.416 * [taylor]: Taking taylor expansion of n in n 8.416 * [backup-simplify]: Simplify 0 into 0 8.416 * [backup-simplify]: Simplify 1 into 1 8.417 * [backup-simplify]: Simplify (/ PI 1) into PI 8.417 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.418 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.418 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.418 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.418 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.419 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.419 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.420 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.420 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 8.420 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.420 * [taylor]: Taking taylor expansion of k in k 8.420 * [backup-simplify]: Simplify 0 into 0 8.420 * [backup-simplify]: Simplify 1 into 1 8.421 * [backup-simplify]: Simplify (sqrt 0) into 0 8.421 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.421 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 8.421 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 8.421 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 8.421 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 8.421 * [taylor]: Taking taylor expansion of 1/2 in k 8.421 * [backup-simplify]: Simplify 1/2 into 1/2 8.421 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.421 * [taylor]: Taking taylor expansion of 1/2 in k 8.421 * [backup-simplify]: Simplify 1/2 into 1/2 8.422 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.422 * [taylor]: Taking taylor expansion of k in k 8.422 * [backup-simplify]: Simplify 0 into 0 8.422 * [backup-simplify]: Simplify 1 into 1 8.422 * [backup-simplify]: Simplify (/ 1 1) into 1 8.422 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 8.422 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 8.422 * [taylor]: Taking taylor expansion of 2 in k 8.422 * [backup-simplify]: Simplify 2 into 2 8.422 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.422 * [taylor]: Taking taylor expansion of PI in k 8.422 * [backup-simplify]: Simplify PI into PI 8.422 * [taylor]: Taking taylor expansion of n in k 8.422 * [backup-simplify]: Simplify n into n 8.422 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.422 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 8.422 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 8.422 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.423 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.423 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.423 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 8.423 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 8.423 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 8.423 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.423 * [taylor]: Taking taylor expansion of k in k 8.423 * [backup-simplify]: Simplify 0 into 0 8.423 * [backup-simplify]: Simplify 1 into 1 8.423 * [backup-simplify]: Simplify (sqrt 0) into 0 8.424 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.424 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 8.424 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 8.424 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 8.424 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 8.424 * [taylor]: Taking taylor expansion of 1/2 in k 8.424 * [backup-simplify]: Simplify 1/2 into 1/2 8.424 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.424 * [taylor]: Taking taylor expansion of 1/2 in k 8.424 * [backup-simplify]: Simplify 1/2 into 1/2 8.424 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.424 * [taylor]: Taking taylor expansion of k in k 8.424 * [backup-simplify]: Simplify 0 into 0 8.424 * [backup-simplify]: Simplify 1 into 1 8.425 * [backup-simplify]: Simplify (/ 1 1) into 1 8.425 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 8.425 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 8.425 * [taylor]: Taking taylor expansion of 2 in k 8.425 * [backup-simplify]: Simplify 2 into 2 8.425 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.425 * [taylor]: Taking taylor expansion of PI in k 8.425 * [backup-simplify]: Simplify PI into PI 8.425 * [taylor]: Taking taylor expansion of n in k 8.425 * [backup-simplify]: Simplify n into n 8.425 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.425 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 8.425 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 8.425 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.425 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.426 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.426 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 8.426 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 8.426 * [backup-simplify]: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 8.426 * [taylor]: Taking taylor expansion of 0 in n 8.426 * [backup-simplify]: Simplify 0 into 0 8.426 * [backup-simplify]: Simplify 0 into 0 8.427 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 8.427 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.427 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.427 * [taylor]: Taking taylor expansion of +nan.0 in n 8.427 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.427 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.427 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.427 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.427 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.427 * [taylor]: Taking taylor expansion of 1/2 in n 8.427 * [backup-simplify]: Simplify 1/2 into 1/2 8.427 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.427 * [taylor]: Taking taylor expansion of 1/2 in n 8.427 * [backup-simplify]: Simplify 1/2 into 1/2 8.427 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.427 * [taylor]: Taking taylor expansion of k in n 8.427 * [backup-simplify]: Simplify k into k 8.427 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.427 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.427 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.427 * [taylor]: Taking taylor expansion of 2 in n 8.427 * [backup-simplify]: Simplify 2 into 2 8.427 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.427 * [taylor]: Taking taylor expansion of PI in n 8.427 * [backup-simplify]: Simplify PI into PI 8.427 * [taylor]: Taking taylor expansion of n in n 8.427 * [backup-simplify]: Simplify 0 into 0 8.427 * [backup-simplify]: Simplify 1 into 1 8.427 * [backup-simplify]: Simplify (/ PI 1) into PI 8.428 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.428 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.428 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.428 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.428 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.429 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.430 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.431 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.432 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.432 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.433 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.433 * [backup-simplify]: Simplify 0 into 0 8.435 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.435 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 8.435 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.435 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.436 * [taylor]: Taking taylor expansion of +nan.0 in n 8.436 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.436 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.436 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.436 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.436 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.436 * [taylor]: Taking taylor expansion of 1/2 in n 8.436 * [backup-simplify]: Simplify 1/2 into 1/2 8.436 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.436 * [taylor]: Taking taylor expansion of 1/2 in n 8.436 * [backup-simplify]: Simplify 1/2 into 1/2 8.436 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.436 * [taylor]: Taking taylor expansion of k in n 8.436 * [backup-simplify]: Simplify k into k 8.436 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.436 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.436 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.436 * [taylor]: Taking taylor expansion of 2 in n 8.436 * [backup-simplify]: Simplify 2 into 2 8.436 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.436 * [taylor]: Taking taylor expansion of PI in n 8.436 * [backup-simplify]: Simplify PI into PI 8.436 * [taylor]: Taking taylor expansion of n in n 8.436 * [backup-simplify]: Simplify 0 into 0 8.436 * [backup-simplify]: Simplify 1 into 1 8.436 * [backup-simplify]: Simplify (/ PI 1) into PI 8.437 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.437 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.437 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.437 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.437 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.438 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.439 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.440 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.441 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.441 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.442 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.443 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.443 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 8.444 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 8.444 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.445 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 8.445 * [backup-simplify]: Simplify (- 0) into 0 8.445 * [backup-simplify]: Simplify (+ 0 0) into 0 8.446 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.447 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 8.448 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.449 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 8.449 * [backup-simplify]: Simplify (- 0) into 0 8.449 * [backup-simplify]: Simplify 0 into 0 8.449 * [backup-simplify]: Simplify 0 into 0 8.452 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.453 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 8.453 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.453 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.453 * [taylor]: Taking taylor expansion of +nan.0 in n 8.453 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.453 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.453 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.453 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.453 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.453 * [taylor]: Taking taylor expansion of 1/2 in n 8.453 * [backup-simplify]: Simplify 1/2 into 1/2 8.453 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.453 * [taylor]: Taking taylor expansion of 1/2 in n 8.453 * [backup-simplify]: Simplify 1/2 into 1/2 8.453 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.453 * [taylor]: Taking taylor expansion of k in n 8.453 * [backup-simplify]: Simplify k into k 8.453 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.453 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.453 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.453 * [taylor]: Taking taylor expansion of 2 in n 8.453 * [backup-simplify]: Simplify 2 into 2 8.453 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.453 * [taylor]: Taking taylor expansion of PI in n 8.453 * [backup-simplify]: Simplify PI into PI 8.453 * [taylor]: Taking taylor expansion of n in n 8.453 * [backup-simplify]: Simplify 0 into 0 8.453 * [backup-simplify]: Simplify 1 into 1 8.453 * [backup-simplify]: Simplify (/ PI 1) into PI 8.454 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.454 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.455 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.455 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.455 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.456 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.456 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.457 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.458 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.459 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.459 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.465 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 8.466 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 8.466 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 8.466 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 8.466 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.466 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 8.466 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 8.466 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.466 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.466 * [taylor]: Taking taylor expansion of 1/2 in n 8.466 * [backup-simplify]: Simplify 1/2 into 1/2 8.466 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.466 * [taylor]: Taking taylor expansion of k in n 8.466 * [backup-simplify]: Simplify k into k 8.466 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.466 * [taylor]: Taking taylor expansion of 1/2 in n 8.466 * [backup-simplify]: Simplify 1/2 into 1/2 8.466 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.466 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.466 * [taylor]: Taking taylor expansion of -2 in n 8.466 * [backup-simplify]: Simplify -2 into -2 8.466 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.466 * [taylor]: Taking taylor expansion of PI in n 8.466 * [backup-simplify]: Simplify PI into PI 8.466 * [taylor]: Taking taylor expansion of n in n 8.466 * [backup-simplify]: Simplify 0 into 0 8.466 * [backup-simplify]: Simplify 1 into 1 8.466 * [backup-simplify]: Simplify (/ PI 1) into PI 8.467 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.467 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.467 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.467 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.468 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.469 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.470 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.470 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 8.470 * [taylor]: Taking taylor expansion of (/ -1 k) in n 8.470 * [taylor]: Taking taylor expansion of -1 in n 8.470 * [backup-simplify]: Simplify -1 into -1 8.470 * [taylor]: Taking taylor expansion of k in n 8.470 * [backup-simplify]: Simplify k into k 8.470 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 8.471 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 8.471 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 8.471 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 8.472 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 8.472 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 8.472 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 8.472 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 8.472 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 8.472 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 8.472 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.472 * [taylor]: Taking taylor expansion of 1/2 in k 8.472 * [backup-simplify]: Simplify 1/2 into 1/2 8.472 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.472 * [taylor]: Taking taylor expansion of k in k 8.472 * [backup-simplify]: Simplify 0 into 0 8.472 * [backup-simplify]: Simplify 1 into 1 8.472 * [backup-simplify]: Simplify (/ 1 1) into 1 8.472 * [taylor]: Taking taylor expansion of 1/2 in k 8.472 * [backup-simplify]: Simplify 1/2 into 1/2 8.473 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 8.473 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 8.473 * [taylor]: Taking taylor expansion of -2 in k 8.473 * [backup-simplify]: Simplify -2 into -2 8.473 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.473 * [taylor]: Taking taylor expansion of PI in k 8.473 * [backup-simplify]: Simplify PI into PI 8.473 * [taylor]: Taking taylor expansion of n in k 8.473 * [backup-simplify]: Simplify n into n 8.473 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.473 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 8.473 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 8.473 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.474 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.474 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 8.474 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 8.474 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.474 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.474 * [taylor]: Taking taylor expansion of -1 in k 8.474 * [backup-simplify]: Simplify -1 into -1 8.474 * [taylor]: Taking taylor expansion of k in k 8.474 * [backup-simplify]: Simplify 0 into 0 8.474 * [backup-simplify]: Simplify 1 into 1 8.475 * [backup-simplify]: Simplify (/ -1 1) into -1 8.475 * [backup-simplify]: Simplify (sqrt 0) into 0 8.477 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.477 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 8.477 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 8.477 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 8.477 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 8.477 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 8.477 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 8.477 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.477 * [taylor]: Taking taylor expansion of 1/2 in k 8.477 * [backup-simplify]: Simplify 1/2 into 1/2 8.477 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.477 * [taylor]: Taking taylor expansion of k in k 8.477 * [backup-simplify]: Simplify 0 into 0 8.477 * [backup-simplify]: Simplify 1 into 1 8.478 * [backup-simplify]: Simplify (/ 1 1) into 1 8.478 * [taylor]: Taking taylor expansion of 1/2 in k 8.478 * [backup-simplify]: Simplify 1/2 into 1/2 8.478 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 8.478 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 8.478 * [taylor]: Taking taylor expansion of -2 in k 8.478 * [backup-simplify]: Simplify -2 into -2 8.478 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.478 * [taylor]: Taking taylor expansion of PI in k 8.478 * [backup-simplify]: Simplify PI into PI 8.478 * [taylor]: Taking taylor expansion of n in k 8.478 * [backup-simplify]: Simplify n into n 8.478 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.478 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 8.478 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 8.479 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.479 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.479 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 8.480 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 8.480 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.480 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.480 * [taylor]: Taking taylor expansion of -1 in k 8.480 * [backup-simplify]: Simplify -1 into -1 8.480 * [taylor]: Taking taylor expansion of k in k 8.480 * [backup-simplify]: Simplify 0 into 0 8.480 * [backup-simplify]: Simplify 1 into 1 8.480 * [backup-simplify]: Simplify (/ -1 1) into -1 8.481 * [backup-simplify]: Simplify (sqrt 0) into 0 8.482 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.482 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 8.482 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.482 * [taylor]: Taking taylor expansion of +nan.0 in n 8.482 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.482 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.483 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.483 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.483 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.483 * [taylor]: Taking taylor expansion of -2 in n 8.483 * [backup-simplify]: Simplify -2 into -2 8.483 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.483 * [taylor]: Taking taylor expansion of PI in n 8.483 * [backup-simplify]: Simplify PI into PI 8.483 * [taylor]: Taking taylor expansion of n in n 8.483 * [backup-simplify]: Simplify 0 into 0 8.483 * [backup-simplify]: Simplify 1 into 1 8.483 * [backup-simplify]: Simplify (/ PI 1) into PI 8.484 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.485 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.485 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.485 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.485 * [taylor]: Taking taylor expansion of 1/2 in n 8.485 * [backup-simplify]: Simplify 1/2 into 1/2 8.485 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.485 * [taylor]: Taking taylor expansion of k in n 8.485 * [backup-simplify]: Simplify k into k 8.486 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.486 * [taylor]: Taking taylor expansion of 1/2 in n 8.486 * [backup-simplify]: Simplify 1/2 into 1/2 8.487 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.488 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.488 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.489 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.490 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.492 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.493 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.494 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.497 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.498 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 8.498 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 8.498 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.498 * [taylor]: Taking taylor expansion of +nan.0 in n 8.498 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.498 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.498 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.498 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.498 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.499 * [taylor]: Taking taylor expansion of -2 in n 8.499 * [backup-simplify]: Simplify -2 into -2 8.499 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.499 * [taylor]: Taking taylor expansion of PI in n 8.499 * [backup-simplify]: Simplify PI into PI 8.499 * [taylor]: Taking taylor expansion of n in n 8.499 * [backup-simplify]: Simplify 0 into 0 8.499 * [backup-simplify]: Simplify 1 into 1 8.499 * [backup-simplify]: Simplify (/ PI 1) into PI 8.500 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.501 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.501 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.501 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.501 * [taylor]: Taking taylor expansion of 1/2 in n 8.501 * [backup-simplify]: Simplify 1/2 into 1/2 8.501 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.501 * [taylor]: Taking taylor expansion of k in n 8.501 * [backup-simplify]: Simplify k into k 8.501 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.501 * [taylor]: Taking taylor expansion of 1/2 in n 8.501 * [backup-simplify]: Simplify 1/2 into 1/2 8.503 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.503 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.503 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.504 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.505 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.507 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.508 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 8.509 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 8.511 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.511 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.511 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 8.512 * [backup-simplify]: Simplify (+ 0 0) into 0 8.513 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.513 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 8.515 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 8.517 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 8.519 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.521 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 8.521 * [backup-simplify]: Simplify 0 into 0 8.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.526 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.528 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 8.528 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 8.528 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.528 * [taylor]: Taking taylor expansion of +nan.0 in n 8.528 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.528 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.528 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.528 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.528 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.528 * [taylor]: Taking taylor expansion of -2 in n 8.528 * [backup-simplify]: Simplify -2 into -2 8.528 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.528 * [taylor]: Taking taylor expansion of PI in n 8.528 * [backup-simplify]: Simplify PI into PI 8.528 * [taylor]: Taking taylor expansion of n in n 8.528 * [backup-simplify]: Simplify 0 into 0 8.528 * [backup-simplify]: Simplify 1 into 1 8.529 * [backup-simplify]: Simplify (/ PI 1) into PI 8.530 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.531 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.531 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.531 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.531 * [taylor]: Taking taylor expansion of 1/2 in n 8.531 * [backup-simplify]: Simplify 1/2 into 1/2 8.531 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.531 * [taylor]: Taking taylor expansion of k in n 8.531 * [backup-simplify]: Simplify k into k 8.531 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.531 * [taylor]: Taking taylor expansion of 1/2 in n 8.531 * [backup-simplify]: Simplify 1/2 into 1/2 8.532 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.533 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.533 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.534 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.535 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.536 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.538 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 8.539 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 8.543 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 8.544 * * * [progress]: simplifying candidates 8.544 * * * * [progress]: [ 1 / 1611 ] simplifiying candidate # 8.544 * * * * [progress]: [ 2 / 1611 ] simplifiying candidate # 8.544 * * * * [progress]: [ 3 / 1611 ] simplifiying candidate # 8.544 * * * * [progress]: [ 4 / 1611 ] simplifiying candidate # 8.544 * * * * [progress]: [ 5 / 1611 ] simplifiying candidate # 8.544 * * * * [progress]: [ 6 / 1611 ] simplifiying candidate # 8.544 * * * * [progress]: [ 7 / 1611 ] simplifiying candidate # 8.544 * * * * [progress]: [ 8 / 1611 ] simplifiying candidate # 8.544 * * * * [progress]: [ 9 / 1611 ] simplifiying candidate # 8.545 * * * * [progress]: [ 10 / 1611 ] simplifiying candidate # 8.545 * * * * [progress]: [ 11 / 1611 ] simplifiying candidate # 8.545 * * * * [progress]: [ 12 / 1611 ] simplifiying 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2))))))> 8.551 * * * * [progress]: [ 88 / 1611 ] simplifiying candidate # 8.551 * * * * [progress]: [ 89 / 1611 ] simplifiying candidate # 8.551 * * * * [progress]: [ 90 / 1611 ] simplifiying candidate # 8.551 * * * * [progress]: [ 91 / 1611 ] simplifiying candidate # 8.552 * * * * [progress]: [ 92 / 1611 ] simplifiying candidate # 8.552 * * * * [progress]: [ 93 / 1611 ] simplifiying candidate # 8.552 * * * * [progress]: [ 94 / 1611 ] simplifiying candidate # 8.552 * * * * [progress]: [ 95 / 1611 ] simplifiying candidate # 8.552 * * * * [progress]: [ 96 / 1611 ] simplifiying candidate # 8.552 * * * * [progress]: [ 97 / 1611 ] simplifiying candidate # 8.552 * * * * [progress]: [ 98 / 1611 ] simplifiying candidate # 8.552 * * * * [progress]: [ 99 / 1611 ] simplifiying candidate # 8.552 * * * * [progress]: [ 100 / 1611 ] simplifiying candidate # 8.552 * * * * [progress]: [ 101 / 1611 ] simplifiying candidate # 8.552 * * * * [progress]: [ 102 / 1611 ] simplifiying candidate # 8.552 * * * * 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[progress]: [ 1597 / 1611 ] simplifiying candidate # 8.704 * * * * [progress]: [ 1598 / 1611 ] simplifiying candidate # 8.704 * * * * [progress]: [ 1599 / 1611 ] simplifiying candidate #real (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))> 8.704 * * * * [progress]: [ 1600 / 1611 ] simplifiying candidate # 8.704 * * * * [progress]: [ 1601 / 1611 ] simplifiying candidate # 8.704 * * * * [progress]: [ 1602 / 1611 ] simplifiying candidate # 8.705 * * * * [progress]: [ 1603 / 1611 ] simplifiying candidate # 8.705 * * * * [progress]: [ 1604 / 1611 ] simplifiying candidate # 8.705 * * * * [progress]: [ 1605 / 1611 ] simplifiying candidate # 8.705 * * * * [progress]: [ 1606 / 1611 ] simplifiying candidate # 8.705 * * * * [progress]: [ 1607 / 1611 ] simplifiying candidate # 8.706 * * * * [progress]: [ 1608 / 1611 ] simplifiying candidate # 8.706 * * * * [progress]: [ 1609 / 1611 ] simplifiying candidate # 8.706 * * * * [progress]: [ 1610 / 1611 ] simplifiying candidate # 8.706 * * * * [progress]: [ 1611 / 1611 ] simplifiying candidate # 8.758 * [simplify]: Simplifying: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) 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(- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 8.847 * * [simplify]: iteration 0: 1728 enodes 9.774 * * [simplify]: iteration complete: 2002 enodes 9.777 * * [simplify]: Extracting #0: cost 1206 inf + 0 9.784 * * [simplify]: Extracting #1: cost 1366 inf + 42 9.796 * * [simplify]: Extracting #2: cost 1480 inf + 1030 9.804 * * [simplify]: Extracting #3: cost 1478 inf + 4950 9.822 * * [simplify]: Extracting #4: cost 1363 inf + 55431 9.850 * * [simplify]: Extracting #5: cost 1062 inf + 220654 9.889 * * [simplify]: Extracting #6: cost 798 inf + 382302 9.984 * * [simplify]: Extracting #7: cost 548 inf + 555326 10.069 * * [simplify]: Extracting #8: cost 311 inf + 744460 10.223 * * [simplify]: Extracting #9: cost 149 inf + 884289 10.338 * * [simplify]: Extracting #10: cost 72 inf + 952676 10.449 * * [simplify]: Extracting #11: cost 37 inf + 980879 10.569 * * [simplify]: Extracting #12: cost 21 inf + 989015 10.713 * * [simplify]: Extracting #13: cost 17 inf + 990253 10.829 * * [simplify]: Extracting #14: cost 11 inf + 994390 10.984 * * [simplify]: Extracting #15: cost 6 inf + 999751 11.119 * * [simplify]: Extracting #16: cost 4 inf + 1001443 11.235 * * [simplify]: Extracting #17: cost 1 inf + 1004851 11.355 * * [simplify]: Extracting #18: cost 0 inf + 1006257 11.478 * [simplify]: Simplified to: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* n (* 2 PI))) (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (* n (* 2 PI)) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (* n (* 2 PI)) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- 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(/ k 2)) 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (sqrt k))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (sqrt k))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (/ k 2)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) 2) (sqrt k))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (/ k 2)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (/ k 2)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))) (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (pow n (- 1/2 (/ k 2))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1 (/ 1 (sqrt k)) (/ 1 (/ (sqrt k) (sqrt (* n (* 2 PI))))) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt 1)) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)) (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (- (fma 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (log (* n (* 2 PI))))) (* (log n) (* k k)))) (fma 1/8 (* (exp (* 1/2 (log (* n (* 2 PI))))) (* (* (log n) (log n)) (* k k))) (+ (exp (* 1/2 (log (* n (* 2 PI))))) (* 1/8 (* (* (log (* 2 PI)) (log (* 2 PI))) (* (exp (* 1/2 (log (* n (* 2 PI))))) (* k k))))))) (fma 1/2 (* (exp (* 1/2 (log (* n (* 2 PI))))) (* (log n) k)) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (log (* n (* 2 PI))))) k))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (fma +nan.0 (/ (* (sqrt 2) (* (* k k) (* (* (sqrt 1/2) (sqrt 1/2)) (log (* 2 PI))))) PI) (- (fma +nan.0 (/ (* (sqrt 1/2) (* k k)) PI) (- (fma +nan.0 (/ (* n (* (sqrt 1/2) k)) (* PI PI)) (- (fma +nan.0 (/ (* (log n) (* (sqrt 2) (* (* (sqrt 1/2) (sqrt 1/2)) (* k k)))) PI) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) k)) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n)))))))))))) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k k))) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (* +nan.0 (exp (- (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) (- (fma +nan.0 (* (sqrt 2) (* n (* PI k))) (- (fma +nan.0 (* (sqrt 2) (* n PI)) (- (fma +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k)))) (- (fma +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k)))) (- (* +nan.0 (* (sqrt 2) (* (* n n) (* PI PI))))))))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k (* k k))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) k) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k k)))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k k)) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 11.973 * * * [progress]: adding candidates to table 23.229 * * [progress]: iteration 3 / 4 23.229 * * * [progress]: picking best candidate 23.257 * * * * [pick]: Picked # 23.257 * * * [progress]: localizing error 23.297 * * * [progress]: generating rewritten candidates 23.297 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 1) 23.321 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1) 23.341 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 23.376 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1) 23.749 * * * [progress]: generating series expansions 23.749 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 1) 23.750 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 23.750 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 23.750 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 23.750 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 23.750 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 23.750 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 23.750 * [taylor]: Taking taylor expansion of 1/2 in k 23.750 * [backup-simplify]: Simplify 1/2 into 1/2 23.750 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 23.750 * [taylor]: Taking taylor expansion of 1/2 in k 23.750 * [backup-simplify]: Simplify 1/2 into 1/2 23.750 * [taylor]: Taking taylor expansion of k in k 23.750 * [backup-simplify]: Simplify 0 into 0 23.750 * [backup-simplify]: Simplify 1 into 1 23.751 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 23.751 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 23.751 * [taylor]: Taking taylor expansion of 2 in k 23.751 * [backup-simplify]: Simplify 2 into 2 23.751 * [taylor]: Taking taylor expansion of (* n PI) in k 23.751 * [taylor]: Taking taylor expansion of n in k 23.751 * [backup-simplify]: Simplify n into n 23.751 * [taylor]: Taking taylor expansion of PI in k 23.751 * [backup-simplify]: Simplify PI into PI 23.751 * [backup-simplify]: Simplify (* n PI) into (* n PI) 23.751 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 23.751 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 23.751 * [backup-simplify]: Simplify (* 1/2 0) into 0 23.751 * [backup-simplify]: Simplify (- 0) into 0 23.752 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 23.752 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 23.752 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 23.752 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 23.752 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 23.752 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 23.752 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 23.752 * [taylor]: Taking taylor expansion of 1/2 in n 23.752 * [backup-simplify]: Simplify 1/2 into 1/2 23.752 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 23.752 * [taylor]: Taking taylor expansion of 1/2 in n 23.752 * [backup-simplify]: Simplify 1/2 into 1/2 23.752 * [taylor]: Taking taylor expansion of k in n 23.752 * [backup-simplify]: Simplify k into k 23.752 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 23.752 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 23.752 * [taylor]: Taking taylor expansion of 2 in n 23.752 * [backup-simplify]: Simplify 2 into 2 23.752 * [taylor]: Taking taylor expansion of (* n PI) in n 23.752 * [taylor]: Taking taylor expansion of n in n 23.752 * [backup-simplify]: Simplify 0 into 0 23.752 * [backup-simplify]: Simplify 1 into 1 23.752 * [taylor]: Taking taylor expansion of PI in n 23.752 * [backup-simplify]: Simplify PI into PI 23.753 * [backup-simplify]: Simplify (* 0 PI) into 0 23.753 * [backup-simplify]: Simplify (* 2 0) into 0 23.754 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 23.755 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 23.755 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 23.756 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 23.756 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 23.756 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 23.757 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 23.758 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 23.760 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 23.760 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 23.760 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 23.760 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 23.760 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 23.760 * [taylor]: Taking taylor expansion of 1/2 in n 23.760 * [backup-simplify]: Simplify 1/2 into 1/2 23.760 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 23.760 * [taylor]: Taking taylor expansion of 1/2 in n 23.760 * [backup-simplify]: Simplify 1/2 into 1/2 23.760 * [taylor]: Taking taylor expansion of k in n 23.760 * [backup-simplify]: Simplify k into k 23.760 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 23.760 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 23.760 * [taylor]: Taking taylor expansion of 2 in n 23.760 * [backup-simplify]: Simplify 2 into 2 23.760 * [taylor]: Taking taylor expansion of (* n PI) in n 23.760 * [taylor]: Taking taylor expansion of n in n 23.760 * [backup-simplify]: Simplify 0 into 0 23.760 * [backup-simplify]: Simplify 1 into 1 23.760 * [taylor]: Taking taylor expansion of PI in n 23.760 * [backup-simplify]: Simplify PI into PI 23.761 * [backup-simplify]: Simplify (* 0 PI) into 0 23.761 * [backup-simplify]: Simplify (* 2 0) into 0 23.763 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 23.764 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 23.766 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 23.766 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 23.766 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 23.766 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 23.767 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 23.769 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 23.770 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 23.770 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 23.770 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 23.770 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 23.770 * [taylor]: Taking taylor expansion of 1/2 in k 23.770 * [backup-simplify]: Simplify 1/2 into 1/2 23.770 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 23.770 * [taylor]: Taking taylor expansion of 1/2 in k 23.770 * [backup-simplify]: Simplify 1/2 into 1/2 23.770 * [taylor]: Taking taylor expansion of k in k 23.770 * [backup-simplify]: Simplify 0 into 0 23.770 * [backup-simplify]: Simplify 1 into 1 23.770 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 23.771 * [taylor]: Taking taylor expansion of (log n) in k 23.771 * [taylor]: Taking taylor expansion of n in k 23.771 * [backup-simplify]: Simplify n into n 23.771 * [backup-simplify]: Simplify (log n) into (log n) 23.771 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 23.771 * [taylor]: Taking taylor expansion of (* 2 PI) in k 23.771 * [taylor]: Taking taylor expansion of 2 in k 23.771 * [backup-simplify]: Simplify 2 into 2 23.771 * [taylor]: Taking taylor expansion of PI in k 23.771 * [backup-simplify]: Simplify PI into PI 23.771 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 23.772 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 23.773 * [backup-simplify]: Simplify (* 1/2 0) into 0 23.773 * [backup-simplify]: Simplify (- 0) into 0 23.774 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 23.775 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 23.776 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 23.777 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 23.778 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 23.779 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 23.780 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 23.782 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 23.783 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 23.783 * [backup-simplify]: Simplify (- 0) into 0 23.784 * [backup-simplify]: Simplify (+ 0 0) into 0 23.785 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 23.785 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 23.787 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 23.787 * [taylor]: Taking taylor expansion of 0 in k 23.787 * [backup-simplify]: Simplify 0 into 0 23.787 * [backup-simplify]: Simplify 0 into 0 23.787 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 23.788 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 23.789 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 23.789 * [backup-simplify]: Simplify (+ 0 0) into 0 23.789 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 23.790 * [backup-simplify]: Simplify (- 1/2) into -1/2 23.790 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 23.804 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 23.806 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 23.808 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 23.809 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 23.810 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 23.811 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 23.812 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 23.812 * [backup-simplify]: Simplify (- 0) into 0 23.813 * [backup-simplify]: Simplify (+ 0 0) into 0 23.813 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 23.814 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 23.816 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 23.816 * [taylor]: Taking taylor expansion of 0 in k 23.816 * [backup-simplify]: Simplify 0 into 0 23.816 * [backup-simplify]: Simplify 0 into 0 23.816 * [backup-simplify]: Simplify 0 into 0 23.817 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 23.818 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 23.820 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 23.820 * [backup-simplify]: Simplify (+ 0 0) into 0 23.820 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 23.821 * [backup-simplify]: Simplify (- 0) into 0 23.821 * [backup-simplify]: Simplify (+ 0 0) into 0 23.822 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 23.824 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 23.827 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 23.836 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 23.837 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 23.837 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 23.837 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 23.837 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 23.837 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 23.837 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 23.837 * [taylor]: Taking taylor expansion of 1/2 in k 23.837 * [backup-simplify]: Simplify 1/2 into 1/2 23.837 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 23.837 * [taylor]: Taking taylor expansion of 1/2 in k 23.837 * [backup-simplify]: Simplify 1/2 into 1/2 23.837 * [taylor]: Taking taylor expansion of (/ 1 k) in k 23.837 * [taylor]: Taking taylor expansion of k in k 23.837 * [backup-simplify]: Simplify 0 into 0 23.837 * [backup-simplify]: Simplify 1 into 1 23.837 * [backup-simplify]: Simplify (/ 1 1) into 1 23.837 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 23.837 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 23.837 * [taylor]: Taking taylor expansion of 2 in k 23.837 * [backup-simplify]: Simplify 2 into 2 23.837 * [taylor]: Taking taylor expansion of (/ PI n) in k 23.837 * [taylor]: Taking taylor expansion of PI in k 23.837 * [backup-simplify]: Simplify PI into PI 23.837 * [taylor]: Taking taylor expansion of n in k 23.837 * [backup-simplify]: Simplify n into n 23.837 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 23.837 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 23.837 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 23.838 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 23.838 * [backup-simplify]: Simplify (- 1/2) into -1/2 23.838 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 23.838 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 23.838 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 23.838 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 23.838 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 23.838 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 23.838 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 23.838 * [taylor]: Taking taylor expansion of 1/2 in n 23.838 * [backup-simplify]: Simplify 1/2 into 1/2 23.838 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 23.838 * [taylor]: Taking taylor expansion of 1/2 in n 23.838 * [backup-simplify]: Simplify 1/2 into 1/2 23.838 * [taylor]: Taking taylor expansion of (/ 1 k) in n 23.838 * [taylor]: Taking taylor expansion of k in n 23.838 * [backup-simplify]: Simplify k into k 23.839 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 23.839 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 23.839 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 23.839 * [taylor]: Taking taylor expansion of 2 in n 23.839 * [backup-simplify]: Simplify 2 into 2 23.839 * [taylor]: Taking taylor expansion of (/ PI n) in n 23.839 * [taylor]: Taking taylor expansion of PI in n 23.839 * [backup-simplify]: Simplify PI into PI 23.839 * [taylor]: Taking taylor expansion of n in n 23.839 * [backup-simplify]: Simplify 0 into 0 23.839 * [backup-simplify]: Simplify 1 into 1 23.839 * [backup-simplify]: Simplify (/ PI 1) into PI 23.839 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 23.840 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 23.840 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 23.840 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 23.840 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 23.841 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 23.842 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 23.842 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 23.843 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 23.843 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 23.843 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 23.843 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 23.843 * [taylor]: Taking taylor expansion of 1/2 in n 23.843 * [backup-simplify]: Simplify 1/2 into 1/2 23.843 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 23.843 * [taylor]: Taking taylor expansion of 1/2 in n 23.843 * [backup-simplify]: Simplify 1/2 into 1/2 23.843 * [taylor]: Taking taylor expansion of (/ 1 k) in n 23.843 * [taylor]: Taking taylor expansion of k in n 23.843 * [backup-simplify]: Simplify k into k 23.843 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 23.843 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 23.843 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 23.843 * [taylor]: Taking taylor expansion of 2 in n 23.843 * [backup-simplify]: Simplify 2 into 2 23.843 * [taylor]: Taking taylor expansion of (/ PI n) in n 23.843 * [taylor]: Taking taylor expansion of PI in n 23.843 * [backup-simplify]: Simplify PI into PI 23.843 * [taylor]: Taking taylor expansion of n in n 23.843 * [backup-simplify]: Simplify 0 into 0 23.843 * [backup-simplify]: Simplify 1 into 1 23.843 * [backup-simplify]: Simplify (/ PI 1) into PI 23.844 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 23.844 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 23.844 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 23.844 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 23.844 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 23.845 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 23.846 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 23.847 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 23.847 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 23.847 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 23.847 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 23.847 * [taylor]: Taking taylor expansion of 1/2 in k 23.847 * [backup-simplify]: Simplify 1/2 into 1/2 23.847 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 23.847 * [taylor]: Taking taylor expansion of 1/2 in k 23.847 * [backup-simplify]: Simplify 1/2 into 1/2 23.847 * [taylor]: Taking taylor expansion of (/ 1 k) in k 23.847 * [taylor]: Taking taylor expansion of k in k 23.847 * [backup-simplify]: Simplify 0 into 0 23.847 * [backup-simplify]: Simplify 1 into 1 23.847 * [backup-simplify]: Simplify (/ 1 1) into 1 23.847 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 23.847 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 23.847 * [taylor]: Taking taylor expansion of (* 2 PI) in k 23.847 * [taylor]: Taking taylor expansion of 2 in k 23.847 * [backup-simplify]: Simplify 2 into 2 23.847 * [taylor]: Taking taylor expansion of PI in k 23.847 * [backup-simplify]: Simplify PI into PI 23.848 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 23.848 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 23.848 * [taylor]: Taking taylor expansion of (log n) in k 23.848 * [taylor]: Taking taylor expansion of n in k 23.848 * [backup-simplify]: Simplify n into n 23.848 * [backup-simplify]: Simplify (log n) into (log n) 23.849 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 23.849 * [backup-simplify]: Simplify (- 1/2) into -1/2 23.849 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 23.849 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 23.850 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 23.851 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 23.851 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 23.852 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 23.853 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 23.853 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 23.854 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 23.854 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 23.855 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 23.855 * [backup-simplify]: Simplify (- 0) into 0 23.855 * [backup-simplify]: Simplify (+ 0 0) into 0 23.856 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 23.857 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 23.858 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 23.858 * [taylor]: Taking taylor expansion of 0 in k 23.858 * [backup-simplify]: Simplify 0 into 0 23.858 * [backup-simplify]: Simplify 0 into 0 23.858 * [backup-simplify]: Simplify 0 into 0 23.859 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.859 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 23.861 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 23.861 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 23.862 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 23.862 * [backup-simplify]: Simplify (- 0) into 0 23.862 * [backup-simplify]: Simplify (+ 0 0) into 0 23.863 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 23.864 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 23.866 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 23.866 * [taylor]: Taking taylor expansion of 0 in k 23.866 * [backup-simplify]: Simplify 0 into 0 23.866 * [backup-simplify]: Simplify 0 into 0 23.866 * [backup-simplify]: Simplify 0 into 0 23.866 * [backup-simplify]: Simplify 0 into 0 23.866 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.867 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 23.871 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 23.871 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 23.872 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 23.872 * [backup-simplify]: Simplify (- 0) into 0 23.872 * [backup-simplify]: Simplify (+ 0 0) into 0 23.873 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 23.874 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 23.876 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 23.876 * [taylor]: Taking taylor expansion of 0 in k 23.876 * [backup-simplify]: Simplify 0 into 0 23.876 * [backup-simplify]: Simplify 0 into 0 23.877 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 23.877 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 23.877 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 23.877 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 23.877 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 23.877 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 23.877 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 23.877 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 23.877 * [taylor]: Taking taylor expansion of 1/2 in k 23.877 * [backup-simplify]: Simplify 1/2 into 1/2 23.877 * [taylor]: Taking taylor expansion of (/ 1 k) in k 23.877 * [taylor]: Taking taylor expansion of k in k 23.877 * [backup-simplify]: Simplify 0 into 0 23.878 * [backup-simplify]: Simplify 1 into 1 23.878 * [backup-simplify]: Simplify (/ 1 1) into 1 23.878 * [taylor]: Taking taylor expansion of 1/2 in k 23.878 * [backup-simplify]: Simplify 1/2 into 1/2 23.878 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 23.878 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 23.878 * [taylor]: Taking taylor expansion of -2 in k 23.878 * [backup-simplify]: Simplify -2 into -2 23.878 * [taylor]: Taking taylor expansion of (/ PI n) in k 23.878 * [taylor]: Taking taylor expansion of PI in k 23.878 * [backup-simplify]: Simplify PI into PI 23.878 * [taylor]: Taking taylor expansion of n in k 23.878 * [backup-simplify]: Simplify n into n 23.878 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 23.878 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 23.878 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 23.878 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 23.879 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 23.879 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 23.879 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 23.879 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 23.879 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 23.879 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 23.879 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 23.879 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 23.879 * [taylor]: Taking taylor expansion of 1/2 in n 23.879 * [backup-simplify]: Simplify 1/2 into 1/2 23.879 * [taylor]: Taking taylor expansion of (/ 1 k) in n 23.879 * [taylor]: Taking taylor expansion of k in n 23.879 * [backup-simplify]: Simplify k into k 23.879 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 23.879 * [taylor]: Taking taylor expansion of 1/2 in n 23.879 * [backup-simplify]: Simplify 1/2 into 1/2 23.879 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 23.879 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 23.879 * [taylor]: Taking taylor expansion of -2 in n 23.879 * [backup-simplify]: Simplify -2 into -2 23.879 * [taylor]: Taking taylor expansion of (/ PI n) in n 23.879 * [taylor]: Taking taylor expansion of PI in n 23.879 * [backup-simplify]: Simplify PI into PI 23.879 * [taylor]: Taking taylor expansion of n in n 23.879 * [backup-simplify]: Simplify 0 into 0 23.879 * [backup-simplify]: Simplify 1 into 1 23.880 * [backup-simplify]: Simplify (/ PI 1) into PI 23.880 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 23.880 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 23.881 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 23.881 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 23.881 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 23.882 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 23.883 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 23.883 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 23.883 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 23.883 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 23.883 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 23.883 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 23.883 * [taylor]: Taking taylor expansion of 1/2 in n 23.883 * [backup-simplify]: Simplify 1/2 into 1/2 23.883 * [taylor]: Taking taylor expansion of (/ 1 k) in n 23.883 * [taylor]: Taking taylor expansion of k in n 23.883 * [backup-simplify]: Simplify k into k 23.883 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 23.883 * [taylor]: Taking taylor expansion of 1/2 in n 23.883 * [backup-simplify]: Simplify 1/2 into 1/2 23.883 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 23.883 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 23.883 * [taylor]: Taking taylor expansion of -2 in n 23.883 * [backup-simplify]: Simplify -2 into -2 23.883 * [taylor]: Taking taylor expansion of (/ PI n) in n 23.883 * [taylor]: Taking taylor expansion of PI in n 23.883 * [backup-simplify]: Simplify PI into PI 23.883 * [taylor]: Taking taylor expansion of n in n 23.883 * [backup-simplify]: Simplify 0 into 0 23.883 * [backup-simplify]: Simplify 1 into 1 23.884 * [backup-simplify]: Simplify (/ PI 1) into PI 23.884 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 23.886 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 23.886 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 23.886 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 23.887 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 23.888 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 23.890 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 23.890 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 23.890 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 23.890 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 23.890 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 23.890 * [taylor]: Taking taylor expansion of 1/2 in k 23.890 * [backup-simplify]: Simplify 1/2 into 1/2 23.890 * [taylor]: Taking taylor expansion of (/ 1 k) in k 23.890 * [taylor]: Taking taylor expansion of k in k 23.890 * [backup-simplify]: Simplify 0 into 0 23.890 * [backup-simplify]: Simplify 1 into 1 23.890 * [backup-simplify]: Simplify (/ 1 1) into 1 23.891 * [taylor]: Taking taylor expansion of 1/2 in k 23.891 * [backup-simplify]: Simplify 1/2 into 1/2 23.891 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 23.891 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 23.891 * [taylor]: Taking taylor expansion of (* -2 PI) in k 23.891 * [taylor]: Taking taylor expansion of -2 in k 23.891 * [backup-simplify]: Simplify -2 into -2 23.891 * [taylor]: Taking taylor expansion of PI in k 23.891 * [backup-simplify]: Simplify PI into PI 23.891 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 23.892 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 23.892 * [taylor]: Taking taylor expansion of (log n) in k 23.893 * [taylor]: Taking taylor expansion of n in k 23.893 * [backup-simplify]: Simplify n into n 23.893 * [backup-simplify]: Simplify (log n) into (log n) 23.893 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 23.894 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 23.894 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 23.895 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 23.896 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 23.897 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 23.907 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 23.908 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 23.909 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 23.911 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 23.911 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 23.912 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 23.912 * [backup-simplify]: Simplify (+ 0 0) into 0 23.913 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 23.914 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 23.915 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 23.915 * [taylor]: Taking taylor expansion of 0 in k 23.915 * [backup-simplify]: Simplify 0 into 0 23.915 * [backup-simplify]: Simplify 0 into 0 23.915 * [backup-simplify]: Simplify 0 into 0 23.915 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.916 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 23.919 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 23.919 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 23.920 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 23.920 * [backup-simplify]: Simplify (+ 0 0) into 0 23.921 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 23.922 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 23.924 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 23.924 * [taylor]: Taking taylor expansion of 0 in k 23.924 * [backup-simplify]: Simplify 0 into 0 23.924 * [backup-simplify]: Simplify 0 into 0 23.924 * [backup-simplify]: Simplify 0 into 0 23.924 * [backup-simplify]: Simplify 0 into 0 23.924 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.925 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 23.928 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 23.928 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 23.929 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 23.929 * [backup-simplify]: Simplify (+ 0 0) into 0 23.930 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 23.931 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 23.933 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 23.933 * [taylor]: Taking taylor expansion of 0 in k 23.933 * [backup-simplify]: Simplify 0 into 0 23.933 * [backup-simplify]: Simplify 0 into 0 23.934 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 23.934 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1) 23.934 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 23.934 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 23.934 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 23.934 * [taylor]: Taking taylor expansion of 2 in n 23.934 * [backup-simplify]: Simplify 2 into 2 23.934 * [taylor]: Taking taylor expansion of (* n PI) in n 23.934 * [taylor]: Taking taylor expansion of n in n 23.934 * [backup-simplify]: Simplify 0 into 0 23.934 * [backup-simplify]: Simplify 1 into 1 23.934 * [taylor]: Taking taylor expansion of PI in n 23.934 * [backup-simplify]: Simplify PI into PI 23.934 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 23.934 * [taylor]: Taking taylor expansion of 2 in n 23.934 * [backup-simplify]: Simplify 2 into 2 23.935 * [taylor]: Taking taylor expansion of (* n PI) in n 23.935 * [taylor]: Taking taylor expansion of n in n 23.935 * [backup-simplify]: Simplify 0 into 0 23.935 * [backup-simplify]: Simplify 1 into 1 23.935 * [taylor]: Taking taylor expansion of PI in n 23.935 * [backup-simplify]: Simplify PI into PI 23.935 * [backup-simplify]: Simplify (* 0 PI) into 0 23.935 * [backup-simplify]: Simplify (* 2 0) into 0 23.935 * [backup-simplify]: Simplify 0 into 0 23.936 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 23.937 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 23.937 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 23.938 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 23.939 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 23.939 * [backup-simplify]: Simplify 0 into 0 23.939 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 23.940 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 23.940 * [backup-simplify]: Simplify 0 into 0 23.941 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 23.942 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 23.942 * [backup-simplify]: Simplify 0 into 0 23.943 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 23.943 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 23.943 * [backup-simplify]: Simplify 0 into 0 23.945 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 23.947 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 23.947 * [backup-simplify]: Simplify 0 into 0 23.949 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 23.951 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 23.951 * [backup-simplify]: Simplify 0 into 0 23.952 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 23.952 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 23.952 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 23.952 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 23.952 * [taylor]: Taking taylor expansion of 2 in n 23.952 * [backup-simplify]: Simplify 2 into 2 23.952 * [taylor]: Taking taylor expansion of (/ PI n) in n 23.952 * [taylor]: Taking taylor expansion of PI in n 23.953 * [backup-simplify]: Simplify PI into PI 23.953 * [taylor]: Taking taylor expansion of n in n 23.953 * [backup-simplify]: Simplify 0 into 0 23.953 * [backup-simplify]: Simplify 1 into 1 23.953 * [backup-simplify]: Simplify (/ PI 1) into PI 23.953 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 23.953 * [taylor]: Taking taylor expansion of 2 in n 23.953 * [backup-simplify]: Simplify 2 into 2 23.953 * [taylor]: Taking taylor expansion of (/ PI n) in n 23.953 * [taylor]: Taking taylor expansion of PI in n 23.953 * [backup-simplify]: Simplify PI into PI 23.953 * [taylor]: Taking taylor expansion of n in n 23.953 * [backup-simplify]: Simplify 0 into 0 23.953 * [backup-simplify]: Simplify 1 into 1 23.954 * [backup-simplify]: Simplify (/ PI 1) into PI 23.954 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 23.955 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 23.956 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 23.957 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 23.957 * [backup-simplify]: Simplify 0 into 0 23.958 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.959 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 23.959 * [backup-simplify]: Simplify 0 into 0 23.960 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.961 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 23.961 * [backup-simplify]: Simplify 0 into 0 23.963 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.964 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 23.964 * [backup-simplify]: Simplify 0 into 0 23.964 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.965 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 23.965 * [backup-simplify]: Simplify 0 into 0 23.966 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.967 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 23.967 * [backup-simplify]: Simplify 0 into 0 23.967 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 23.968 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 23.968 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 23.968 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 23.968 * [taylor]: Taking taylor expansion of -2 in n 23.968 * [backup-simplify]: Simplify -2 into -2 23.968 * [taylor]: Taking taylor expansion of (/ PI n) in n 23.968 * [taylor]: Taking taylor expansion of PI in n 23.968 * [backup-simplify]: Simplify PI into PI 23.968 * [taylor]: Taking taylor expansion of n in n 23.968 * [backup-simplify]: Simplify 0 into 0 23.968 * [backup-simplify]: Simplify 1 into 1 23.968 * [backup-simplify]: Simplify (/ PI 1) into PI 23.968 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 23.968 * [taylor]: Taking taylor expansion of -2 in n 23.968 * [backup-simplify]: Simplify -2 into -2 23.968 * [taylor]: Taking taylor expansion of (/ PI n) in n 23.968 * [taylor]: Taking taylor expansion of PI in n 23.968 * [backup-simplify]: Simplify PI into PI 23.968 * [taylor]: Taking taylor expansion of n in n 23.968 * [backup-simplify]: Simplify 0 into 0 23.968 * [backup-simplify]: Simplify 1 into 1 23.969 * [backup-simplify]: Simplify (/ PI 1) into PI 23.969 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 23.970 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 23.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 23.971 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 23.971 * [backup-simplify]: Simplify 0 into 0 23.971 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.972 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 23.972 * [backup-simplify]: Simplify 0 into 0 23.973 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.973 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 23.973 * [backup-simplify]: Simplify 0 into 0 23.974 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.975 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 23.975 * [backup-simplify]: Simplify 0 into 0 23.975 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.976 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 23.976 * [backup-simplify]: Simplify 0 into 0 23.977 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 23.978 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 23.978 * [backup-simplify]: Simplify 0 into 0 23.978 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 23.978 * * * * [progress]: [ 3 / 4 ] generating series at (2) 23.979 * [backup-simplify]: Simplify (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))) into (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 23.979 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 23.979 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 23.979 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 23.979 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 23.979 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 23.979 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 23.979 * [taylor]: Taking taylor expansion of 1/2 in k 23.979 * [backup-simplify]: Simplify 1/2 into 1/2 23.979 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 23.979 * [taylor]: Taking taylor expansion of 1/2 in k 23.979 * [backup-simplify]: Simplify 1/2 into 1/2 23.979 * [taylor]: Taking taylor expansion of k in k 23.979 * [backup-simplify]: Simplify 0 into 0 23.979 * [backup-simplify]: Simplify 1 into 1 23.979 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 23.979 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 23.979 * [taylor]: Taking taylor expansion of 2 in k 23.979 * [backup-simplify]: Simplify 2 into 2 23.979 * [taylor]: Taking taylor expansion of (* n PI) in k 23.979 * [taylor]: Taking taylor expansion of n in k 23.979 * [backup-simplify]: Simplify n into n 23.979 * [taylor]: Taking taylor expansion of PI in k 23.979 * [backup-simplify]: Simplify PI into PI 23.979 * [backup-simplify]: Simplify (* n PI) into (* n PI) 23.979 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 23.979 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 23.980 * [backup-simplify]: Simplify (* 1/2 0) into 0 23.980 * [backup-simplify]: Simplify (- 0) into 0 23.980 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 23.980 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 23.980 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 23.980 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 23.980 * [taylor]: Taking taylor expansion of (/ 1 k) in k 23.980 * [taylor]: Taking taylor expansion of k in k 23.980 * [backup-simplify]: Simplify 0 into 0 23.980 * [backup-simplify]: Simplify 1 into 1 23.981 * [backup-simplify]: Simplify (/ 1 1) into 1 23.981 * [backup-simplify]: Simplify (sqrt 0) into 0 23.982 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 23.982 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 23.982 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 23.982 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 23.982 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 23.982 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 23.982 * [taylor]: Taking taylor expansion of 1/2 in n 23.982 * [backup-simplify]: Simplify 1/2 into 1/2 23.982 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 23.982 * [taylor]: Taking taylor expansion of 1/2 in n 23.982 * [backup-simplify]: Simplify 1/2 into 1/2 23.982 * [taylor]: Taking taylor expansion of k in n 23.982 * [backup-simplify]: Simplify k into k 23.982 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 23.982 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 23.982 * [taylor]: Taking taylor expansion of 2 in n 23.982 * [backup-simplify]: Simplify 2 into 2 23.982 * [taylor]: Taking taylor expansion of (* n PI) in n 23.982 * [taylor]: Taking taylor expansion of n in n 23.982 * [backup-simplify]: Simplify 0 into 0 23.982 * [backup-simplify]: Simplify 1 into 1 23.982 * [taylor]: Taking taylor expansion of PI in n 23.982 * [backup-simplify]: Simplify PI into PI 23.982 * [backup-simplify]: Simplify (* 0 PI) into 0 23.983 * [backup-simplify]: Simplify (* 2 0) into 0 23.984 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 23.985 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 23.985 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 23.985 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 23.985 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 23.985 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 23.986 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 23.987 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 23.988 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 23.988 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 23.988 * [taylor]: Taking taylor expansion of (/ 1 k) in n 23.988 * [taylor]: Taking taylor expansion of k in n 23.988 * [backup-simplify]: Simplify k into k 23.988 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 23.988 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 23.988 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 23.988 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 23.988 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 23.988 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 23.988 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 23.988 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 23.988 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 23.988 * [taylor]: Taking taylor expansion of 1/2 in n 23.988 * [backup-simplify]: Simplify 1/2 into 1/2 23.988 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 23.988 * [taylor]: Taking taylor expansion of 1/2 in n 23.988 * [backup-simplify]: Simplify 1/2 into 1/2 23.988 * [taylor]: Taking taylor expansion of k in n 23.988 * [backup-simplify]: Simplify k into k 23.988 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 23.988 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 23.988 * [taylor]: Taking taylor expansion of 2 in n 23.988 * [backup-simplify]: Simplify 2 into 2 23.989 * [taylor]: Taking taylor expansion of (* n PI) in n 23.989 * [taylor]: Taking taylor expansion of n in n 23.989 * [backup-simplify]: Simplify 0 into 0 23.989 * [backup-simplify]: Simplify 1 into 1 23.989 * [taylor]: Taking taylor expansion of PI in n 23.989 * [backup-simplify]: Simplify PI into PI 23.989 * [backup-simplify]: Simplify (* 0 PI) into 0 23.989 * [backup-simplify]: Simplify (* 2 0) into 0 23.990 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 23.991 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 23.992 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 23.992 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 23.992 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 23.992 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 23.993 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 23.993 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 23.994 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 23.994 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 23.994 * [taylor]: Taking taylor expansion of (/ 1 k) in n 23.994 * [taylor]: Taking taylor expansion of k in n 23.994 * [backup-simplify]: Simplify k into k 23.994 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 23.994 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 23.994 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 23.994 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 23.995 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 23.995 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 23.995 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 23.995 * [taylor]: Taking taylor expansion of (/ 1 k) in k 23.995 * [taylor]: Taking taylor expansion of k in k 23.995 * [backup-simplify]: Simplify 0 into 0 23.995 * [backup-simplify]: Simplify 1 into 1 23.996 * [backup-simplify]: Simplify (/ 1 1) into 1 23.996 * [backup-simplify]: Simplify (sqrt 0) into 0 23.997 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 23.997 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 23.997 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 23.997 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 23.997 * [taylor]: Taking taylor expansion of 1/2 in k 23.997 * [backup-simplify]: Simplify 1/2 into 1/2 23.997 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 23.997 * [taylor]: Taking taylor expansion of 1/2 in k 23.997 * [backup-simplify]: Simplify 1/2 into 1/2 23.997 * [taylor]: Taking taylor expansion of k in k 23.997 * [backup-simplify]: Simplify 0 into 0 23.997 * [backup-simplify]: Simplify 1 into 1 23.997 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 23.997 * [taylor]: Taking taylor expansion of (log n) in k 23.997 * [taylor]: Taking taylor expansion of n in k 23.997 * [backup-simplify]: Simplify n into n 23.997 * [backup-simplify]: Simplify (log n) into (log n) 23.997 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 23.997 * [taylor]: Taking taylor expansion of (* 2 PI) in k 23.997 * [taylor]: Taking taylor expansion of 2 in k 23.997 * [backup-simplify]: Simplify 2 into 2 23.997 * [taylor]: Taking taylor expansion of PI in k 23.997 * [backup-simplify]: Simplify PI into PI 23.997 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 23.998 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 23.998 * [backup-simplify]: Simplify (* 1/2 0) into 0 23.998 * [backup-simplify]: Simplify (- 0) into 0 23.999 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 23.999 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 24.000 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 24.001 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 24.002 * [backup-simplify]: Simplify (* 0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into 0 24.002 * [backup-simplify]: Simplify 0 into 0 24.003 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 24.004 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 24.006 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 24.007 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 24.007 * [backup-simplify]: Simplify (- 0) into 0 24.007 * [backup-simplify]: Simplify (+ 0 0) into 0 24.015 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 24.017 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 24.018 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 24.019 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 24.020 * [taylor]: Taking taylor expansion of 0 in k 24.020 * [backup-simplify]: Simplify 0 into 0 24.020 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 24.021 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 24.022 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 24.022 * [backup-simplify]: Simplify (+ 0 0) into 0 24.022 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 24.023 * [backup-simplify]: Simplify (- 1/2) into -1/2 24.023 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 24.024 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 24.026 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 24.028 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 24.029 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 24.029 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 24.030 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 24.030 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 24.031 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 24.033 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 24.033 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 24.034 * [backup-simplify]: Simplify (- 0) into 0 24.034 * [backup-simplify]: Simplify (+ 0 0) into 0 24.035 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 24.036 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 24.037 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 24.038 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 24.038 * [taylor]: Taking taylor expansion of 0 in k 24.038 * [backup-simplify]: Simplify 0 into 0 24.038 * [backup-simplify]: Simplify 0 into 0 24.039 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 24.040 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 24.042 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 24.042 * [backup-simplify]: Simplify (+ 0 0) into 0 24.043 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 24.043 * [backup-simplify]: Simplify (- 0) into 0 24.043 * [backup-simplify]: Simplify (+ 0 0) into 0 24.044 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 24.047 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 24.047 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 24.049 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 24.054 * [backup-simplify]: Simplify (+ (* 0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))) 24.057 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 24.058 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 24.058 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 24.059 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 24.060 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 24.063 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 24.065 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 24.065 * [backup-simplify]: Simplify (- 0) into 0 24.065 * [backup-simplify]: Simplify (+ 0 0) into 0 24.067 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 24.069 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 24.072 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 24.074 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 24.074 * [taylor]: Taking taylor expansion of 0 in k 24.074 * [backup-simplify]: Simplify 0 into 0 24.074 * [backup-simplify]: Simplify 0 into 0 24.074 * [backup-simplify]: Simplify 0 into 0 24.077 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 24.078 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 24.084 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 24.084 * [backup-simplify]: Simplify (+ 0 0) into 0 24.085 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 24.086 * [backup-simplify]: Simplify (- 0) into 0 24.086 * [backup-simplify]: Simplify (+ 0 0) into 0 24.088 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 24.095 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 24.096 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 24.100 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 24.118 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))))))))))))) 24.139 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 24.157 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 24.158 * [backup-simplify]: Simplify (/ (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 24.158 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 24.158 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 24.158 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 24.158 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 24.158 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 24.158 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 24.158 * [taylor]: Taking taylor expansion of 1/2 in k 24.158 * [backup-simplify]: Simplify 1/2 into 1/2 24.158 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 24.158 * [taylor]: Taking taylor expansion of 1/2 in k 24.158 * [backup-simplify]: Simplify 1/2 into 1/2 24.158 * [taylor]: Taking taylor expansion of (/ 1 k) in k 24.158 * [taylor]: Taking taylor expansion of k in k 24.158 * [backup-simplify]: Simplify 0 into 0 24.158 * [backup-simplify]: Simplify 1 into 1 24.158 * [backup-simplify]: Simplify (/ 1 1) into 1 24.158 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 24.158 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 24.158 * [taylor]: Taking taylor expansion of 2 in k 24.158 * [backup-simplify]: Simplify 2 into 2 24.158 * [taylor]: Taking taylor expansion of (/ PI n) in k 24.158 * [taylor]: Taking taylor expansion of PI in k 24.158 * [backup-simplify]: Simplify PI into PI 24.158 * [taylor]: Taking taylor expansion of n in k 24.158 * [backup-simplify]: Simplify n into n 24.159 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 24.159 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 24.159 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 24.159 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 24.159 * [backup-simplify]: Simplify (- 1/2) into -1/2 24.159 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 24.159 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 24.160 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 24.160 * [taylor]: Taking taylor expansion of (sqrt k) in k 24.160 * [taylor]: Taking taylor expansion of k in k 24.160 * [backup-simplify]: Simplify 0 into 0 24.160 * [backup-simplify]: Simplify 1 into 1 24.160 * [backup-simplify]: Simplify (sqrt 0) into 0 24.161 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 24.161 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 24.161 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 24.161 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 24.161 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 24.161 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 24.161 * [taylor]: Taking taylor expansion of 1/2 in n 24.161 * [backup-simplify]: Simplify 1/2 into 1/2 24.161 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 24.161 * [taylor]: Taking taylor expansion of 1/2 in n 24.161 * [backup-simplify]: Simplify 1/2 into 1/2 24.161 * [taylor]: Taking taylor expansion of (/ 1 k) in n 24.161 * [taylor]: Taking taylor expansion of k in n 24.161 * [backup-simplify]: Simplify k into k 24.161 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 24.161 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 24.161 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 24.161 * [taylor]: Taking taylor expansion of 2 in n 24.161 * [backup-simplify]: Simplify 2 into 2 24.161 * [taylor]: Taking taylor expansion of (/ PI n) in n 24.161 * [taylor]: Taking taylor expansion of PI in n 24.161 * [backup-simplify]: Simplify PI into PI 24.161 * [taylor]: Taking taylor expansion of n in n 24.161 * [backup-simplify]: Simplify 0 into 0 24.161 * [backup-simplify]: Simplify 1 into 1 24.161 * [backup-simplify]: Simplify (/ PI 1) into PI 24.162 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 24.162 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 24.162 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 24.163 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 24.163 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 24.163 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 24.164 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 24.165 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 24.165 * [taylor]: Taking taylor expansion of (sqrt k) in n 24.165 * [taylor]: Taking taylor expansion of k in n 24.165 * [backup-simplify]: Simplify k into k 24.165 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 24.165 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 24.165 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 24.165 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 24.165 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 24.165 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 24.165 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 24.165 * [taylor]: Taking taylor expansion of 1/2 in n 24.165 * [backup-simplify]: Simplify 1/2 into 1/2 24.165 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 24.165 * [taylor]: Taking taylor expansion of 1/2 in n 24.165 * [backup-simplify]: Simplify 1/2 into 1/2 24.165 * [taylor]: Taking taylor expansion of (/ 1 k) in n 24.165 * [taylor]: Taking taylor expansion of k in n 24.165 * [backup-simplify]: Simplify k into k 24.165 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 24.165 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 24.165 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 24.165 * [taylor]: Taking taylor expansion of 2 in n 24.165 * [backup-simplify]: Simplify 2 into 2 24.165 * [taylor]: Taking taylor expansion of (/ PI n) in n 24.165 * [taylor]: Taking taylor expansion of PI in n 24.165 * [backup-simplify]: Simplify PI into PI 24.165 * [taylor]: Taking taylor expansion of n in n 24.165 * [backup-simplify]: Simplify 0 into 0 24.165 * [backup-simplify]: Simplify 1 into 1 24.166 * [backup-simplify]: Simplify (/ PI 1) into PI 24.166 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 24.167 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 24.167 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 24.167 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 24.167 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 24.168 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 24.168 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 24.169 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 24.169 * [taylor]: Taking taylor expansion of (sqrt k) in n 24.169 * [taylor]: Taking taylor expansion of k in n 24.169 * [backup-simplify]: Simplify k into k 24.169 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 24.169 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 24.170 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 24.170 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 24.170 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 24.170 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 24.170 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 24.170 * [taylor]: Taking taylor expansion of 1/2 in k 24.170 * [backup-simplify]: Simplify 1/2 into 1/2 24.170 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 24.170 * [taylor]: Taking taylor expansion of 1/2 in k 24.170 * [backup-simplify]: Simplify 1/2 into 1/2 24.170 * [taylor]: Taking taylor expansion of (/ 1 k) in k 24.170 * [taylor]: Taking taylor expansion of k in k 24.170 * [backup-simplify]: Simplify 0 into 0 24.170 * [backup-simplify]: Simplify 1 into 1 24.171 * [backup-simplify]: Simplify (/ 1 1) into 1 24.171 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 24.171 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 24.171 * [taylor]: Taking taylor expansion of (* 2 PI) in k 24.171 * [taylor]: Taking taylor expansion of 2 in k 24.171 * [backup-simplify]: Simplify 2 into 2 24.171 * [taylor]: Taking taylor expansion of PI in k 24.171 * [backup-simplify]: Simplify PI into PI 24.171 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 24.172 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 24.172 * [taylor]: Taking taylor expansion of (log n) in k 24.172 * [taylor]: Taking taylor expansion of n in k 24.172 * [backup-simplify]: Simplify n into n 24.172 * [backup-simplify]: Simplify (log n) into (log n) 24.172 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 24.173 * [backup-simplify]: Simplify (- 1/2) into -1/2 24.173 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 24.173 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 24.174 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 24.174 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 24.175 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 24.175 * [taylor]: Taking taylor expansion of (sqrt k) in k 24.175 * [taylor]: Taking taylor expansion of k in k 24.175 * [backup-simplify]: Simplify 0 into 0 24.175 * [backup-simplify]: Simplify 1 into 1 24.176 * [backup-simplify]: Simplify (sqrt 0) into 0 24.176 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 24.177 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 24.177 * [backup-simplify]: Simplify 0 into 0 24.178 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 24.178 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 24.179 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 24.179 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 24.180 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 24.180 * [backup-simplify]: Simplify (- 0) into 0 24.180 * [backup-simplify]: Simplify (+ 0 0) into 0 24.181 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 24.182 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 24.183 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 24.184 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (* 0 (sqrt k))) into 0 24.184 * [taylor]: Taking taylor expansion of 0 in k 24.184 * [backup-simplify]: Simplify 0 into 0 24.184 * [backup-simplify]: Simplify 0 into 0 24.185 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 24.186 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 24.186 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 24.187 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 24.187 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 24.191 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 24.191 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 24.192 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 24.192 * [backup-simplify]: Simplify (- 0) into 0 24.193 * [backup-simplify]: Simplify (+ 0 0) into 0 24.194 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 24.196 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 24.198 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 24.200 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 24.200 * [taylor]: Taking taylor expansion of 0 in k 24.200 * [backup-simplify]: Simplify 0 into 0 24.200 * [backup-simplify]: Simplify 0 into 0 24.200 * [backup-simplify]: Simplify 0 into 0 24.203 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 24.205 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 24.206 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 24.207 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 24.208 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 24.209 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 24.215 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 24.215 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 24.217 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 24.217 * [backup-simplify]: Simplify (- 0) into 0 24.217 * [backup-simplify]: Simplify (+ 0 0) into 0 24.219 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 24.221 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 24.224 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 24.226 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 24.226 * [taylor]: Taking taylor expansion of 0 in k 24.226 * [backup-simplify]: Simplify 0 into 0 24.226 * [backup-simplify]: Simplify 0 into 0 24.226 * [backup-simplify]: Simplify 0 into 0 24.226 * [backup-simplify]: Simplify 0 into 0 24.230 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 24.232 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 24.233 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 24.237 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 24.238 * [backup-simplify]: Simplify (/ (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 24.238 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 24.238 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 24.238 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 24.239 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 24.239 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 24.239 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 24.239 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 24.239 * [taylor]: Taking taylor expansion of 1/2 in k 24.239 * [backup-simplify]: Simplify 1/2 into 1/2 24.239 * [taylor]: Taking taylor expansion of (/ 1 k) in k 24.239 * [taylor]: Taking taylor expansion of k in k 24.239 * [backup-simplify]: Simplify 0 into 0 24.239 * [backup-simplify]: Simplify 1 into 1 24.239 * [backup-simplify]: Simplify (/ 1 1) into 1 24.239 * [taylor]: Taking taylor expansion of 1/2 in k 24.239 * [backup-simplify]: Simplify 1/2 into 1/2 24.239 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 24.239 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 24.239 * [taylor]: Taking taylor expansion of -2 in k 24.239 * [backup-simplify]: Simplify -2 into -2 24.239 * [taylor]: Taking taylor expansion of (/ PI n) in k 24.239 * [taylor]: Taking taylor expansion of PI in k 24.239 * [backup-simplify]: Simplify PI into PI 24.239 * [taylor]: Taking taylor expansion of n in k 24.239 * [backup-simplify]: Simplify n into n 24.240 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 24.240 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 24.240 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 24.240 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 24.241 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 24.241 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 24.241 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 24.241 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 24.241 * [taylor]: Taking taylor expansion of (/ -1 k) in k 24.241 * [taylor]: Taking taylor expansion of -1 in k 24.241 * [backup-simplify]: Simplify -1 into -1 24.241 * [taylor]: Taking taylor expansion of k in k 24.241 * [backup-simplify]: Simplify 0 into 0 24.241 * [backup-simplify]: Simplify 1 into 1 24.242 * [backup-simplify]: Simplify (/ -1 1) into -1 24.242 * [backup-simplify]: Simplify (sqrt 0) into 0 24.243 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 24.243 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 24.243 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 24.243 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 24.244 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 24.244 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 24.244 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 24.244 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 24.244 * [taylor]: Taking taylor expansion of 1/2 in n 24.244 * [backup-simplify]: Simplify 1/2 into 1/2 24.244 * [taylor]: Taking taylor expansion of (/ 1 k) in n 24.244 * [taylor]: Taking taylor expansion of k in n 24.244 * [backup-simplify]: Simplify k into k 24.244 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 24.244 * [taylor]: Taking taylor expansion of 1/2 in n 24.244 * [backup-simplify]: Simplify 1/2 into 1/2 24.244 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 24.244 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 24.244 * [taylor]: Taking taylor expansion of -2 in n 24.244 * [backup-simplify]: Simplify -2 into -2 24.244 * [taylor]: Taking taylor expansion of (/ PI n) in n 24.244 * [taylor]: Taking taylor expansion of PI in n 24.244 * [backup-simplify]: Simplify PI into PI 24.244 * [taylor]: Taking taylor expansion of n in n 24.244 * [backup-simplify]: Simplify 0 into 0 24.244 * [backup-simplify]: Simplify 1 into 1 24.245 * [backup-simplify]: Simplify (/ PI 1) into PI 24.245 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 24.246 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 24.246 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 24.246 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 24.248 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 24.255 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 24.256 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 24.256 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 24.256 * [taylor]: Taking taylor expansion of (/ -1 k) in n 24.256 * [taylor]: Taking taylor expansion of -1 in n 24.256 * [backup-simplify]: Simplify -1 into -1 24.256 * [taylor]: Taking taylor expansion of k in n 24.256 * [backup-simplify]: Simplify k into k 24.256 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 24.257 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 24.257 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 24.257 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 24.258 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 24.258 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 24.258 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 24.258 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 24.258 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 24.258 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 24.258 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 24.258 * [taylor]: Taking taylor expansion of 1/2 in n 24.258 * [backup-simplify]: Simplify 1/2 into 1/2 24.258 * [taylor]: Taking taylor expansion of (/ 1 k) in n 24.258 * [taylor]: Taking taylor expansion of k in n 24.258 * [backup-simplify]: Simplify k into k 24.258 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 24.258 * [taylor]: Taking taylor expansion of 1/2 in n 24.258 * [backup-simplify]: Simplify 1/2 into 1/2 24.258 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 24.259 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 24.259 * [taylor]: Taking taylor expansion of -2 in n 24.259 * [backup-simplify]: Simplify -2 into -2 24.259 * [taylor]: Taking taylor expansion of (/ PI n) in n 24.259 * [taylor]: Taking taylor expansion of PI in n 24.259 * [backup-simplify]: Simplify PI into PI 24.259 * [taylor]: Taking taylor expansion of n in n 24.259 * [backup-simplify]: Simplify 0 into 0 24.259 * [backup-simplify]: Simplify 1 into 1 24.259 * [backup-simplify]: Simplify (/ PI 1) into PI 24.260 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 24.261 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 24.261 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 24.261 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 24.262 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 24.263 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 24.265 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 24.265 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 24.265 * [taylor]: Taking taylor expansion of (/ -1 k) in n 24.265 * [taylor]: Taking taylor expansion of -1 in n 24.265 * [backup-simplify]: Simplify -1 into -1 24.265 * [taylor]: Taking taylor expansion of k in n 24.265 * [backup-simplify]: Simplify k into k 24.265 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 24.265 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 24.265 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 24.265 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 24.266 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 24.267 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 24.267 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 24.267 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 24.267 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 24.267 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 24.267 * [taylor]: Taking taylor expansion of 1/2 in k 24.267 * [backup-simplify]: Simplify 1/2 into 1/2 24.267 * [taylor]: Taking taylor expansion of (/ 1 k) in k 24.267 * [taylor]: Taking taylor expansion of k in k 24.267 * [backup-simplify]: Simplify 0 into 0 24.267 * [backup-simplify]: Simplify 1 into 1 24.267 * [backup-simplify]: Simplify (/ 1 1) into 1 24.267 * [taylor]: Taking taylor expansion of 1/2 in k 24.267 * [backup-simplify]: Simplify 1/2 into 1/2 24.267 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 24.267 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 24.267 * [taylor]: Taking taylor expansion of (* -2 PI) in k 24.267 * [taylor]: Taking taylor expansion of -2 in k 24.267 * [backup-simplify]: Simplify -2 into -2 24.267 * [taylor]: Taking taylor expansion of PI in k 24.267 * [backup-simplify]: Simplify PI into PI 24.268 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 24.269 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 24.269 * [taylor]: Taking taylor expansion of (log n) in k 24.269 * [taylor]: Taking taylor expansion of n in k 24.269 * [backup-simplify]: Simplify n into n 24.269 * [backup-simplify]: Simplify (log n) into (log n) 24.270 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 24.270 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 24.270 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 24.271 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 24.273 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 24.274 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 24.274 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 24.274 * [taylor]: Taking taylor expansion of (/ -1 k) in k 24.274 * [taylor]: Taking taylor expansion of -1 in k 24.274 * [backup-simplify]: Simplify -1 into -1 24.274 * [taylor]: Taking taylor expansion of k in k 24.274 * [backup-simplify]: Simplify 0 into 0 24.274 * [backup-simplify]: Simplify 1 into 1 24.274 * [backup-simplify]: Simplify (/ -1 1) into -1 24.275 * [backup-simplify]: Simplify (sqrt 0) into 0 24.276 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 24.277 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 24.279 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 24.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 24.280 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 24.282 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 24.282 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 24.283 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 24.283 * [backup-simplify]: Simplify (+ 0 0) into 0 24.285 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 24.286 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 24.288 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 24.289 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 24.289 * [taylor]: Taking taylor expansion of 0 in k 24.289 * [backup-simplify]: Simplify 0 into 0 24.290 * [backup-simplify]: Simplify 0 into 0 24.290 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 24.293 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 24.295 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 24.297 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 24.298 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 24.299 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 24.302 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 24.303 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 24.303 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 24.304 * [backup-simplify]: Simplify (+ 0 0) into 0 24.305 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 24.307 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 24.309 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 24.309 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 24.310 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 24.312 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 24.312 * [taylor]: Taking taylor expansion of 0 in k 24.312 * [backup-simplify]: Simplify 0 into 0 24.312 * [backup-simplify]: Simplify 0 into 0 24.312 * [backup-simplify]: Simplify 0 into 0 24.313 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 24.317 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 24.319 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 24.320 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 24.323 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 24.323 * * * * [progress]: [ 4 / 4 ] generating series at (2 1) 24.323 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) into (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 24.323 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 24.323 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 24.323 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 24.323 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 24.323 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 24.323 * [taylor]: Taking taylor expansion of 1/4 in k 24.324 * [backup-simplify]: Simplify 1/4 into 1/4 24.324 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 24.324 * [taylor]: Taking taylor expansion of (/ 1 k) in k 24.324 * [taylor]: Taking taylor expansion of k in k 24.324 * [backup-simplify]: Simplify 0 into 0 24.324 * [backup-simplify]: Simplify 1 into 1 24.324 * [backup-simplify]: Simplify (/ 1 1) into 1 24.324 * [backup-simplify]: Simplify (log 1) into 0 24.325 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 24.325 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 24.325 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 24.325 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 24.325 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 24.325 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 24.325 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 24.325 * [taylor]: Taking taylor expansion of 1/2 in k 24.325 * [backup-simplify]: Simplify 1/2 into 1/2 24.325 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 24.325 * [taylor]: Taking taylor expansion of 1/2 in k 24.325 * [backup-simplify]: Simplify 1/2 into 1/2 24.325 * [taylor]: Taking taylor expansion of k in k 24.325 * [backup-simplify]: Simplify 0 into 0 24.325 * [backup-simplify]: Simplify 1 into 1 24.325 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 24.325 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 24.325 * [taylor]: Taking taylor expansion of 2 in k 24.325 * [backup-simplify]: Simplify 2 into 2 24.325 * [taylor]: Taking taylor expansion of (* n PI) in k 24.325 * [taylor]: Taking taylor expansion of n in k 24.325 * [backup-simplify]: Simplify n into n 24.325 * [taylor]: Taking taylor expansion of PI in k 24.325 * [backup-simplify]: Simplify PI into PI 24.325 * [backup-simplify]: Simplify (* n PI) into (* n PI) 24.325 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 24.325 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 24.326 * [backup-simplify]: Simplify (* 1/2 0) into 0 24.326 * [backup-simplify]: Simplify (- 0) into 0 24.327 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 24.327 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 24.327 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 24.327 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 24.327 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 24.327 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 24.327 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 24.327 * [taylor]: Taking taylor expansion of 1/4 in n 24.327 * [backup-simplify]: Simplify 1/4 into 1/4 24.327 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 24.327 * [taylor]: Taking taylor expansion of (/ 1 k) in n 24.327 * [taylor]: Taking taylor expansion of k in n 24.327 * [backup-simplify]: Simplify k into k 24.327 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 24.327 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 24.327 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 24.327 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 24.327 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 24.327 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 24.328 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 24.328 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 24.328 * [taylor]: Taking taylor expansion of 1/2 in n 24.328 * [backup-simplify]: Simplify 1/2 into 1/2 24.328 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 24.328 * [taylor]: Taking taylor expansion of 1/2 in n 24.328 * [backup-simplify]: Simplify 1/2 into 1/2 24.328 * [taylor]: Taking taylor expansion of k in n 24.328 * [backup-simplify]: Simplify k into k 24.328 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 24.328 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 24.328 * [taylor]: Taking taylor expansion of 2 in n 24.328 * [backup-simplify]: Simplify 2 into 2 24.328 * [taylor]: Taking taylor expansion of (* n PI) in n 24.328 * [taylor]: Taking taylor expansion of n in n 24.328 * [backup-simplify]: Simplify 0 into 0 24.328 * [backup-simplify]: Simplify 1 into 1 24.328 * [taylor]: Taking taylor expansion of PI in n 24.328 * [backup-simplify]: Simplify PI into PI 24.329 * [backup-simplify]: Simplify (* 0 PI) into 0 24.329 * [backup-simplify]: Simplify (* 2 0) into 0 24.330 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 24.332 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 24.332 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 24.333 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 24.333 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 24.333 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 24.334 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 24.335 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 24.336 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 24.336 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 24.336 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 24.336 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 24.336 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 24.336 * [taylor]: Taking taylor expansion of 1/4 in n 24.336 * [backup-simplify]: Simplify 1/4 into 1/4 24.336 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 24.336 * [taylor]: Taking taylor expansion of (/ 1 k) in n 24.336 * [taylor]: Taking taylor expansion of k in n 24.336 * [backup-simplify]: Simplify k into k 24.336 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 24.336 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 24.336 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 24.336 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 24.336 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 24.336 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 24.336 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 24.336 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 24.336 * [taylor]: Taking taylor expansion of 1/2 in n 24.336 * [backup-simplify]: Simplify 1/2 into 1/2 24.336 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 24.336 * [taylor]: Taking taylor expansion of 1/2 in n 24.336 * [backup-simplify]: Simplify 1/2 into 1/2 24.336 * [taylor]: Taking taylor expansion of k in n 24.336 * [backup-simplify]: Simplify k into k 24.336 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 24.336 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 24.336 * [taylor]: Taking taylor expansion of 2 in n 24.336 * [backup-simplify]: Simplify 2 into 2 24.336 * [taylor]: Taking taylor expansion of (* n PI) in n 24.336 * [taylor]: Taking taylor expansion of n in n 24.336 * [backup-simplify]: Simplify 0 into 0 24.336 * [backup-simplify]: Simplify 1 into 1 24.336 * [taylor]: Taking taylor expansion of PI in n 24.336 * [backup-simplify]: Simplify PI into PI 24.337 * [backup-simplify]: Simplify (* 0 PI) into 0 24.337 * [backup-simplify]: Simplify (* 2 0) into 0 24.339 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 24.340 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 24.341 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 24.341 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 24.341 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 24.341 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 24.343 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 24.344 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 24.345 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 24.346 * [backup-simplify]: Simplify (* (pow (/ 1 k) 1/4) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 24.346 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) in k 24.346 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 24.346 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 24.346 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 24.346 * [taylor]: Taking taylor expansion of 1/2 in k 24.346 * [backup-simplify]: Simplify 1/2 into 1/2 24.346 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 24.346 * [taylor]: Taking taylor expansion of 1/2 in k 24.346 * [backup-simplify]: Simplify 1/2 into 1/2 24.346 * [taylor]: Taking taylor expansion of k in k 24.346 * [backup-simplify]: Simplify 0 into 0 24.346 * [backup-simplify]: Simplify 1 into 1 24.346 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 24.346 * [taylor]: Taking taylor expansion of (log n) in k 24.346 * [taylor]: Taking taylor expansion of n in k 24.346 * [backup-simplify]: Simplify n into n 24.346 * [backup-simplify]: Simplify (log n) into (log n) 24.346 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 24.346 * [taylor]: Taking taylor expansion of (* 2 PI) in k 24.346 * [taylor]: Taking taylor expansion of 2 in k 24.346 * [backup-simplify]: Simplify 2 into 2 24.346 * [taylor]: Taking taylor expansion of PI in k 24.346 * [backup-simplify]: Simplify PI into PI 24.347 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 24.348 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 24.348 * [backup-simplify]: Simplify (* 1/2 0) into 0 24.349 * [backup-simplify]: Simplify (- 0) into 0 24.349 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 24.350 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 24.351 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 24.352 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 24.352 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 24.352 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 24.352 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 24.352 * [taylor]: Taking taylor expansion of 1/4 in k 24.352 * [backup-simplify]: Simplify 1/4 into 1/4 24.352 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 24.352 * [taylor]: Taking taylor expansion of (/ 1 k) in k 24.352 * [taylor]: Taking taylor expansion of k in k 24.352 * [backup-simplify]: Simplify 0 into 0 24.352 * [backup-simplify]: Simplify 1 into 1 24.353 * [backup-simplify]: Simplify (/ 1 1) into 1 24.353 * [backup-simplify]: Simplify (log 1) into 0 24.353 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 24.353 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 24.354 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 24.355 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k -1/4)) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 24.356 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 24.357 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 24.358 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 24.360 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 24.360 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 24.360 * [backup-simplify]: Simplify (- 0) into 0 24.361 * [backup-simplify]: Simplify (+ 0 0) into 0 24.362 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 24.363 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 24.365 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 24.365 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 24.366 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 1 k) 1)))) 1) into 0 24.367 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log (/ 1 k)))) into 0 24.368 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 24.369 * [backup-simplify]: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 24.369 * [taylor]: Taking taylor expansion of 0 in k 24.369 * [backup-simplify]: Simplify 0 into 0 24.369 * [backup-simplify]: Simplify 0 into 0 24.370 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 24.371 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 24.371 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 24.372 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 24.373 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 24.374 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 24.375 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 24.376 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 24.377 * [backup-simplify]: Simplify (+ 0 0) into 0 24.378 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 24.378 * [backup-simplify]: Simplify (- 1/2) into -1/2 24.378 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 24.380 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 24.383 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 24.394 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (pow k -1/4))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) 24.398 * [backup-simplify]: Simplify (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) 24.399 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 24.400 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 24.404 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 24.405 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 24.405 * [backup-simplify]: Simplify (- 0) into 0 24.405 * [backup-simplify]: Simplify (+ 0 0) into 0 24.407 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 24.408 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 24.410 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 24.410 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 24.412 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (/ 1 k) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (/ 1 k) 1)))) 2) into 0 24.413 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log (/ 1 k))))) into 0 24.414 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 24.416 * [backup-simplify]: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 24.416 * [taylor]: Taking taylor expansion of 0 in k 24.416 * [backup-simplify]: Simplify 0 into 0 24.416 * [backup-simplify]: Simplify 0 into 0 24.416 * [backup-simplify]: Simplify 0 into 0 24.417 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 24.419 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 24.420 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 24.420 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 24.422 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 24.424 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 24.424 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 24.428 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 24.428 * [backup-simplify]: Simplify (+ 0 0) into 0 24.429 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 24.429 * [backup-simplify]: Simplify (- 0) into 0 24.430 * [backup-simplify]: Simplify (+ 0 0) into 0 24.431 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 24.435 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 24.444 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow k -1/4)))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) 24.451 * [backup-simplify]: Simplify (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) 24.463 * [backup-simplify]: Simplify (+ (* (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) (* k 1)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)))) into (- (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/4 (* (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (pow (pow k 7) 1/4))) (* 1/8 (* (* (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (pow k 3) 1/4))))) 24.464 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (sqrt (/ 1 k)))) into (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 24.464 * [approximate]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 24.464 * [taylor]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 24.464 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 24.464 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 24.464 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 24.464 * [taylor]: Taking taylor expansion of 1/4 in k 24.464 * [backup-simplify]: Simplify 1/4 into 1/4 24.464 * [taylor]: Taking taylor expansion of (log k) in k 24.464 * [taylor]: Taking taylor expansion of k in k 24.464 * [backup-simplify]: Simplify 0 into 0 24.464 * [backup-simplify]: Simplify 1 into 1 24.465 * [backup-simplify]: Simplify (log 1) into 0 24.465 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 24.465 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 24.465 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 24.465 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 24.465 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 24.465 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 24.465 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 24.466 * [taylor]: Taking taylor expansion of 1/2 in k 24.466 * [backup-simplify]: Simplify 1/2 into 1/2 24.466 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 24.466 * [taylor]: Taking taylor expansion of 1/2 in k 24.466 * [backup-simplify]: Simplify 1/2 into 1/2 24.466 * [taylor]: Taking taylor expansion of (/ 1 k) in k 24.466 * [taylor]: Taking taylor expansion of k in k 24.466 * [backup-simplify]: Simplify 0 into 0 24.466 * [backup-simplify]: Simplify 1 into 1 24.466 * [backup-simplify]: Simplify (/ 1 1) into 1 24.466 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 24.466 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 24.466 * [taylor]: Taking taylor expansion of 2 in k 24.467 * [backup-simplify]: Simplify 2 into 2 24.467 * [taylor]: Taking taylor expansion of (/ PI n) in k 24.467 * [taylor]: Taking taylor expansion of PI in k 24.467 * [backup-simplify]: Simplify PI into PI 24.467 * [taylor]: Taking taylor expansion of n in k 24.467 * [backup-simplify]: Simplify n into n 24.467 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 24.467 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 24.467 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 24.468 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 24.468 * [backup-simplify]: Simplify (- 1/2) into -1/2 24.468 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 24.469 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 24.469 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 24.469 * [taylor]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 24.469 * [taylor]: Taking taylor expansion of (pow k 1/4) in n 24.469 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in n 24.469 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in n 24.469 * [taylor]: Taking taylor expansion of 1/4 in n 24.469 * [backup-simplify]: Simplify 1/4 into 1/4 24.469 * [taylor]: Taking taylor expansion of (log k) in n 24.469 * [taylor]: Taking taylor expansion of k in n 24.469 * [backup-simplify]: Simplify k into k 24.469 * [backup-simplify]: Simplify (log k) into (log k) 24.469 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 24.469 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 24.469 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 24.469 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 24.469 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 24.469 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 24.469 * [taylor]: Taking taylor expansion of 1/2 in n 24.469 * [backup-simplify]: Simplify 1/2 into 1/2 24.469 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 24.469 * [taylor]: Taking taylor expansion of 1/2 in n 24.469 * [backup-simplify]: Simplify 1/2 into 1/2 24.469 * [taylor]: Taking taylor expansion of (/ 1 k) in n 24.469 * [taylor]: Taking taylor expansion of k in n 24.470 * [backup-simplify]: Simplify k into k 24.470 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 24.470 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 24.470 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 24.470 * [taylor]: Taking taylor expansion of 2 in n 24.470 * [backup-simplify]: Simplify 2 into 2 24.470 * [taylor]: Taking taylor expansion of (/ PI n) in n 24.470 * [taylor]: Taking taylor expansion of PI in n 24.470 * [backup-simplify]: Simplify PI into PI 24.470 * [taylor]: Taking taylor expansion of n in n 24.470 * [backup-simplify]: Simplify 0 into 0 24.470 * [backup-simplify]: Simplify 1 into 1 24.470 * [backup-simplify]: Simplify (/ PI 1) into PI 24.471 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 24.472 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 24.472 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 24.472 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 24.472 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 24.473 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 24.474 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 24.476 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 24.476 * [taylor]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 24.476 * [taylor]: Taking taylor expansion of (pow k 1/4) in n 24.476 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in n 24.476 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in n 24.476 * [taylor]: Taking taylor expansion of 1/4 in n 24.476 * [backup-simplify]: Simplify 1/4 into 1/4 24.476 * [taylor]: Taking taylor expansion of (log k) in n 24.476 * [taylor]: Taking taylor expansion of k in n 24.476 * [backup-simplify]: Simplify k into k 24.476 * [backup-simplify]: Simplify (log k) into (log k) 24.476 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 24.476 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 24.476 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 24.476 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 24.476 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 24.476 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 24.476 * [taylor]: Taking taylor expansion of 1/2 in n 24.476 * [backup-simplify]: Simplify 1/2 into 1/2 24.476 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 24.476 * [taylor]: Taking taylor expansion of 1/2 in n 24.476 * [backup-simplify]: Simplify 1/2 into 1/2 24.476 * [taylor]: Taking taylor expansion of (/ 1 k) in n 24.476 * [taylor]: Taking taylor expansion of k in n 24.476 * [backup-simplify]: Simplify k into k 24.476 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 24.477 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 24.477 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 24.477 * [taylor]: Taking taylor expansion of 2 in n 24.477 * [backup-simplify]: Simplify 2 into 2 24.477 * [taylor]: Taking taylor expansion of (/ PI n) in n 24.477 * [taylor]: Taking taylor expansion of PI in n 24.477 * [backup-simplify]: Simplify PI into PI 24.477 * [taylor]: Taking taylor expansion of n in n 24.477 * [backup-simplify]: Simplify 0 into 0 24.477 * [backup-simplify]: Simplify 1 into 1 24.477 * [backup-simplify]: Simplify (/ PI 1) into PI 24.478 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 24.479 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 24.479 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 24.479 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 24.479 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 24.480 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 24.481 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 24.483 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 24.484 * [backup-simplify]: Simplify (* (pow k 1/4) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) 24.484 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) in k 24.484 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 24.484 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 24.484 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 24.484 * [taylor]: Taking taylor expansion of 1/2 in k 24.484 * [backup-simplify]: Simplify 1/2 into 1/2 24.484 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 24.484 * [taylor]: Taking taylor expansion of 1/2 in k 24.484 * [backup-simplify]: Simplify 1/2 into 1/2 24.484 * [taylor]: Taking taylor expansion of (/ 1 k) in k 24.484 * [taylor]: Taking taylor expansion of k in k 24.484 * [backup-simplify]: Simplify 0 into 0 24.484 * [backup-simplify]: Simplify 1 into 1 24.485 * [backup-simplify]: Simplify (/ 1 1) into 1 24.485 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 24.485 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 24.485 * [taylor]: Taking taylor expansion of (* 2 PI) in k 24.485 * [taylor]: Taking taylor expansion of 2 in k 24.485 * [backup-simplify]: Simplify 2 into 2 24.485 * [taylor]: Taking taylor expansion of PI in k 24.485 * [backup-simplify]: Simplify PI into PI 24.486 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 24.486 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 24.487 * [taylor]: Taking taylor expansion of (log n) in k 24.487 * [taylor]: Taking taylor expansion of n in k 24.487 * [backup-simplify]: Simplify n into n 24.487 * [backup-simplify]: Simplify (log n) into (log n) 24.487 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 24.487 * [backup-simplify]: Simplify (- 1/2) into -1/2 24.488 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 24.488 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 24.489 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 24.490 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 24.491 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 24.491 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 24.491 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 24.491 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 24.491 * [taylor]: Taking taylor expansion of 1/4 in k 24.491 * [backup-simplify]: Simplify 1/4 into 1/4 24.491 * [taylor]: Taking taylor expansion of (log k) in k 24.491 * [taylor]: Taking taylor expansion of k in k 24.491 * [backup-simplify]: Simplify 0 into 0 24.491 * [backup-simplify]: Simplify 1 into 1 24.492 * [backup-simplify]: Simplify (log 1) into 0 24.492 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 24.492 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 24.492 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 24.493 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) 24.495 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) 24.496 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 24.496 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 24.498 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 24.498 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 24.499 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 24.499 * [backup-simplify]: Simplify (- 0) into 0 24.499 * [backup-simplify]: Simplify (+ 0 0) into 0 24.501 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 24.502 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 24.504 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 24.504 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow k 1)))) 1) into 0 24.505 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 24.506 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 24.507 * [backup-simplify]: Simplify (+ (* (pow k 1/4) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 24.507 * [taylor]: Taking taylor expansion of 0 in k 24.507 * [backup-simplify]: Simplify 0 into 0 24.507 * [backup-simplify]: Simplify 0 into 0 24.508 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 24.509 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 24.509 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 24.510 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 24.511 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (* 0 (pow k 1/4))) into 0 24.511 * [backup-simplify]: Simplify 0 into 0 24.512 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 24.513 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 24.516 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 24.517 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 24.517 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 24.518 * [backup-simplify]: Simplify (- 0) into 0 24.518 * [backup-simplify]: Simplify (+ 0 0) into 0 24.519 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 24.521 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 24.523 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 24.531 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow k 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow k 1)))) 2) into 0 24.532 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 24.533 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 24.534 * [backup-simplify]: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 24.534 * [taylor]: Taking taylor expansion of 0 in k 24.534 * [backup-simplify]: Simplify 0 into 0 24.534 * [backup-simplify]: Simplify 0 into 0 24.534 * [backup-simplify]: Simplify 0 into 0 24.536 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 24.536 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 24.536 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 24.537 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 24.538 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 24.538 * [backup-simplify]: Simplify 0 into 0 24.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 24.540 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 24.543 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 24.543 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 24.544 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 24.544 * [backup-simplify]: Simplify (- 0) into 0 24.544 * [backup-simplify]: Simplify (+ 0 0) into 0 24.545 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 24.546 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 24.548 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 24.550 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow k 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow k 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow k 1)))) 6) into 0 24.550 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 24.551 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 24.553 * [backup-simplify]: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 24.553 * [taylor]: Taking taylor expansion of 0 in k 24.553 * [backup-simplify]: Simplify 0 into 0 24.553 * [backup-simplify]: Simplify 0 into 0 24.555 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) into (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) 24.555 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (sqrt (/ 1 (- k))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 24.555 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 24.555 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 24.555 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 24.555 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 24.555 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 24.555 * [taylor]: Taking taylor expansion of (/ -1 k) in k 24.555 * [taylor]: Taking taylor expansion of -1 in k 24.556 * [backup-simplify]: Simplify -1 into -1 24.556 * [taylor]: Taking taylor expansion of k in k 24.556 * [backup-simplify]: Simplify 0 into 0 24.556 * [backup-simplify]: Simplify 1 into 1 24.556 * [backup-simplify]: Simplify (/ -1 1) into -1 24.556 * [backup-simplify]: Simplify (sqrt 0) into 0 24.558 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 24.558 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 24.559 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 24.560 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 24.563 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 24.565 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 24.567 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 24.567 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 24.567 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 24.567 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 24.567 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 24.567 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 24.567 * [taylor]: Taking taylor expansion of 1/2 in k 24.567 * [backup-simplify]: Simplify 1/2 into 1/2 24.567 * [taylor]: Taking taylor expansion of (/ 1 k) in k 24.567 * [taylor]: Taking taylor expansion of k in k 24.567 * [backup-simplify]: Simplify 0 into 0 24.567 * [backup-simplify]: Simplify 1 into 1 24.568 * [backup-simplify]: Simplify (/ 1 1) into 1 24.568 * [taylor]: Taking taylor expansion of 1/2 in k 24.568 * [backup-simplify]: Simplify 1/2 into 1/2 24.568 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 24.568 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 24.568 * [taylor]: Taking taylor expansion of -2 in k 24.568 * [backup-simplify]: Simplify -2 into -2 24.568 * [taylor]: Taking taylor expansion of (/ PI n) in k 24.568 * [taylor]: Taking taylor expansion of PI in k 24.568 * [backup-simplify]: Simplify PI into PI 24.568 * [taylor]: Taking taylor expansion of n in k 24.568 * [backup-simplify]: Simplify n into n 24.568 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 24.568 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 24.568 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 24.569 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 24.569 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 24.569 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 24.569 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 24.569 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 24.569 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 24.569 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 24.569 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 24.569 * [taylor]: Taking taylor expansion of (/ -1 k) in n 24.570 * [taylor]: Taking taylor expansion of -1 in n 24.570 * [backup-simplify]: Simplify -1 into -1 24.570 * [taylor]: Taking taylor expansion of k in n 24.570 * [backup-simplify]: Simplify k into k 24.570 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 24.570 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 24.570 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 24.570 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 24.570 * [backup-simplify]: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 24.570 * [backup-simplify]: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 24.570 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 24.570 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 24.571 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 24.571 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 24.571 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 24.571 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 24.571 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 24.571 * [taylor]: Taking taylor expansion of 1/2 in n 24.571 * [backup-simplify]: Simplify 1/2 into 1/2 24.571 * [taylor]: Taking taylor expansion of (/ 1 k) in n 24.571 * [taylor]: Taking taylor expansion of k in n 24.571 * [backup-simplify]: Simplify k into k 24.571 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 24.571 * [taylor]: Taking taylor expansion of 1/2 in n 24.571 * [backup-simplify]: Simplify 1/2 into 1/2 24.571 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 24.571 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 24.571 * [taylor]: Taking taylor expansion of -2 in n 24.571 * [backup-simplify]: Simplify -2 into -2 24.571 * [taylor]: Taking taylor expansion of (/ PI n) in n 24.571 * [taylor]: Taking taylor expansion of PI in n 24.571 * [backup-simplify]: Simplify PI into PI 24.571 * [taylor]: Taking taylor expansion of n in n 24.571 * [backup-simplify]: Simplify 0 into 0 24.571 * [backup-simplify]: Simplify 1 into 1 24.572 * [backup-simplify]: Simplify (/ PI 1) into PI 24.572 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 24.573 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 24.573 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 24.573 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 24.575 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 24.576 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 24.577 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 24.577 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 24.577 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 24.577 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 24.577 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 24.578 * [taylor]: Taking taylor expansion of (/ -1 k) in n 24.578 * [taylor]: Taking taylor expansion of -1 in n 24.578 * [backup-simplify]: Simplify -1 into -1 24.578 * [taylor]: Taking taylor expansion of k in n 24.578 * [backup-simplify]: Simplify k into k 24.578 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 24.578 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 24.578 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 24.578 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 24.578 * [backup-simplify]: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 24.578 * [backup-simplify]: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 24.578 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 24.579 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 24.579 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 24.579 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 24.579 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 24.579 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 24.579 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 24.579 * [taylor]: Taking taylor expansion of 1/2 in n 24.579 * [backup-simplify]: Simplify 1/2 into 1/2 24.579 * [taylor]: Taking taylor expansion of (/ 1 k) in n 24.579 * [taylor]: Taking taylor expansion of k in n 24.579 * [backup-simplify]: Simplify k into k 24.579 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 24.579 * [taylor]: Taking taylor expansion of 1/2 in n 24.579 * [backup-simplify]: Simplify 1/2 into 1/2 24.579 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 24.579 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 24.579 * [taylor]: Taking taylor expansion of -2 in n 24.579 * [backup-simplify]: Simplify -2 into -2 24.579 * [taylor]: Taking taylor expansion of (/ PI n) in n 24.579 * [taylor]: Taking taylor expansion of PI in n 24.579 * [backup-simplify]: Simplify PI into PI 24.579 * [taylor]: Taking taylor expansion of n in n 24.579 * [backup-simplify]: Simplify 0 into 0 24.579 * [backup-simplify]: Simplify 1 into 1 24.580 * [backup-simplify]: Simplify (/ PI 1) into PI 24.580 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 24.581 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 24.581 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 24.581 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 24.583 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 24.584 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 24.585 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 24.587 * [backup-simplify]: Simplify (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 24.587 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 24.587 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 24.587 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 24.587 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 24.587 * [taylor]: Taking taylor expansion of (/ -1 k) in k 24.587 * [taylor]: Taking taylor expansion of -1 in k 24.587 * [backup-simplify]: Simplify -1 into -1 24.587 * [taylor]: Taking taylor expansion of k in k 24.587 * [backup-simplify]: Simplify 0 into 0 24.587 * [backup-simplify]: Simplify 1 into 1 24.587 * [backup-simplify]: Simplify (/ -1 1) into -1 24.588 * [backup-simplify]: Simplify (sqrt 0) into 0 24.589 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 24.590 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 24.590 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 24.591 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 24.594 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 24.596 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 24.598 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 24.598 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 24.598 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 24.598 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 24.598 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 24.598 * [taylor]: Taking taylor expansion of 1/2 in k 24.598 * [backup-simplify]: Simplify 1/2 into 1/2 24.598 * [taylor]: Taking taylor expansion of (/ 1 k) in k 24.598 * [taylor]: Taking taylor expansion of k in k 24.598 * [backup-simplify]: Simplify 0 into 0 24.598 * [backup-simplify]: Simplify 1 into 1 24.599 * [backup-simplify]: Simplify (/ 1 1) into 1 24.599 * [taylor]: Taking taylor expansion of 1/2 in k 24.599 * [backup-simplify]: Simplify 1/2 into 1/2 24.599 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 24.599 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 24.599 * [taylor]: Taking taylor expansion of (* -2 PI) in k 24.599 * [taylor]: Taking taylor expansion of -2 in k 24.599 * [backup-simplify]: Simplify -2 into -2 24.599 * [taylor]: Taking taylor expansion of PI in k 24.599 * [backup-simplify]: Simplify PI into PI 24.599 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 24.601 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 24.601 * [taylor]: Taking taylor expansion of (log n) in k 24.601 * [taylor]: Taking taylor expansion of n in k 24.601 * [backup-simplify]: Simplify n into n 24.601 * [backup-simplify]: Simplify (log n) into (log n) 24.601 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 24.602 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 24.602 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 24.603 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 24.604 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 24.605 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 24.607 * [backup-simplify]: Simplify (* (sqrt +nan.0) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)) 24.608 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)) 24.609 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 24.610 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 24.612 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 24.612 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 24.612 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 24.613 * [backup-simplify]: Simplify (+ 0 0) into 0 24.614 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 24.615 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 24.617 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 24.619 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (sqrt (/ -1 k)))) 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 24.619 * [taylor]: Taking taylor expansion of 0 in k 24.619 * [backup-simplify]: Simplify 0 into 0 24.619 * [backup-simplify]: Simplify 0 into 0 24.621 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (* (/ +nan.0 (sqrt +nan.0)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))) 24.622 * [backup-simplify]: Simplify (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))) 24.622 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 24.623 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 24.625 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 24.625 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 24.626 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 24.626 * [backup-simplify]: Simplify (+ 0 0) into 0 24.627 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 24.628 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 24.629 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 24.629 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 24.630 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 24.630 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 24.630 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 24.631 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (sqrt (/ -1 k)))) 0) (+ (* 0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into 0 24.632 * [taylor]: Taking taylor expansion of 0 in k 24.632 * [backup-simplify]: Simplify 0 into 0 24.632 * [backup-simplify]: Simplify 0 into 0 24.632 * [backup-simplify]: Simplify 0 into 0 24.632 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 24.635 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 24.637 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 24.640 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 24.652 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (+ (* (/ +nan.0 (sqrt +nan.0)) 0) (* (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) 24.655 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) into (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) 24.660 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))) (* (/ 1 (- k)) 1)) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))) into (- (* (sqrt +nan.0) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) (pow k 2))))))))) 24.660 * * * [progress]: simplifying candidates 24.660 * * * * [progress]: [ 1 / 4800 ] simplifiying candidate # 24.660 * * * * [progress]: [ 2 / 4800 ] simplifiying candidate # 24.660 * * * * [progress]: [ 3 / 4800 ] simplifiying candidate # 24.660 * * * * [progress]: [ 4 / 4800 ] simplifiying candidate # 24.661 * * * * [progress]: [ 5 / 4800 ] simplifiying candidate # 24.661 * * * * [progress]: [ 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simplifiying candidate # 24.664 * * * * [progress]: [ 67 / 4800 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (sqrt (sqrt k))))> 24.664 * * * * [progress]: [ 68 / 4800 ] simplifiying candidate # 24.664 * * * * [progress]: [ 69 / 4800 ] simplifiying candidate # 24.664 * * * * [progress]: [ 70 / 4800 ] simplifiying candidate # 24.664 * * * * [progress]: [ 71 / 4800 ] simplifiying candidate # 24.664 * * * * [progress]: [ 72 / 4800 ] simplifiying candidate # 24.664 * * * * [progress]: [ 73 / 4800 ] simplifiying candidate # 24.664 * * * * [progress]: [ 74 / 4800 ] simplifiying candidate # 24.664 * * * * [progress]: [ 75 / 4800 ] simplifiying candidate # 24.664 * * * * [progress]: [ 76 / 4800 ] simplifiying candidate # 24.665 * * * * [progress]: [ 77 / 4800 ] simplifiying candidate # 24.665 * * * * [progress]: [ 78 / 4800 ] simplifiying candidate # 24.665 * * * * [progress]: [ 79 / 4800 ] simplifiying candidate # 24.665 * * * * 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* * * * [progress]: [ 4797 / 4800 ] simplifiying candidate # 25.004 * * * * [progress]: [ 4798 / 4800 ] simplifiying candidate # 25.004 * * * * [progress]: [ 4799 / 4800 ] simplifiying candidate # 25.004 * * * * [progress]: [ 4800 / 4800 ] simplifiying candidate # 25.138 * [simplify]: Simplifying: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 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[simplify]: Extracting #0: cost 3382 inf + 0 26.627 * * [simplify]: Extracting #1: cost 3485 inf + 0 26.636 * * [simplify]: Extracting #2: cost 3563 inf + 239 26.646 * * [simplify]: Extracting #3: cost 3568 inf + 3072 26.656 * * [simplify]: Extracting #4: cost 3512 inf + 24308 26.680 * * [simplify]: Extracting #5: cost 3237 inf + 174233 26.759 * * [simplify]: Extracting #6: cost 2223 inf + 930626 26.904 * * [simplify]: Extracting #7: cost 1405 inf + 1605118 27.086 * * [simplify]: Extracting #8: cost 736 inf + 2189681 27.345 * * [simplify]: Extracting #9: cost 305 inf + 2596859 27.635 * * [simplify]: Extracting #10: cost 47 inf + 2855789 27.919 * * [simplify]: Extracting #11: cost 16 inf + 2889478 28.230 * * [simplify]: Extracting #12: cost 15 inf + 2895596 28.544 * * [simplify]: Extracting #13: cost 14 inf + 2897991 28.931 * * [simplify]: Extracting #14: cost 16 inf + 2897991 29.223 * * [simplify]: Extracting #15: cost 16 inf + 2898657 29.500 * * [simplify]: Extracting #16: cost 18 inf + 2898657 29.757 * * [simplify]: Extracting #17: cost 18 inf + 2899283 30.035 * * [simplify]: Extracting #18: cost 20 inf + 2899283 30.308 * * [simplify]: Extracting #19: cost 20 inf + 2899739 30.678 * * [simplify]: Extracting #20: cost 17 inf + 2901347 30.955 * * [simplify]: Extracting #21: cost 14 inf + 2904135 31.232 * * [simplify]: Extracting #22: cost 12 inf + 2906627 31.496 * * [simplify]: Extracting #23: cost 10 inf + 2909859 31.806 * * [simplify]: Extracting #24: cost 8 inf + 2913331 32.111 * * [simplify]: Extracting #25: cost 6 inf + 2917043 32.425 * * [simplify]: Extracting #26: cost 2 inf + 2926427 32.735 * * [simplify]: Extracting #27: cost 0 inf + 2931599 33.187 * [simplify]: Simplified to: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ 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(* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) (- (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/4 (* (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (pow (pow k 7) 1/4))) (* 1/8 (* (* (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (pow k 3) 1/4))))) (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) (- (* (sqrt +nan.0) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) (pow k 2))))))))) 34.685 * * * [progress]: adding candidates to table 66.950 * * [progress]: iteration 4 / 4 66.950 * * * [progress]: picking best candidate 66.980 * * * * [pick]: Picked # 66.981 * * * [progress]: localizing error 67.045 * * * [progress]: generating rewritten candidates 67.045 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 67.076 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 67.107 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 67.134 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1) 67.156 * * * [progress]: generating series expansions 67.156 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 67.157 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) 67.157 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0 67.157 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k 67.157 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k 67.157 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k 67.157 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k 67.157 * [taylor]: Taking taylor expansion of 1/2 in k 67.157 * [backup-simplify]: Simplify 1/2 into 1/2 67.157 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 67.157 * [taylor]: Taking taylor expansion of 1/2 in k 67.157 * [backup-simplify]: Simplify 1/2 into 1/2 67.157 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 67.157 * [taylor]: Taking taylor expansion of 1/2 in k 67.157 * [backup-simplify]: Simplify 1/2 into 1/2 67.157 * [taylor]: Taking taylor expansion of k in k 67.157 * [backup-simplify]: Simplify 0 into 0 67.157 * [backup-simplify]: Simplify 1 into 1 67.157 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 67.157 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 67.157 * [taylor]: Taking taylor expansion of 2 in k 67.157 * [backup-simplify]: Simplify 2 into 2 67.157 * [taylor]: Taking taylor expansion of (* n PI) in k 67.157 * [taylor]: Taking taylor expansion of n in k 67.157 * [backup-simplify]: Simplify n into n 67.157 * [taylor]: Taking taylor expansion of PI in k 67.157 * [backup-simplify]: Simplify PI into PI 67.157 * [backup-simplify]: Simplify (* n PI) into (* n PI) 67.157 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 67.157 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 67.158 * [backup-simplify]: Simplify (* 1/2 0) into 0 67.158 * [backup-simplify]: Simplify (- 0) into 0 67.158 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 67.159 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 67.159 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI)))) 67.159 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4) 67.159 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 67.159 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 67.159 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 67.159 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 67.159 * [taylor]: Taking taylor expansion of 1/2 in n 67.159 * [backup-simplify]: Simplify 1/2 into 1/2 67.159 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 67.159 * [taylor]: Taking taylor expansion of 1/2 in n 67.159 * [backup-simplify]: Simplify 1/2 into 1/2 67.159 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 67.159 * [taylor]: Taking taylor expansion of 1/2 in n 67.159 * [backup-simplify]: Simplify 1/2 into 1/2 67.159 * [taylor]: Taking taylor expansion of k in n 67.159 * [backup-simplify]: Simplify k into k 67.159 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 67.159 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 67.159 * [taylor]: Taking taylor expansion of 2 in n 67.159 * [backup-simplify]: Simplify 2 into 2 67.159 * [taylor]: Taking taylor expansion of (* n PI) in n 67.159 * [taylor]: Taking taylor expansion of n in n 67.159 * [backup-simplify]: Simplify 0 into 0 67.159 * [backup-simplify]: Simplify 1 into 1 67.159 * [taylor]: Taking taylor expansion of PI in n 67.159 * [backup-simplify]: Simplify PI into PI 67.159 * [backup-simplify]: Simplify (* 0 PI) into 0 67.160 * [backup-simplify]: Simplify (* 2 0) into 0 67.161 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 67.162 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 67.162 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.162 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 67.162 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 67.162 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 67.163 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 67.163 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 67.164 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 67.165 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 67.165 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 67.165 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 67.165 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 67.165 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 67.165 * [taylor]: Taking taylor expansion of 1/2 in n 67.165 * [backup-simplify]: Simplify 1/2 into 1/2 67.165 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 67.165 * [taylor]: Taking taylor expansion of 1/2 in n 67.165 * [backup-simplify]: Simplify 1/2 into 1/2 67.165 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 67.165 * [taylor]: Taking taylor expansion of 1/2 in n 67.165 * [backup-simplify]: Simplify 1/2 into 1/2 67.165 * [taylor]: Taking taylor expansion of k in n 67.165 * [backup-simplify]: Simplify k into k 67.165 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 67.165 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 67.165 * [taylor]: Taking taylor expansion of 2 in n 67.165 * [backup-simplify]: Simplify 2 into 2 67.165 * [taylor]: Taking taylor expansion of (* n PI) in n 67.165 * [taylor]: Taking taylor expansion of n in n 67.165 * [backup-simplify]: Simplify 0 into 0 67.165 * [backup-simplify]: Simplify 1 into 1 67.165 * [taylor]: Taking taylor expansion of PI in n 67.165 * [backup-simplify]: Simplify PI into PI 67.166 * [backup-simplify]: Simplify (* 0 PI) into 0 67.166 * [backup-simplify]: Simplify (* 2 0) into 0 67.167 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 67.168 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 67.168 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.168 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 67.168 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 67.169 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 67.169 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 67.169 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 67.170 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 67.171 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 67.171 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 67.171 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 67.171 * [taylor]: Taking taylor expansion of 1/2 in k 67.171 * [backup-simplify]: Simplify 1/2 into 1/2 67.171 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 67.171 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 67.171 * [taylor]: Taking taylor expansion of 1/2 in k 67.171 * [backup-simplify]: Simplify 1/2 into 1/2 67.171 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 67.171 * [taylor]: Taking taylor expansion of 1/2 in k 67.171 * [backup-simplify]: Simplify 1/2 into 1/2 67.171 * [taylor]: Taking taylor expansion of k in k 67.171 * [backup-simplify]: Simplify 0 into 0 67.171 * [backup-simplify]: Simplify 1 into 1 67.171 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 67.171 * [taylor]: Taking taylor expansion of (log n) in k 67.171 * [taylor]: Taking taylor expansion of n in k 67.171 * [backup-simplify]: Simplify n into n 67.171 * [backup-simplify]: Simplify (log n) into (log n) 67.171 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 67.171 * [taylor]: Taking taylor expansion of (* 2 PI) in k 67.171 * [taylor]: Taking taylor expansion of 2 in k 67.171 * [backup-simplify]: Simplify 2 into 2 67.171 * [taylor]: Taking taylor expansion of PI in k 67.171 * [backup-simplify]: Simplify PI into PI 67.172 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.172 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.173 * [backup-simplify]: Simplify (* 1/2 0) into 0 67.173 * [backup-simplify]: Simplify (- 0) into 0 67.173 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 67.174 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 67.174 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 67.175 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI)))) 67.176 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 67.177 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 67.177 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 67.178 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 67.179 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 67.179 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 67.179 * [backup-simplify]: Simplify (- 0) into 0 67.180 * [backup-simplify]: Simplify (+ 0 0) into 0 67.180 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0 67.182 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 67.183 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 67.185 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 67.185 * [taylor]: Taking taylor expansion of 0 in k 67.185 * [backup-simplify]: Simplify 0 into 0 67.185 * [backup-simplify]: Simplify 0 into 0 67.186 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 67.187 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 67.189 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 67.189 * [backup-simplify]: Simplify (+ 0 0) into 0 67.190 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 67.190 * [backup-simplify]: Simplify (- 1/2) into -1/2 67.190 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 67.192 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 67.196 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 67.199 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 67.202 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 67.203 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 67.204 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 67.208 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 67.209 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 67.210 * [backup-simplify]: Simplify (- 0) into 0 67.210 * [backup-simplify]: Simplify (+ 0 0) into 0 67.211 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0 67.212 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 67.214 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 67.216 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 67.217 * [taylor]: Taking taylor expansion of 0 in k 67.217 * [backup-simplify]: Simplify 0 into 0 67.217 * [backup-simplify]: Simplify 0 into 0 67.217 * [backup-simplify]: Simplify 0 into 0 67.218 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 67.219 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 67.223 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 67.223 * [backup-simplify]: Simplify (+ 0 0) into 0 67.224 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 67.225 * [backup-simplify]: Simplify (- 0) into 0 67.225 * [backup-simplify]: Simplify (+ 0 0) into 0 67.227 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 67.231 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0 67.234 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 67.240 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 67.249 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) 67.250 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) 67.250 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 67.250 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k 67.250 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k 67.250 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k 67.250 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k 67.250 * [taylor]: Taking taylor expansion of 1/2 in k 67.250 * [backup-simplify]: Simplify 1/2 into 1/2 67.250 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 67.250 * [taylor]: Taking taylor expansion of 1/2 in k 67.250 * [backup-simplify]: Simplify 1/2 into 1/2 67.250 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.250 * [taylor]: Taking taylor expansion of 1/2 in k 67.250 * [backup-simplify]: Simplify 1/2 into 1/2 67.250 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.251 * [taylor]: Taking taylor expansion of k in k 67.251 * [backup-simplify]: Simplify 0 into 0 67.251 * [backup-simplify]: Simplify 1 into 1 67.251 * [backup-simplify]: Simplify (/ 1 1) into 1 67.251 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 67.251 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 67.251 * [taylor]: Taking taylor expansion of 2 in k 67.251 * [backup-simplify]: Simplify 2 into 2 67.251 * [taylor]: Taking taylor expansion of (/ PI n) in k 67.251 * [taylor]: Taking taylor expansion of PI in k 67.251 * [backup-simplify]: Simplify PI into PI 67.251 * [taylor]: Taking taylor expansion of n in k 67.251 * [backup-simplify]: Simplify n into n 67.251 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 67.251 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 67.251 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 67.252 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.252 * [backup-simplify]: Simplify (- 1/2) into -1/2 67.252 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 67.253 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4 67.253 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n)))) 67.253 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))))) 67.253 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 67.253 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 67.253 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 67.253 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 67.253 * [taylor]: Taking taylor expansion of 1/2 in n 67.253 * [backup-simplify]: Simplify 1/2 into 1/2 67.253 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 67.253 * [taylor]: Taking taylor expansion of 1/2 in n 67.253 * [backup-simplify]: Simplify 1/2 into 1/2 67.253 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.253 * [taylor]: Taking taylor expansion of 1/2 in n 67.253 * [backup-simplify]: Simplify 1/2 into 1/2 67.253 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.253 * [taylor]: Taking taylor expansion of k in n 67.253 * [backup-simplify]: Simplify k into k 67.253 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.253 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 67.253 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.253 * [taylor]: Taking taylor expansion of 2 in n 67.253 * [backup-simplify]: Simplify 2 into 2 67.253 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.253 * [taylor]: Taking taylor expansion of PI in n 67.253 * [backup-simplify]: Simplify PI into PI 67.253 * [taylor]: Taking taylor expansion of n in n 67.253 * [backup-simplify]: Simplify 0 into 0 67.253 * [backup-simplify]: Simplify 1 into 1 67.254 * [backup-simplify]: Simplify (/ PI 1) into PI 67.254 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.255 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.255 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.255 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 67.255 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 67.255 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 67.256 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.257 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 67.257 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.257 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 67.257 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 67.257 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 67.257 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 67.257 * [taylor]: Taking taylor expansion of 1/2 in n 67.257 * [backup-simplify]: Simplify 1/2 into 1/2 67.257 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 67.257 * [taylor]: Taking taylor expansion of 1/2 in n 67.257 * [backup-simplify]: Simplify 1/2 into 1/2 67.257 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.257 * [taylor]: Taking taylor expansion of 1/2 in n 67.258 * [backup-simplify]: Simplify 1/2 into 1/2 67.258 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.258 * [taylor]: Taking taylor expansion of k in n 67.258 * [backup-simplify]: Simplify k into k 67.258 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.258 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 67.258 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.258 * [taylor]: Taking taylor expansion of 2 in n 67.258 * [backup-simplify]: Simplify 2 into 2 67.258 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.258 * [taylor]: Taking taylor expansion of PI in n 67.258 * [backup-simplify]: Simplify PI into PI 67.258 * [taylor]: Taking taylor expansion of n in n 67.258 * [backup-simplify]: Simplify 0 into 0 67.258 * [backup-simplify]: Simplify 1 into 1 67.258 * [backup-simplify]: Simplify (/ PI 1) into PI 67.258 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.259 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.259 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.259 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 67.259 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 67.259 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 67.266 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.267 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 67.268 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.268 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k 67.268 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 67.268 * [taylor]: Taking taylor expansion of 1/2 in k 67.268 * [backup-simplify]: Simplify 1/2 into 1/2 67.268 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 67.268 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 67.268 * [taylor]: Taking taylor expansion of 1/2 in k 67.268 * [backup-simplify]: Simplify 1/2 into 1/2 67.268 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.268 * [taylor]: Taking taylor expansion of 1/2 in k 67.268 * [backup-simplify]: Simplify 1/2 into 1/2 67.268 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.268 * [taylor]: Taking taylor expansion of k in k 67.268 * [backup-simplify]: Simplify 0 into 0 67.268 * [backup-simplify]: Simplify 1 into 1 67.269 * [backup-simplify]: Simplify (/ 1 1) into 1 67.269 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 67.269 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 67.269 * [taylor]: Taking taylor expansion of (* 2 PI) in k 67.269 * [taylor]: Taking taylor expansion of 2 in k 67.269 * [backup-simplify]: Simplify 2 into 2 67.269 * [taylor]: Taking taylor expansion of PI in k 67.269 * [backup-simplify]: Simplify PI into PI 67.269 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.270 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.270 * [taylor]: Taking taylor expansion of (log n) in k 67.270 * [taylor]: Taking taylor expansion of n in k 67.270 * [backup-simplify]: Simplify n into n 67.270 * [backup-simplify]: Simplify (log n) into (log n) 67.270 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.270 * [backup-simplify]: Simplify (- 1/2) into -1/2 67.271 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 67.271 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 67.271 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 67.272 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 67.273 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n))) 67.273 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.274 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.275 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.275 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 67.276 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 67.276 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 67.277 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 67.277 * [backup-simplify]: Simplify (- 0) into 0 67.277 * [backup-simplify]: Simplify (+ 0 0) into 0 67.277 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 67.278 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.279 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 67.280 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 67.280 * [taylor]: Taking taylor expansion of 0 in k 67.280 * [backup-simplify]: Simplify 0 into 0 67.280 * [backup-simplify]: Simplify 0 into 0 67.280 * [backup-simplify]: Simplify 0 into 0 67.281 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.282 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 67.284 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 67.284 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.284 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 67.285 * [backup-simplify]: Simplify (- 0) into 0 67.285 * [backup-simplify]: Simplify (+ 0 0) into 0 67.285 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0 67.286 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.287 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 67.290 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 67.290 * [taylor]: Taking taylor expansion of 0 in k 67.290 * [backup-simplify]: Simplify 0 into 0 67.290 * [backup-simplify]: Simplify 0 into 0 67.290 * [backup-simplify]: Simplify 0 into 0 67.290 * [backup-simplify]: Simplify 0 into 0 67.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.292 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.299 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 67.299 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.300 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 67.301 * [backup-simplify]: Simplify (- 0) into 0 67.301 * [backup-simplify]: Simplify (+ 0 0) into 0 67.303 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0 67.304 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.307 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 67.309 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 67.309 * [taylor]: Taking taylor expansion of 0 in k 67.309 * [backup-simplify]: Simplify 0 into 0 67.309 * [backup-simplify]: Simplify 0 into 0 67.311 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 67.311 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) 67.312 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 67.312 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 67.312 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k 67.312 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k 67.312 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 67.312 * [taylor]: Taking taylor expansion of 1/2 in k 67.312 * [backup-simplify]: Simplify 1/2 into 1/2 67.312 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 67.312 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.312 * [taylor]: Taking taylor expansion of 1/2 in k 67.312 * [backup-simplify]: Simplify 1/2 into 1/2 67.312 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.312 * [taylor]: Taking taylor expansion of k in k 67.312 * [backup-simplify]: Simplify 0 into 0 67.312 * [backup-simplify]: Simplify 1 into 1 67.312 * [backup-simplify]: Simplify (/ 1 1) into 1 67.312 * [taylor]: Taking taylor expansion of 1/2 in k 67.312 * [backup-simplify]: Simplify 1/2 into 1/2 67.312 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 67.312 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 67.312 * [taylor]: Taking taylor expansion of -2 in k 67.312 * [backup-simplify]: Simplify -2 into -2 67.313 * [taylor]: Taking taylor expansion of (/ PI n) in k 67.313 * [taylor]: Taking taylor expansion of PI in k 67.313 * [backup-simplify]: Simplify PI into PI 67.313 * [taylor]: Taking taylor expansion of n in k 67.313 * [backup-simplify]: Simplify n into n 67.313 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 67.313 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 67.313 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 67.313 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.314 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 67.314 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 67.314 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n)))) 67.314 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 67.314 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 67.314 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 67.315 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 67.315 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 67.315 * [taylor]: Taking taylor expansion of 1/2 in n 67.315 * [backup-simplify]: Simplify 1/2 into 1/2 67.315 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 67.315 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.315 * [taylor]: Taking taylor expansion of 1/2 in n 67.315 * [backup-simplify]: Simplify 1/2 into 1/2 67.315 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.315 * [taylor]: Taking taylor expansion of k in n 67.315 * [backup-simplify]: Simplify k into k 67.315 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.315 * [taylor]: Taking taylor expansion of 1/2 in n 67.315 * [backup-simplify]: Simplify 1/2 into 1/2 67.315 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 67.315 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.315 * [taylor]: Taking taylor expansion of -2 in n 67.315 * [backup-simplify]: Simplify -2 into -2 67.315 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.315 * [taylor]: Taking taylor expansion of PI in n 67.315 * [backup-simplify]: Simplify PI into PI 67.315 * [taylor]: Taking taylor expansion of n in n 67.315 * [backup-simplify]: Simplify 0 into 0 67.315 * [backup-simplify]: Simplify 1 into 1 67.316 * [backup-simplify]: Simplify (/ PI 1) into PI 67.316 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.317 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 67.317 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.317 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 67.318 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 67.319 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.320 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 67.322 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.322 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 67.322 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 67.322 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 67.322 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 67.322 * [taylor]: Taking taylor expansion of 1/2 in n 67.322 * [backup-simplify]: Simplify 1/2 into 1/2 67.322 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 67.322 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.322 * [taylor]: Taking taylor expansion of 1/2 in n 67.322 * [backup-simplify]: Simplify 1/2 into 1/2 67.322 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.322 * [taylor]: Taking taylor expansion of k in n 67.322 * [backup-simplify]: Simplify k into k 67.322 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.322 * [taylor]: Taking taylor expansion of 1/2 in n 67.322 * [backup-simplify]: Simplify 1/2 into 1/2 67.322 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 67.322 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.322 * [taylor]: Taking taylor expansion of -2 in n 67.322 * [backup-simplify]: Simplify -2 into -2 67.322 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.322 * [taylor]: Taking taylor expansion of PI in n 67.322 * [backup-simplify]: Simplify PI into PI 67.322 * [taylor]: Taking taylor expansion of n in n 67.322 * [backup-simplify]: Simplify 0 into 0 67.322 * [backup-simplify]: Simplify 1 into 1 67.323 * [backup-simplify]: Simplify (/ PI 1) into PI 67.324 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.325 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 67.325 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.325 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 67.325 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 67.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.328 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 67.329 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.329 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 67.329 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 67.329 * [taylor]: Taking taylor expansion of 1/2 in k 67.329 * [backup-simplify]: Simplify 1/2 into 1/2 67.329 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 67.329 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 67.329 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.329 * [taylor]: Taking taylor expansion of 1/2 in k 67.329 * [backup-simplify]: Simplify 1/2 into 1/2 67.329 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.329 * [taylor]: Taking taylor expansion of k in k 67.329 * [backup-simplify]: Simplify 0 into 0 67.329 * [backup-simplify]: Simplify 1 into 1 67.330 * [backup-simplify]: Simplify (/ 1 1) into 1 67.330 * [taylor]: Taking taylor expansion of 1/2 in k 67.330 * [backup-simplify]: Simplify 1/2 into 1/2 67.330 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 67.330 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 67.330 * [taylor]: Taking taylor expansion of (* -2 PI) in k 67.330 * [taylor]: Taking taylor expansion of -2 in k 67.330 * [backup-simplify]: Simplify -2 into -2 67.330 * [taylor]: Taking taylor expansion of PI in k 67.330 * [backup-simplify]: Simplify PI into PI 67.331 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.332 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 67.332 * [taylor]: Taking taylor expansion of (log n) in k 67.332 * [taylor]: Taking taylor expansion of n in k 67.332 * [backup-simplify]: Simplify n into n 67.332 * [backup-simplify]: Simplify (log n) into (log n) 67.332 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.333 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 67.333 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 67.334 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 67.335 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 67.336 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n))) 67.337 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.338 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.339 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.340 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 67.342 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 67.342 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 67.343 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 67.343 * [backup-simplify]: Simplify (+ 0 0) into 0 67.344 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 67.345 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.346 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 67.349 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 67.349 * [taylor]: Taking taylor expansion of 0 in k 67.349 * [backup-simplify]: Simplify 0 into 0 67.349 * [backup-simplify]: Simplify 0 into 0 67.349 * [backup-simplify]: Simplify 0 into 0 67.350 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.351 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 67.354 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 67.355 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.355 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 67.356 * [backup-simplify]: Simplify (+ 0 0) into 0 67.357 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 67.358 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.360 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 67.363 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 67.363 * [taylor]: Taking taylor expansion of 0 in k 67.363 * [backup-simplify]: Simplify 0 into 0 67.363 * [backup-simplify]: Simplify 0 into 0 67.363 * [backup-simplify]: Simplify 0 into 0 67.363 * [backup-simplify]: Simplify 0 into 0 67.364 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.366 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.372 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 67.372 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.373 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 67.374 * [backup-simplify]: Simplify (+ 0 0) into 0 67.375 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 67.377 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.379 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 67.381 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 67.381 * [taylor]: Taking taylor expansion of 0 in k 67.381 * [backup-simplify]: Simplify 0 into 0 67.381 * [backup-simplify]: Simplify 0 into 0 67.381 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 67.382 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 67.382 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) 67.382 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0 67.382 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k 67.382 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k 67.382 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k 67.382 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k 67.382 * [taylor]: Taking taylor expansion of 1/2 in k 67.382 * [backup-simplify]: Simplify 1/2 into 1/2 67.382 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 67.382 * [taylor]: Taking taylor expansion of 1/2 in k 67.382 * [backup-simplify]: Simplify 1/2 into 1/2 67.382 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 67.382 * [taylor]: Taking taylor expansion of 1/2 in k 67.382 * [backup-simplify]: Simplify 1/2 into 1/2 67.382 * [taylor]: Taking taylor expansion of k in k 67.382 * [backup-simplify]: Simplify 0 into 0 67.382 * [backup-simplify]: Simplify 1 into 1 67.382 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 67.382 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 67.382 * [taylor]: Taking taylor expansion of 2 in k 67.382 * [backup-simplify]: Simplify 2 into 2 67.382 * [taylor]: Taking taylor expansion of (* n PI) in k 67.382 * [taylor]: Taking taylor expansion of n in k 67.382 * [backup-simplify]: Simplify n into n 67.382 * [taylor]: Taking taylor expansion of PI in k 67.382 * [backup-simplify]: Simplify PI into PI 67.382 * [backup-simplify]: Simplify (* n PI) into (* n PI) 67.382 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 67.382 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 67.383 * [backup-simplify]: Simplify (* 1/2 0) into 0 67.383 * [backup-simplify]: Simplify (- 0) into 0 67.383 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 67.384 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 67.384 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI)))) 67.384 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4) 67.384 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 67.384 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 67.384 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 67.384 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 67.384 * [taylor]: Taking taylor expansion of 1/2 in n 67.384 * [backup-simplify]: Simplify 1/2 into 1/2 67.384 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 67.384 * [taylor]: Taking taylor expansion of 1/2 in n 67.384 * [backup-simplify]: Simplify 1/2 into 1/2 67.384 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 67.384 * [taylor]: Taking taylor expansion of 1/2 in n 67.384 * [backup-simplify]: Simplify 1/2 into 1/2 67.384 * [taylor]: Taking taylor expansion of k in n 67.384 * [backup-simplify]: Simplify k into k 67.384 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 67.384 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 67.384 * [taylor]: Taking taylor expansion of 2 in n 67.384 * [backup-simplify]: Simplify 2 into 2 67.384 * [taylor]: Taking taylor expansion of (* n PI) in n 67.384 * [taylor]: Taking taylor expansion of n in n 67.384 * [backup-simplify]: Simplify 0 into 0 67.384 * [backup-simplify]: Simplify 1 into 1 67.384 * [taylor]: Taking taylor expansion of PI in n 67.384 * [backup-simplify]: Simplify PI into PI 67.384 * [backup-simplify]: Simplify (* 0 PI) into 0 67.385 * [backup-simplify]: Simplify (* 2 0) into 0 67.386 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 67.387 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 67.387 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.387 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 67.387 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 67.387 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 67.387 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 67.388 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 67.389 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 67.396 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 67.396 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 67.396 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 67.396 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 67.396 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 67.396 * [taylor]: Taking taylor expansion of 1/2 in n 67.396 * [backup-simplify]: Simplify 1/2 into 1/2 67.396 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 67.396 * [taylor]: Taking taylor expansion of 1/2 in n 67.396 * [backup-simplify]: Simplify 1/2 into 1/2 67.396 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 67.396 * [taylor]: Taking taylor expansion of 1/2 in n 67.396 * [backup-simplify]: Simplify 1/2 into 1/2 67.396 * [taylor]: Taking taylor expansion of k in n 67.396 * [backup-simplify]: Simplify k into k 67.396 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 67.396 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 67.396 * [taylor]: Taking taylor expansion of 2 in n 67.396 * [backup-simplify]: Simplify 2 into 2 67.396 * [taylor]: Taking taylor expansion of (* n PI) in n 67.396 * [taylor]: Taking taylor expansion of n in n 67.396 * [backup-simplify]: Simplify 0 into 0 67.396 * [backup-simplify]: Simplify 1 into 1 67.396 * [taylor]: Taking taylor expansion of PI in n 67.396 * [backup-simplify]: Simplify PI into PI 67.397 * [backup-simplify]: Simplify (* 0 PI) into 0 67.397 * [backup-simplify]: Simplify (* 2 0) into 0 67.398 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 67.399 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 67.400 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.400 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 67.400 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 67.400 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 67.400 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 67.401 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 67.402 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 67.402 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 67.403 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 67.403 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 67.403 * [taylor]: Taking taylor expansion of 1/2 in k 67.403 * [backup-simplify]: Simplify 1/2 into 1/2 67.403 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 67.403 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 67.403 * [taylor]: Taking taylor expansion of 1/2 in k 67.403 * [backup-simplify]: Simplify 1/2 into 1/2 67.403 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 67.403 * [taylor]: Taking taylor expansion of 1/2 in k 67.403 * [backup-simplify]: Simplify 1/2 into 1/2 67.403 * [taylor]: Taking taylor expansion of k in k 67.403 * [backup-simplify]: Simplify 0 into 0 67.403 * [backup-simplify]: Simplify 1 into 1 67.403 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 67.403 * [taylor]: Taking taylor expansion of (log n) in k 67.403 * [taylor]: Taking taylor expansion of n in k 67.403 * [backup-simplify]: Simplify n into n 67.403 * [backup-simplify]: Simplify (log n) into (log n) 67.403 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 67.403 * [taylor]: Taking taylor expansion of (* 2 PI) in k 67.403 * [taylor]: Taking taylor expansion of 2 in k 67.403 * [backup-simplify]: Simplify 2 into 2 67.403 * [taylor]: Taking taylor expansion of PI in k 67.403 * [backup-simplify]: Simplify PI into PI 67.403 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.404 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.404 * [backup-simplify]: Simplify (* 1/2 0) into 0 67.404 * [backup-simplify]: Simplify (- 0) into 0 67.405 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 67.405 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 67.406 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 67.407 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI)))) 67.407 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 67.409 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 67.410 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 67.411 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 67.412 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 67.413 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 67.413 * [backup-simplify]: Simplify (- 0) into 0 67.413 * [backup-simplify]: Simplify (+ 0 0) into 0 67.413 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0 67.414 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 67.415 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 67.416 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 67.416 * [taylor]: Taking taylor expansion of 0 in k 67.416 * [backup-simplify]: Simplify 0 into 0 67.416 * [backup-simplify]: Simplify 0 into 0 67.417 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 67.417 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 67.418 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 67.418 * [backup-simplify]: Simplify (+ 0 0) into 0 67.419 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 67.419 * [backup-simplify]: Simplify (- 1/2) into -1/2 67.419 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 67.420 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 67.422 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 67.424 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 67.426 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 67.427 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 67.427 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 67.429 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 67.430 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 67.430 * [backup-simplify]: Simplify (- 0) into 0 67.430 * [backup-simplify]: Simplify (+ 0 0) into 0 67.431 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0 67.432 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 67.433 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 67.434 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 67.434 * [taylor]: Taking taylor expansion of 0 in k 67.434 * [backup-simplify]: Simplify 0 into 0 67.434 * [backup-simplify]: Simplify 0 into 0 67.434 * [backup-simplify]: Simplify 0 into 0 67.435 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 67.436 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 67.438 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 67.438 * [backup-simplify]: Simplify (+ 0 0) into 0 67.439 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 67.439 * [backup-simplify]: Simplify (- 0) into 0 67.439 * [backup-simplify]: Simplify (+ 0 0) into 0 67.440 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 67.442 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0 67.445 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 67.450 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 67.460 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) 67.460 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) 67.460 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 67.461 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k 67.461 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k 67.461 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k 67.461 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k 67.461 * [taylor]: Taking taylor expansion of 1/2 in k 67.461 * [backup-simplify]: Simplify 1/2 into 1/2 67.461 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 67.461 * [taylor]: Taking taylor expansion of 1/2 in k 67.461 * [backup-simplify]: Simplify 1/2 into 1/2 67.461 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.461 * [taylor]: Taking taylor expansion of 1/2 in k 67.461 * [backup-simplify]: Simplify 1/2 into 1/2 67.461 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.461 * [taylor]: Taking taylor expansion of k in k 67.461 * [backup-simplify]: Simplify 0 into 0 67.461 * [backup-simplify]: Simplify 1 into 1 67.461 * [backup-simplify]: Simplify (/ 1 1) into 1 67.461 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 67.461 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 67.461 * [taylor]: Taking taylor expansion of 2 in k 67.461 * [backup-simplify]: Simplify 2 into 2 67.461 * [taylor]: Taking taylor expansion of (/ PI n) in k 67.461 * [taylor]: Taking taylor expansion of PI in k 67.461 * [backup-simplify]: Simplify PI into PI 67.461 * [taylor]: Taking taylor expansion of n in k 67.461 * [backup-simplify]: Simplify n into n 67.462 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 67.462 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 67.462 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 67.462 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.463 * [backup-simplify]: Simplify (- 1/2) into -1/2 67.463 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 67.463 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4 67.463 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n)))) 67.464 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))))) 67.464 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 67.464 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 67.464 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 67.464 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 67.464 * [taylor]: Taking taylor expansion of 1/2 in n 67.464 * [backup-simplify]: Simplify 1/2 into 1/2 67.464 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 67.464 * [taylor]: Taking taylor expansion of 1/2 in n 67.464 * [backup-simplify]: Simplify 1/2 into 1/2 67.464 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.464 * [taylor]: Taking taylor expansion of 1/2 in n 67.464 * [backup-simplify]: Simplify 1/2 into 1/2 67.464 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.464 * [taylor]: Taking taylor expansion of k in n 67.464 * [backup-simplify]: Simplify k into k 67.464 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.464 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 67.464 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.464 * [taylor]: Taking taylor expansion of 2 in n 67.464 * [backup-simplify]: Simplify 2 into 2 67.464 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.464 * [taylor]: Taking taylor expansion of PI in n 67.464 * [backup-simplify]: Simplify PI into PI 67.464 * [taylor]: Taking taylor expansion of n in n 67.464 * [backup-simplify]: Simplify 0 into 0 67.464 * [backup-simplify]: Simplify 1 into 1 67.464 * [backup-simplify]: Simplify (/ PI 1) into PI 67.465 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.465 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.465 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.465 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 67.466 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 67.466 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 67.466 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.467 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 67.468 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.468 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 67.468 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 67.468 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 67.468 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 67.468 * [taylor]: Taking taylor expansion of 1/2 in n 67.468 * [backup-simplify]: Simplify 1/2 into 1/2 67.468 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 67.468 * [taylor]: Taking taylor expansion of 1/2 in n 67.468 * [backup-simplify]: Simplify 1/2 into 1/2 67.468 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.468 * [taylor]: Taking taylor expansion of 1/2 in n 67.468 * [backup-simplify]: Simplify 1/2 into 1/2 67.468 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.468 * [taylor]: Taking taylor expansion of k in n 67.468 * [backup-simplify]: Simplify k into k 67.468 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.468 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 67.468 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.468 * [taylor]: Taking taylor expansion of 2 in n 67.468 * [backup-simplify]: Simplify 2 into 2 67.468 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.468 * [taylor]: Taking taylor expansion of PI in n 67.468 * [backup-simplify]: Simplify PI into PI 67.468 * [taylor]: Taking taylor expansion of n in n 67.468 * [backup-simplify]: Simplify 0 into 0 67.468 * [backup-simplify]: Simplify 1 into 1 67.469 * [backup-simplify]: Simplify (/ PI 1) into PI 67.469 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.470 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.470 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.470 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 67.470 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 67.470 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 67.471 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.472 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 67.473 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.473 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k 67.473 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 67.473 * [taylor]: Taking taylor expansion of 1/2 in k 67.473 * [backup-simplify]: Simplify 1/2 into 1/2 67.473 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 67.473 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 67.473 * [taylor]: Taking taylor expansion of 1/2 in k 67.473 * [backup-simplify]: Simplify 1/2 into 1/2 67.473 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.473 * [taylor]: Taking taylor expansion of 1/2 in k 67.473 * [backup-simplify]: Simplify 1/2 into 1/2 67.473 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.473 * [taylor]: Taking taylor expansion of k in k 67.473 * [backup-simplify]: Simplify 0 into 0 67.473 * [backup-simplify]: Simplify 1 into 1 67.473 * [backup-simplify]: Simplify (/ 1 1) into 1 67.473 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 67.473 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 67.473 * [taylor]: Taking taylor expansion of (* 2 PI) in k 67.473 * [taylor]: Taking taylor expansion of 2 in k 67.473 * [backup-simplify]: Simplify 2 into 2 67.473 * [taylor]: Taking taylor expansion of PI in k 67.473 * [backup-simplify]: Simplify PI into PI 67.474 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.474 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.474 * [taylor]: Taking taylor expansion of (log n) in k 67.474 * [taylor]: Taking taylor expansion of n in k 67.474 * [backup-simplify]: Simplify n into n 67.474 * [backup-simplify]: Simplify (log n) into (log n) 67.475 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.475 * [backup-simplify]: Simplify (- 1/2) into -1/2 67.475 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 67.475 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 67.476 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 67.477 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 67.477 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n))) 67.478 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.479 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.479 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.480 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 67.481 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 67.481 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 67.481 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 67.482 * [backup-simplify]: Simplify (- 0) into 0 67.482 * [backup-simplify]: Simplify (+ 0 0) into 0 67.482 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 67.483 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.484 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 67.485 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 67.485 * [taylor]: Taking taylor expansion of 0 in k 67.485 * [backup-simplify]: Simplify 0 into 0 67.485 * [backup-simplify]: Simplify 0 into 0 67.485 * [backup-simplify]: Simplify 0 into 0 67.486 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.486 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 67.488 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 67.488 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.489 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 67.489 * [backup-simplify]: Simplify (- 0) into 0 67.495 * [backup-simplify]: Simplify (+ 0 0) into 0 67.496 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0 67.497 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.498 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 67.500 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 67.500 * [taylor]: Taking taylor expansion of 0 in k 67.500 * [backup-simplify]: Simplify 0 into 0 67.500 * [backup-simplify]: Simplify 0 into 0 67.500 * [backup-simplify]: Simplify 0 into 0 67.500 * [backup-simplify]: Simplify 0 into 0 67.501 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.501 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.505 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 67.505 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.506 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 67.506 * [backup-simplify]: Simplify (- 0) into 0 67.506 * [backup-simplify]: Simplify (+ 0 0) into 0 67.507 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0 67.508 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.509 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 67.511 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 67.511 * [taylor]: Taking taylor expansion of 0 in k 67.511 * [backup-simplify]: Simplify 0 into 0 67.511 * [backup-simplify]: Simplify 0 into 0 67.511 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 67.512 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) 67.512 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 67.512 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 67.512 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k 67.512 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k 67.512 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 67.512 * [taylor]: Taking taylor expansion of 1/2 in k 67.512 * [backup-simplify]: Simplify 1/2 into 1/2 67.512 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 67.513 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.513 * [taylor]: Taking taylor expansion of 1/2 in k 67.513 * [backup-simplify]: Simplify 1/2 into 1/2 67.513 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.513 * [taylor]: Taking taylor expansion of k in k 67.513 * [backup-simplify]: Simplify 0 into 0 67.513 * [backup-simplify]: Simplify 1 into 1 67.513 * [backup-simplify]: Simplify (/ 1 1) into 1 67.513 * [taylor]: Taking taylor expansion of 1/2 in k 67.513 * [backup-simplify]: Simplify 1/2 into 1/2 67.513 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 67.513 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 67.513 * [taylor]: Taking taylor expansion of -2 in k 67.513 * [backup-simplify]: Simplify -2 into -2 67.513 * [taylor]: Taking taylor expansion of (/ PI n) in k 67.513 * [taylor]: Taking taylor expansion of PI in k 67.513 * [backup-simplify]: Simplify PI into PI 67.513 * [taylor]: Taking taylor expansion of n in k 67.513 * [backup-simplify]: Simplify n into n 67.513 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 67.513 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 67.514 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 67.514 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.514 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 67.515 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 67.515 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n)))) 67.515 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 67.515 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 67.515 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 67.515 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 67.515 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 67.515 * [taylor]: Taking taylor expansion of 1/2 in n 67.515 * [backup-simplify]: Simplify 1/2 into 1/2 67.515 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 67.515 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.515 * [taylor]: Taking taylor expansion of 1/2 in n 67.515 * [backup-simplify]: Simplify 1/2 into 1/2 67.516 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.516 * [taylor]: Taking taylor expansion of k in n 67.516 * [backup-simplify]: Simplify k into k 67.516 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.516 * [taylor]: Taking taylor expansion of 1/2 in n 67.516 * [backup-simplify]: Simplify 1/2 into 1/2 67.516 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 67.516 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.516 * [taylor]: Taking taylor expansion of -2 in n 67.516 * [backup-simplify]: Simplify -2 into -2 67.516 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.516 * [taylor]: Taking taylor expansion of PI in n 67.516 * [backup-simplify]: Simplify PI into PI 67.516 * [taylor]: Taking taylor expansion of n in n 67.516 * [backup-simplify]: Simplify 0 into 0 67.516 * [backup-simplify]: Simplify 1 into 1 67.516 * [backup-simplify]: Simplify (/ PI 1) into PI 67.517 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.518 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 67.518 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.518 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 67.518 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 67.520 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.521 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 67.522 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.522 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 67.522 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 67.523 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 67.523 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 67.523 * [taylor]: Taking taylor expansion of 1/2 in n 67.523 * [backup-simplify]: Simplify 1/2 into 1/2 67.523 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 67.523 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.523 * [taylor]: Taking taylor expansion of 1/2 in n 67.523 * [backup-simplify]: Simplify 1/2 into 1/2 67.523 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.523 * [taylor]: Taking taylor expansion of k in n 67.523 * [backup-simplify]: Simplify k into k 67.523 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.523 * [taylor]: Taking taylor expansion of 1/2 in n 67.523 * [backup-simplify]: Simplify 1/2 into 1/2 67.523 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 67.523 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.523 * [taylor]: Taking taylor expansion of -2 in n 67.523 * [backup-simplify]: Simplify -2 into -2 67.523 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.523 * [taylor]: Taking taylor expansion of PI in n 67.523 * [backup-simplify]: Simplify PI into PI 67.523 * [taylor]: Taking taylor expansion of n in n 67.523 * [backup-simplify]: Simplify 0 into 0 67.523 * [backup-simplify]: Simplify 1 into 1 67.524 * [backup-simplify]: Simplify (/ PI 1) into PI 67.524 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.526 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 67.526 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.526 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 67.526 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 67.527 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.529 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 67.530 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.530 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 67.530 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 67.530 * [taylor]: Taking taylor expansion of 1/2 in k 67.530 * [backup-simplify]: Simplify 1/2 into 1/2 67.530 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 67.530 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 67.530 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.530 * [taylor]: Taking taylor expansion of 1/2 in k 67.530 * [backup-simplify]: Simplify 1/2 into 1/2 67.530 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.530 * [taylor]: Taking taylor expansion of k in k 67.530 * [backup-simplify]: Simplify 0 into 0 67.530 * [backup-simplify]: Simplify 1 into 1 67.531 * [backup-simplify]: Simplify (/ 1 1) into 1 67.531 * [taylor]: Taking taylor expansion of 1/2 in k 67.531 * [backup-simplify]: Simplify 1/2 into 1/2 67.531 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 67.531 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 67.531 * [taylor]: Taking taylor expansion of (* -2 PI) in k 67.531 * [taylor]: Taking taylor expansion of -2 in k 67.531 * [backup-simplify]: Simplify -2 into -2 67.531 * [taylor]: Taking taylor expansion of PI in k 67.531 * [backup-simplify]: Simplify PI into PI 67.532 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.533 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 67.533 * [taylor]: Taking taylor expansion of (log n) in k 67.533 * [taylor]: Taking taylor expansion of n in k 67.533 * [backup-simplify]: Simplify n into n 67.533 * [backup-simplify]: Simplify (log n) into (log n) 67.533 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.534 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 67.534 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 67.535 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 67.536 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 67.537 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n))) 67.538 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.539 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.540 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.541 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 67.543 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 67.543 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 67.544 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 67.544 * [backup-simplify]: Simplify (+ 0 0) into 0 67.545 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 67.546 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.547 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 67.549 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 67.549 * [taylor]: Taking taylor expansion of 0 in k 67.549 * [backup-simplify]: Simplify 0 into 0 67.549 * [backup-simplify]: Simplify 0 into 0 67.549 * [backup-simplify]: Simplify 0 into 0 67.550 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.551 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 67.555 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 67.555 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.556 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 67.557 * [backup-simplify]: Simplify (+ 0 0) into 0 67.557 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 67.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.560 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 67.563 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 67.563 * [taylor]: Taking taylor expansion of 0 in k 67.563 * [backup-simplify]: Simplify 0 into 0 67.563 * [backup-simplify]: Simplify 0 into 0 67.563 * [backup-simplify]: Simplify 0 into 0 67.563 * [backup-simplify]: Simplify 0 into 0 67.564 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.566 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.572 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 67.572 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.573 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 67.574 * [backup-simplify]: Simplify (+ 0 0) into 0 67.575 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 67.577 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.579 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 67.581 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 67.582 * [taylor]: Taking taylor expansion of 0 in k 67.582 * [backup-simplify]: Simplify 0 into 0 67.582 * [backup-simplify]: Simplify 0 into 0 67.583 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 67.583 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 67.584 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 67.584 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 67.584 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 67.584 * [taylor]: Taking taylor expansion of 2 in n 67.584 * [backup-simplify]: Simplify 2 into 2 67.584 * [taylor]: Taking taylor expansion of (* n PI) in n 67.584 * [taylor]: Taking taylor expansion of n in n 67.584 * [backup-simplify]: Simplify 0 into 0 67.584 * [backup-simplify]: Simplify 1 into 1 67.584 * [taylor]: Taking taylor expansion of PI in n 67.584 * [backup-simplify]: Simplify PI into PI 67.584 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 67.584 * [taylor]: Taking taylor expansion of 2 in n 67.584 * [backup-simplify]: Simplify 2 into 2 67.584 * [taylor]: Taking taylor expansion of (* n PI) in n 67.584 * [taylor]: Taking taylor expansion of n in n 67.584 * [backup-simplify]: Simplify 0 into 0 67.584 * [backup-simplify]: Simplify 1 into 1 67.584 * [taylor]: Taking taylor expansion of PI in n 67.584 * [backup-simplify]: Simplify PI into PI 67.585 * [backup-simplify]: Simplify (* 0 PI) into 0 67.585 * [backup-simplify]: Simplify (* 2 0) into 0 67.585 * [backup-simplify]: Simplify 0 into 0 67.587 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 67.589 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 67.589 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.590 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 67.591 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 67.591 * [backup-simplify]: Simplify 0 into 0 67.592 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 67.593 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 67.593 * [backup-simplify]: Simplify 0 into 0 67.594 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 67.594 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 67.594 * [backup-simplify]: Simplify 0 into 0 67.595 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 67.596 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 67.596 * [backup-simplify]: Simplify 0 into 0 67.597 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 67.598 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 67.598 * [backup-simplify]: Simplify 0 into 0 67.599 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 67.600 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 67.601 * [backup-simplify]: Simplify 0 into 0 67.601 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 67.601 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 67.601 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 67.601 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.601 * [taylor]: Taking taylor expansion of 2 in n 67.601 * [backup-simplify]: Simplify 2 into 2 67.601 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.601 * [taylor]: Taking taylor expansion of PI in n 67.601 * [backup-simplify]: Simplify PI into PI 67.601 * [taylor]: Taking taylor expansion of n in n 67.601 * [backup-simplify]: Simplify 0 into 0 67.602 * [backup-simplify]: Simplify 1 into 1 67.602 * [backup-simplify]: Simplify (/ PI 1) into PI 67.602 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.602 * [taylor]: Taking taylor expansion of 2 in n 67.602 * [backup-simplify]: Simplify 2 into 2 67.602 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.602 * [taylor]: Taking taylor expansion of PI in n 67.602 * [backup-simplify]: Simplify PI into PI 67.602 * [taylor]: Taking taylor expansion of n in n 67.602 * [backup-simplify]: Simplify 0 into 0 67.602 * [backup-simplify]: Simplify 1 into 1 67.602 * [backup-simplify]: Simplify (/ PI 1) into PI 67.603 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.603 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.604 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.604 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 67.604 * [backup-simplify]: Simplify 0 into 0 67.605 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.605 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 67.605 * [backup-simplify]: Simplify 0 into 0 67.606 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.607 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.607 * [backup-simplify]: Simplify 0 into 0 67.607 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.608 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 67.608 * [backup-simplify]: Simplify 0 into 0 67.609 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.610 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 67.610 * [backup-simplify]: Simplify 0 into 0 67.610 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.611 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 67.611 * [backup-simplify]: Simplify 0 into 0 67.612 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 67.612 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 67.612 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 67.612 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.612 * [taylor]: Taking taylor expansion of -2 in n 67.612 * [backup-simplify]: Simplify -2 into -2 67.612 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.612 * [taylor]: Taking taylor expansion of PI in n 67.612 * [backup-simplify]: Simplify PI into PI 67.612 * [taylor]: Taking taylor expansion of n in n 67.612 * [backup-simplify]: Simplify 0 into 0 67.612 * [backup-simplify]: Simplify 1 into 1 67.613 * [backup-simplify]: Simplify (/ PI 1) into PI 67.613 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.613 * [taylor]: Taking taylor expansion of -2 in n 67.613 * [backup-simplify]: Simplify -2 into -2 67.613 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.613 * [taylor]: Taking taylor expansion of PI in n 67.613 * [backup-simplify]: Simplify PI into PI 67.613 * [taylor]: Taking taylor expansion of n in n 67.613 * [backup-simplify]: Simplify 0 into 0 67.613 * [backup-simplify]: Simplify 1 into 1 67.613 * [backup-simplify]: Simplify (/ PI 1) into PI 67.613 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.614 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.614 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.615 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 67.615 * [backup-simplify]: Simplify 0 into 0 67.621 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.623 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 67.623 * [backup-simplify]: Simplify 0 into 0 67.624 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.625 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.625 * [backup-simplify]: Simplify 0 into 0 67.627 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.628 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 67.628 * [backup-simplify]: Simplify 0 into 0 67.629 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.631 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 67.631 * [backup-simplify]: Simplify 0 into 0 67.632 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.634 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 67.634 * [backup-simplify]: Simplify 0 into 0 67.634 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 67.634 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1) 67.635 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 67.635 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 67.635 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 67.635 * [taylor]: Taking taylor expansion of 2 in n 67.635 * [backup-simplify]: Simplify 2 into 2 67.635 * [taylor]: Taking taylor expansion of (* n PI) in n 67.635 * [taylor]: Taking taylor expansion of n in n 67.636 * [backup-simplify]: Simplify 0 into 0 67.636 * [backup-simplify]: Simplify 1 into 1 67.636 * [taylor]: Taking taylor expansion of PI in n 67.636 * [backup-simplify]: Simplify PI into PI 67.636 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 67.636 * [taylor]: Taking taylor expansion of 2 in n 67.636 * [backup-simplify]: Simplify 2 into 2 67.636 * [taylor]: Taking taylor expansion of (* n PI) in n 67.636 * [taylor]: Taking taylor expansion of n in n 67.636 * [backup-simplify]: Simplify 0 into 0 67.636 * [backup-simplify]: Simplify 1 into 1 67.636 * [taylor]: Taking taylor expansion of PI in n 67.636 * [backup-simplify]: Simplify PI into PI 67.636 * [backup-simplify]: Simplify (* 0 PI) into 0 67.637 * [backup-simplify]: Simplify (* 2 0) into 0 67.637 * [backup-simplify]: Simplify 0 into 0 67.638 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 67.640 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 67.641 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.642 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 67.643 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 67.643 * [backup-simplify]: Simplify 0 into 0 67.644 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 67.645 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 67.645 * [backup-simplify]: Simplify 0 into 0 67.647 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 67.648 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 67.648 * [backup-simplify]: Simplify 0 into 0 67.650 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 67.651 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 67.651 * [backup-simplify]: Simplify 0 into 0 67.653 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 67.655 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 67.655 * [backup-simplify]: Simplify 0 into 0 67.657 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 67.659 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 67.659 * [backup-simplify]: Simplify 0 into 0 67.660 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 67.660 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 67.660 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 67.660 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.660 * [taylor]: Taking taylor expansion of 2 in n 67.660 * [backup-simplify]: Simplify 2 into 2 67.660 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.660 * [taylor]: Taking taylor expansion of PI in n 67.660 * [backup-simplify]: Simplify PI into PI 67.660 * [taylor]: Taking taylor expansion of n in n 67.660 * [backup-simplify]: Simplify 0 into 0 67.660 * [backup-simplify]: Simplify 1 into 1 67.661 * [backup-simplify]: Simplify (/ PI 1) into PI 67.661 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.661 * [taylor]: Taking taylor expansion of 2 in n 67.661 * [backup-simplify]: Simplify 2 into 2 67.661 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.661 * [taylor]: Taking taylor expansion of PI in n 67.661 * [backup-simplify]: Simplify PI into PI 67.661 * [taylor]: Taking taylor expansion of n in n 67.661 * [backup-simplify]: Simplify 0 into 0 67.661 * [backup-simplify]: Simplify 1 into 1 67.662 * [backup-simplify]: Simplify (/ PI 1) into PI 67.662 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.663 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.664 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.664 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 67.664 * [backup-simplify]: Simplify 0 into 0 67.666 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.667 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 67.667 * [backup-simplify]: Simplify 0 into 0 67.668 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.669 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.669 * [backup-simplify]: Simplify 0 into 0 67.670 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.672 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 67.672 * [backup-simplify]: Simplify 0 into 0 67.673 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.674 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 67.674 * [backup-simplify]: Simplify 0 into 0 67.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.677 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 67.677 * [backup-simplify]: Simplify 0 into 0 67.678 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 67.678 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 67.678 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 67.678 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.678 * [taylor]: Taking taylor expansion of -2 in n 67.679 * [backup-simplify]: Simplify -2 into -2 67.679 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.679 * [taylor]: Taking taylor expansion of PI in n 67.679 * [backup-simplify]: Simplify PI into PI 67.679 * [taylor]: Taking taylor expansion of n in n 67.679 * [backup-simplify]: Simplify 0 into 0 67.679 * [backup-simplify]: Simplify 1 into 1 67.679 * [backup-simplify]: Simplify (/ PI 1) into PI 67.679 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.679 * [taylor]: Taking taylor expansion of -2 in n 67.679 * [backup-simplify]: Simplify -2 into -2 67.679 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.679 * [taylor]: Taking taylor expansion of PI in n 67.679 * [backup-simplify]: Simplify PI into PI 67.679 * [taylor]: Taking taylor expansion of n in n 67.679 * [backup-simplify]: Simplify 0 into 0 67.679 * [backup-simplify]: Simplify 1 into 1 67.680 * [backup-simplify]: Simplify (/ PI 1) into PI 67.680 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.681 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.682 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.683 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 67.683 * [backup-simplify]: Simplify 0 into 0 67.684 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.685 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 67.685 * [backup-simplify]: Simplify 0 into 0 67.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.688 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.688 * [backup-simplify]: Simplify 0 into 0 67.689 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.690 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 67.690 * [backup-simplify]: Simplify 0 into 0 67.691 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.693 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 67.693 * [backup-simplify]: Simplify 0 into 0 67.694 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.696 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 67.696 * [backup-simplify]: Simplify 0 into 0 67.697 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 67.697 * * * [progress]: simplifying candidates 67.697 * * * * [progress]: [ 1 / 138 ] simplifiying candidate # 67.697 * * * * [progress]: [ 2 / 138 ] simplifiying candidate # 67.697 * * * * [progress]: [ 3 / 138 ] simplifiying candidate # 67.697 * * * * [progress]: [ 4 / 138 ] simplifiying candidate # 67.697 * * * * [progress]: [ 5 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 6 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 7 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 8 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 9 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 10 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 11 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 12 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 13 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 14 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 15 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 16 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 17 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 18 / 138 ] simplifiying candidate # 67.698 * * * * [progress]: [ 19 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 20 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 21 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 22 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 23 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 24 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 25 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 26 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 27 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 28 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 29 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 30 / 138 ] simplifiying candidate # 67.699 * * * * [progress]: [ 31 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 32 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 33 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 34 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 35 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 36 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 37 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 38 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 39 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 40 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 41 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 42 / 138 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))> 67.700 * * * * [progress]: [ 43 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 44 / 138 ] simplifiying candidate # 67.700 * * * * [progress]: [ 45 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 46 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 47 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 48 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 49 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 50 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 51 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 52 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 53 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 54 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 55 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 56 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 57 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 58 / 138 ] simplifiying candidate # 67.701 * * * * [progress]: [ 59 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 60 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 61 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 62 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 63 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 64 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 65 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 66 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 67 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 68 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 69 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 70 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 71 / 138 ] simplifiying candidate # 67.702 * * * * [progress]: [ 72 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 73 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 74 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 75 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 76 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 77 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 78 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 79 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 80 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 81 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 82 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 83 / 138 ] simplifiying candidate # 67.703 * * * * [progress]: [ 84 / 138 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> 67.703 * * * * [progress]: [ 85 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 86 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 87 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 88 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 89 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 90 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 91 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 92 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 93 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 94 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 95 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 96 / 138 ] simplifiying candidate # 67.704 * * * * [progress]: [ 97 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 98 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 99 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 100 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 101 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 102 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 103 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 104 / 138 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> 67.705 * * * * [progress]: [ 105 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 106 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 107 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 108 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 109 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 110 / 138 ] simplifiying candidate # 67.705 * * * * [progress]: [ 111 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 112 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 113 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 114 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 115 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 116 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 117 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 118 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 119 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 120 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 121 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 122 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 123 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 124 / 138 ] simplifiying candidate # 67.706 * * * * [progress]: [ 125 / 138 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> 67.707 * * * * [progress]: [ 126 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 127 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 128 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 129 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 130 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 131 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 132 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 133 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 134 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 135 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 136 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 137 / 138 ] simplifiying candidate # 67.707 * * * * [progress]: [ 138 / 138 ] simplifiying candidate # 67.710 * [simplify]: Simplifying: (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2)) (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2)) (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (expm1 (* n (* 2 PI))) (log1p (* n (* 2 PI))) (* n (* 2 PI)) (* n (* 2 PI)) (+ (log n) (+ (log 2) (log PI))) (+ (log n) (log (* 2 PI))) (log (* n (* 2 PI))) (exp (* n (* 2 PI))) (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI))) (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI))) (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI))) (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (* n 2) (* (cbrt n) (* 2 PI)) (* (sqrt n) (* 2 PI)) (* n (* 2 PI)) (real->posit16 (* n (* 2 PI))) (expm1 (* n (* 2 PI))) (log1p (* n (* 2 PI))) (* n (* 2 PI)) (* n (* 2 PI)) (+ (log n) (+ (log 2) (log PI))) (+ (log n) (log (* 2 PI))) (log (* n (* 2 PI))) (exp (* n (* 2 PI))) (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI))) (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI))) (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI))) (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (* n 2) (* (cbrt n) (* 2 PI)) (* (sqrt n) (* 2 PI)) (* n (* 2 PI)) (real->posit16 (* n (* 2 PI))) (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) 67.713 * * [simplify]: iteration 0: 165 enodes 67.806 * * [simplify]: iteration 1: 455 enodes 67.962 * * [simplify]: iteration 2: 1480 enodes 68.324 * * [simplify]: iteration complete: 2011 enodes 68.324 * * [simplify]: Extracting #0: cost 49 inf + 0 68.325 * * [simplify]: Extracting #1: cost 326 inf + 0 68.327 * * [simplify]: Extracting #2: cost 577 inf + 3783 68.336 * * [simplify]: Extracting #3: cost 401 inf + 49768 68.357 * * [simplify]: Extracting #4: cost 154 inf + 125993 68.401 * * [simplify]: Extracting #5: cost 51 inf + 172238 68.453 * * [simplify]: Extracting #6: cost 23 inf + 183455 68.506 * * [simplify]: Extracting #7: cost 2 inf + 190999 68.590 * * [simplify]: Extracting #8: cost 0 inf + 190629 68.646 * * [simplify]: Extracting #9: cost 0 inf + 190559 68.706 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (log1p (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (- 1/4 (/ k 4)) (- 1/4 (/ k 4)) (- 1/4 (/ k 4)) (exp (* (log (* (* PI 2) n)) 1/4)) (pow (* (* PI 2) n) (/ k 4)) (pow (* (* PI 2) n) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4))))) (pow (* (* PI 2) n) (sqrt (- 1/4 (/ k 4)))) (pow (* (* PI 2) n) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)))) (pow (* (* PI 2) n) (* (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2)) (cbrt (- 1/2 (/ k 2))))) (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* (* PI 2) n) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2)))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2)) (cbrt 2))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (* (* PI 2) n) (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow n (- 1/4 (/ k 4))) (pow (* PI 2) (- 1/4 (/ k 4))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (exp (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4))))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (pow (pow (* (* PI 2) n) (- 1/4 (/ k 4))) 3) (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (real->posit16 (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (expm1 (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (log1p (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (- 1/4 (/ k 4)) (- 1/4 (/ k 4)) (- 1/4 (/ k 4)) (exp (* (log (* (* PI 2) n)) 1/4)) (pow (* (* PI 2) n) (/ k 4)) (pow (* (* PI 2) n) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4))))) (pow (* (* PI 2) n) (sqrt (- 1/4 (/ k 4)))) (pow (* (* PI 2) n) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)))) (pow (* (* PI 2) n) (* (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2)) (cbrt (- 1/2 (/ k 2))))) (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* (* PI 2) n) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2)))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2)) (cbrt 2))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (* (* PI 2) n) (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow n (- 1/4 (/ k 4))) (pow (* PI 2) (- 1/4 (/ k 4))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (exp (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4))))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (pow (pow (* (* PI 2) n) (- 1/4 (/ k 4))) 3) (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (real->posit16 (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (expm1 (* (* PI 2) n)) (log1p (* (* PI 2) n)) (* (* PI 2) n) (* (* PI 2) n) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (* (exp (* n PI)) (exp (* n PI))) (* (* (* 8 (* (* PI PI) PI)) (* n n)) n) (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n)) (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))) (cbrt (* (* PI 2) n)) (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (* n 2) (* (cbrt n) (* PI 2)) (* PI (* 2 (sqrt n))) (* (* PI 2) n) (real->posit16 (* (* PI 2) n)) (expm1 (* (* PI 2) n)) (log1p (* (* PI 2) n)) (* (* PI 2) n) (* (* PI 2) n) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (* (exp (* n PI)) (exp (* n PI))) (* (* (* 8 (* (* PI PI) PI)) (* n n)) n) (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n)) (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))) (cbrt (* (* PI 2) n)) (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (* n 2) (* (cbrt n) (* PI 2)) (* PI (* 2 (sqrt n))) (* (* PI 2) n) (real->posit16 (* (* PI 2) n)) (fma -1/4 (* k (fma (exp (* (log (* (* PI 2) n)) 1/4)) (log n) (* (log (* PI 2)) (exp (* (log (* (* PI 2) n)) 1/4))))) (fma (fma (* (* k k) (exp (* (log (* (* PI 2) n)) 1/4))) (* (log n) (log n)) (* (* (* k k) (exp (* (log (* (* PI 2) n)) 1/4))) (* (log (* PI 2)) (log (* PI 2))))) 1/32 (fma (* 1/16 (* (log (* PI 2)) (exp (* (log (* (* PI 2) n)) 1/4)))) (* k (* k (log n))) (exp (* (log (* (* PI 2) n)) 1/4))))) (exp (* (log (* (* PI 2) n)) (* (fma k -1/2 1/2) 1/2))) (exp (* 1/2 (* (fma k -1/2 1/2) (- (log (* PI -2)) (log (/ -1 n)))))) (fma -1/4 (* k (fma (exp (* (log (* (* PI 2) n)) 1/4)) (log n) (* (log (* PI 2)) (exp (* (log (* (* PI 2) n)) 1/4))))) (fma (fma (* (* k k) (exp (* (log (* (* PI 2) n)) 1/4))) (* (log n) (log n)) (* (* (* k k) (exp (* (log (* (* PI 2) n)) 1/4))) (* (log (* PI 2)) (log (* PI 2))))) 1/32 (fma (* 1/16 (* (log (* PI 2)) (exp (* (log (* (* PI 2) n)) 1/4)))) (* k (* k (log n))) (exp (* (log (* (* PI 2) n)) 1/4))))) (exp (* (log (* (* PI 2) n)) (* (fma k -1/2 1/2) 1/2))) (exp (* 1/2 (* (fma k -1/2 1/2) (- (log (* PI -2)) (log (/ -1 n)))))) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) 68.729 * * * [progress]: adding candidates to table 69.635 * [progress]: [Phase 3 of 3] Extracting. 69.635 * * [regime]: Finding splitpoints for: (# # # # # # # # #) 69.638 * * * [regime-changes]: Trying 2 branch expressions: (n k) 69.638 * * * * [regimes]: Trying to branch on n from (# # # # # # # # #) 70.093 * * * * [regimes]: Trying to branch on k from (# # # # # # # # #) 70.202 * * * [regime]: Found split indices: #